PROCEEDINGS

of the Tomsk Technological Institute

of Emperor Nicholas II.

Vol. 11. 1908. No. 3.

I.

V. N. Pinegin.

EXPERIMENTAL STUDY OF POISSON’S RATIO FOR CAST IRON.

With an appendix of 9 plates of drawings.

1–67.

Experimental Study

of Poisson’s Ratio for Cast Iron.

Strange as it may seem, the question of Poisson’s ratio, despite all its importance in the theory of the strength of materials, if it has attracted any attention from experimenters, has in any case not attracted enough; owing to this, it remains to this day very little investigated. Of course, for such materials as steel or iron, which obey Hooke’s law, Poisson’s ratio may still be regarded as more or less established, although even for these materials the question of the influence on the ratio of a variable load, of its repetition, and so forth, has by no means been fully investigated. For other materials, especially those that do not obey Hooke’s law, such as, for example, cast iron and stone, the information on Poisson’s ratio is extremely vague and contradictory; meanwhile for these materials the study of Poisson’s ratio acquires special significance, since this study will contribute to the study in general of the elastic properties of the materials themselves; and, for example, the so-called power law, first given by Bülffinger ¹) (in 1729) and now bearing the name of the Schüle and Bach law, will have full significance only after the question of Poisson’s ratio has been resolved ²).

As is known, the determination of Poisson’s ratio is carried out in two ways: by direct determination of this ratio, determining separately the transverse expansions or contractions and the corresponding longitudinal contractions or elongations, and taking their ratio; or by an indirect method—from bending or torsion tests.

The first method is, of course, more reliable, and even the only one that is certain and possible for a comprehensive investigation of the ratio. Meanwhile, very few such direct investigations of the ratio have been carried out. Cagniard

¹) See Mehmke, “Zum Gesetz der elastischen Dehnungen.” Zeitschrift für Mathematik und Physik (founded by Schlömilch). 1897.

²) See Föppl, Festigkeitslehre. 1905. p. 51.

de La Tour (cf. Pogg. Ann. Bd. 12. 1828, p. 516) was, it seems, the first investigator of this kind to determine Poisson’s ratio for brass wire. He was followed by Fr. Neumann¹ and Wertheim²; the former determined the ratio for iron wire, the latter for glass and brass tubes. All three determined the actual changes in volume of the specimens investigated, and from this already derived Poisson’s ratio. The same method was later followed by Götz and Kurz³ and still later by Cardani⁴, who likewise worked with wires. S. Röntgen⁵ determined Poisson’s ratio for rubber. Finally, among investigators of the ratio by the direct determination of transverse and longitudinal deformations one may point to Bauschinger⁶ and Morrow⁷, who, for determining transverse expansions and contractions, used mirror instruments specially constructed by them for this purpose.

Among the investigators of Poisson’s ratio by an indirect method one should mention Kirchhoff⁸, Okatov⁹, Cornu¹⁰, Schneebelli¹¹, Mallock¹², Straubel¹³, etc.¹⁴.

But, unfortunately, all these investigations are not complete, embracing the question under consideration from all sides; they yielded only a few values of the ratio for a very small number of materials, but an investigation that would clarify under the influence of what causes

[For several bodies, however, the influence of raising the temperature to 100° on Poisson’s ratio was investigated by Voigt (W. A. 1894) and Smoluchowski (Wien. Ber. 1894)] whether the values of this coefficient change, and whether they change at all for a given material, had not been done. Of course, to carry out such work, as a comprehensive investigation of Poisson’s ratio for all materials playing one role or another in technology, is an exceedingly large task and hardly feasible for one person; therefore, in undertaking my work, I did not have in mind so extensive a task; my aim was more modest: first, I occupied myself with investigating Poisson’s ratio only for one material—cast iron, and, second, even for this material it is not so easy to resolve the question completely; I would be quite satisfied if I succeeded in clarifying, at least somewhat, the dependence of Poisson’s ratio on the load, its variation, and its repeatability.

In beginning the investigation, I first of all had to take up the question of an apparatus for measuring transverse expansions and contractions, since I did not have at hand such an apparatus satisfying at once the requirement of sensitivity and the requirement of convenience in handling. Having settled on Martens’s idea of measuring increases and decreases of lengths by means of the rotation of mirrors mounted on steel prisms, one edge of which remains fixed while the other moves together with the body being deformed—an idea, in my opinion, exceedingly simple and at the same time exceedingly ingenious—I constructed the apparatus which is shown in the appended drawing (see Drawing 1).

Two crosspieces I, I, having approximately the form of a body of equal resistance to bending, are connected by bolts II, II, on which cylinders a, a... of definite length are fitted, establishing the required distance between the crosspieces.

Through the crosspieces pass small pistons b, b, which, owing to the pressure upon them of springs c, c, press constantly on the tested body d, and this pressure alone is quite sufficient to hold the whole apparatus on the tested body in any place and in any position. On extensions of the small pistons there rest, with one edge, prisms s, s of mirrors analogous to the mirrors in Martens’s apparatus; the other edges of the prisms rest in corresponding recesses of steel plates f, f, pressed as desired more or less strongly (preferably weakly) by means—

by means of springs \(p, p\), and weights \(r, r\). Upon elongation or compression of the body \(d\) under test, the pistons will correspondingly move in one direction or the other, and consequently will cause the prisms \(s, s\), and with them the mirrors, to rotate; from the deflection of the light ray from them on the scale it will be possible to determine the magnitude of the deformation itself of the body under test. The entire arrangement of the mirrors, the determination of errors, and the possible prevention of them are the same as in Martens’s apparatus.

The above-mentioned cylinders \(a, a\ldots\) must be kept with the apparatus in sufficient number and of various lengths, so that, for different specimens under test, the lengths of the protruding parts of the pistons \(b, b\) may, as far as possible, always be the same; thereby an equal pressure of the pistons on the body under test is also achieved. To reduce the weight of the apparatus, the cross-pieces and cylinders are made of aluminum.

It should be noted that, according to my original design, the entire frame \(l, l, ll, ll\) (the cross-piece together with the bolts) constituted one whole; and, in order to establish an always constant pressure for specimens of different transverse dimensions, pistons of various lengths were assumed, or, with the same pistons, special hollow cylinders in which the spring-loaded pistons would be placed; the cylinders would be secured in any position by means of clamping screws in the sockets of the frame. On the advice of Prof. Meyer (Professor of the Charlottenburg Polytechnic), in whose laboratory the present work was carried out and through whose funds this apparatus was ordered, I modified the apparatus in the indicated sense¹. The entire apparatus, together with the mirrors, weighs only 392 g. The experiments themselves, which at first had only the aim of investigating Poisson’s ratio in compression of cast-iron bars, were carried out by me in the spring of 1906, and subsequently—in 1907—were extended also to the tension of cast-iron bars, as well as to the investigation of the dependence of Poisson’s ratio on variable load.

The material used was ordinary gray cast iron employed for casting machine parts; for compression the specimens were of various sections, and in the majority of cases these were specimens left over from other experiments of mine. (See Versuche über den Zusammenhang von Biegungsfestigkeit und Zugfestigkeit bei Gusseisen. Z. d. V. d. I. 1906, Heft 50, or Mitteilungen über Forschungsarbeiten, 1907, Heft 48). Among them,

were specimens that had already been subjected to compression; there were specimens taken from objects that had served for tensile tests; finally, there were specimens that had not undergone any deformations at all. But all these specimens were cast from one ladle and were therefore, as far as possible, of the same composition¹. Thus it was possible to compare the influence of preliminary deformations on changes in Poisson’s ratio.

For specimens with a rectangular cross-section, measurements of transverse expansions were made in three directions: along the axes of symmetry and along the diagonals; and for round specimens—in two directions (diameters inclined to one another at \(90^\circ\)). All this made it possible to elucidate changes in the transverse deformations, and consequently also in Poisson’s ratio, as a function of the form of the specimen and of the direction in which the transverse expansions were measured.

In order to give a clearer idea of the form and number of the specimens that I had at my disposal for compression, I give their list and principal dimensions:

2 specimens of rectangular cross-section (\(7.97 \times 7.98\) cm and \(7.98 \times 7.99\) cm) and of length—one 25 cm, the other 28 cm.

1 round specimen, diameter 7.8 cm, length 25 cm.

These three specimens had not previously been subjected to any deformations.

2 round specimens, diameter 6 cm, length 34 cm.

1 round specimen, diameter 4.7 cm and length 34 cm.

3 specimens of rectangular cross-section (\(4.5 \times 5\) cm) and of length—two 34 cm, one 25 cm.

These specimens had earlier been subjected to compression.

2 round specimens, diameter 4.7 cm and of length—one 34 cm, the other 25 cm.

3 specimens of rectangular cross-section (\(2.4 \times 5\) cm) and of length—two 34 cm, and one 25 cm.

These specimens had previously been subjected to tension.

Finally, for tests in tension and under alternating load I had four specimens of the same gray cast iron, but from another casting, and machined to the form shown in the appended drawing No. 2.

The compression tests were carried out on a Pohlmeyer machine, and the tensile tests on a Werder machine; the form of the bars for tension made it possible to transfer the bars co-

...with all the instruments placed upon them directly from one machine to another, similarly to what Berner did¹ in his experiments on the influence of variable loading on the elongations and compressions of bars. Longitudinal elongations and compressions were determined by Martens’s instrument. In view of the fact that in the instrument described for determining transverse deformations each of the mirrors gave only a part of the total deformation of the bars (the total deformation = the sum of the readings of both mirrors), and, moreover, the deformations themselves are very small, in order to obtain more or less significant readings on the scales it was necessary to increase the distances of the scales from the mirrors; therefore, whereas for Martens’s apparatus the distances were chosen with the calculation that the ratio of the width of the mirror prism to the distance of the mirror from the scale was equal to 250, the same ratio for determining transverse expansions and contractions was equal to 500, i.e., in other words, in the latter case the distances of the scale from the mirror were approximately twice as great as in the former; although the divisions of the scale also appeared in this case not much smaller, the readings could be made with the same accuracy as from the mirrors of Martens’s instrument.

The actual loading of the bars was carried out in two ways: either the bars were loaded in steps through a certain number of tons (the steps were chosen with such a calculation that, for all the bars, the loads per sq. cm. of cross-sectional area would be approximately the same), with the load held at each step for a definite interval of time (5 minutes), or else the bar was loaded to a certain magnitude, then unloaded to the initial load (usually very small, necessary only in order to set the instruments correctly), and then again loaded by the same amount as the first time; then it was again unloaded and again loaded, and this was repeated until the readings of the mirrors within the chosen load interval became constant and the bar was thus brought into a “settled state.” Then the load interval was increased, the experiment was repeated similarly to the preceding one, and so on. In the first method of loading, after it had been brought to a certain magnitude, the bar was unloaded, and then again loaded to the same magnitude, and this was repeated until the bar was brought into a “settled state.” It is clear that only after bringing—

...of the specimen to such a state it was already possible to compare with one another the measurements of deformations in the different directions of the cross-section of the bar.

Throughout the experiments it was ensured that the temperature in the testing room remained constant; for this purpose the heating had to be regulated at all times according to a thermometer placed near the bar being tested.

The loads were applied comparatively slowly; care was taken that the intervals of time required for loading the specimen from one stage to another were, as far as possible, identical, and, in the second form of loading, these intervals had to increase in proportion to the increase of the interval. In calculating the load per sq. cm of the cross-sectional area, the errors of the machines were taken into account; these had been determined by me previously by means of a control specimen, and it proved that Werder’s machine gave loads 3.28% smaller than it should, while Pohlmeyer’s machine gave loads 1.37% greater. After the instruments had been mounted on the specimens, 15 minutes were allowed to elapse before beginning the experiments, so that the instruments could assume the temperature of the surrounding air. Readings under the stepwise form of loading were taken at each stage twice: at the moment the load was applied and after a 5-minute holding period under the same load. In the tables the data of the latter readings are given, as the most reliable.

In calculating the deformations themselves, corrections were introduced into the readings, necessary to eliminate the influence of the increase in the path traveled by the reflected ray when the mirror deviated from its initial position.

In calculating the loads in compression tests, account was taken both of half the bar’s own weight and of the weight of the instruments mounted on it.

The results of the experiments are presented in the order in which they were carried out; therefore the data of the first series of experiments—on the investigation of deformations under compression of bars—are given first. In view of the generally small amount of study of transverse deformations, the tables give all the experimental data in full.

First are given the results obtained for specimens that had not previously undergone any deformations; then for specimens that had already previously undergone compression; and, finally, for specimens that had previously undergone tension. In the tables both the longitudinal and transverse deformations are given in \(\frac{1}{100000}\) cm, i.e. magnified \(10^5\) times.

V. N. PINEGIN.

SPECIMEN No. 1.

Cross-sectional area \(\omega = 7,97 \times 7,98 = 63,6\) sq. cm.
Total length \(L = 25\) cm.
Length for measuring longitudinal elongations \(l = 10\) cm.
Own weight \(G = 11,12\) klgr.

Table No. 1.

Load intervals in klgr. On the machine	Kg./cm², taking into account the error of the machine and the own weight of the bar	Longitudinal compression per 1 cm length in 1/100000 cm or e. 10⁵	Difference of compressions during unloading intervals	Transverse expansion per 1 cm length in 1/100000 cm or q. 10⁵	Difference of transverse expansions during unloading intervals	Transverse expansion, at established state during unloading intervals	Temperature C°	Poisson’s coefficients: for difference of intervals	Poisson’s coefficients: for full intervals
500—5.000	7,844—77,63	8,7	—	1,63	—	—	17,2	—	0,187
500—5.000	7,844—77,63	8,2	—	1,51	—	—	—	—	—
500—5.000	7,844—77,63	7,3	—	1,25	—	—	—	—	—
500—5.000	7,844—77,63	7,3	—	1,25	—	—	—	0,171	0,171
500—10.000	7,844—155,2	17,0	—	3,23	—	—	17,2	—	0,190
500—10.000	7,844—155,2	16,2	—	2,90	—	—	—	—	—
500—10.000	7,844—155,2	16,0	—	2,88	—	—	—	—	—
500—10.000	7,844—155,2	16,0	8,7	2,88	1,63	—	17,2	0,187	0,180
500—15.000	7,844—232,7	25,6	—	4,94	—	—	—	—	0,193
500—15.000	7,844—232,7	24,7	—	4,71	—	—	—	—	—
500—15.000	7,844—232,7	24,7	—	4,64	—	—	—	—	—
500—15.000	7,844—232,7	24,8	—	4,64	—	—	—	—	—
500—15.000	7,844—232,7	24,7	8,7	4,64	1,76	—	17,4	0,202	0,188
500—20.000	7,844—310,2	34,3	—	6,75	—	—	—	—	0,197
500—20.000	7,844—310,2	33,7	—	6,59	—	—	—	—	—
500—20.000	7,844—310,2	33,6	—	6,59	—	—	—	—	—
500—20.000	7,844—310,2	33,5	—	6,53	—	—	—	—	—
500—20.000	7,844—310,2	33,5	8,8	6,53	1,89	—	17,6	0,215	0,195
500—25.000	7,844—387,8	43,1	—	8,66	—	—	—	—	0,201
500—25.000	7,844—387,8	42,4	—	8,60	—	—	—	—	—
500—25.000	7,844—387,8	42,4	—	8,54	—	—	17,6	—	—
500—25.000	7,844—387,8	42,3	—	8,54	—	—	—	—	—
500—25.000	7,844—387,8	42,3	8,8	8,54	2,01	—	—	0,228	0,202
500—30.000	7,844—465,3	52,1	—	10,74	—	—	17,4	—	0,206
500—30.000	7,844—465,3	51,4	—	10,61	—	—	—	—	—
500—30.000	7,844—465,3	51,3	—	10,61	—	—	—	—	—
500—30.000	7,844—465,3	51,2	—	10,55	—	—	—	—	—
500—30.000	7,844—465,3	51,2	8,9	10,55	2,01	—	17,2	0,226	0,206
500—35.000	7,844—542,9	61,2	—	12,81	—	—	—	—	0,209
500—35.000	7,844—542,9	60,3	—	12,69	—	—	—	—	—
500—35.000	7,844—542,9	60,1	—	12,62	—	—	—	—	—
500—35.000	7,844—542,9	60,1	—	12,56	—	—	—	—	—
500—35.000	7,844—542,9	60,0	—	12,56	—	—	—	—	—
500—35.000	7,844—542,9	60,0	8,8	12,56	2,01	—	17,0	0,228	0,209
500—40.000	7,844—620,4	70,9	—	14,95	—	—	—	—	0,211
500—40.000	7,844—620,4	69,4	—	14,76	—	—	—	—	—

Load intervals in kgf. On the machine	kg/cm², taking into account the error of the machine and the weight of the bar	Longitudinal compression per 1 cm length in \( \frac{1}{100000} \) cm, or \(e \cdot 10^5\)	Difference of compressions at constant state, for different load intervals	Transverse expansion per 1 cm width in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Difference of transverse expansions at constant state for different load intervals	Temperature C°.	Poisson’s ratio. For the difference of longitudinal and transverse expansions	Poisson’s ratio. For the full intervals of loads
500—40.000	7,844—620,4	69,0	—	14,70	—	—	—	—
,,	,,	68,9	—	14,70	—	—	—	—
,,	,,	68,8	—	14,70	—	—	—	—
,,	,,	68,8	8,8	14,70	2,14	17,0	0.243	0.214
500—45.000	7,844—697,9	79,9	—	17,26	—	—	—	0.216
,,	,,	78,4	—	17,11	—	—	—	—
,,	,,	78,0	—	17,09	—	—	—	—
,,	,,	77,9	—	16,96	—	—	—	—
,,	,,	77,8	—	16,90	—	—	—	—
,,	,,	77,7	—	16,90	—	—	—	—
,,	,,	77,7	8,9	16,90	2,20	16,7	0.247	0.218
500—50.000	7,844—775,5	89,1	—	19,41	—	—	—	0.218
,,	,,	87,2	—	19,22	—	—	—	—
,,	,,	86,9	—	19,16	—	—	—	—
,,	,,	86,7	—	19,16	—	—	—	—
,,	,,	86,8	—	19,10	—	—	—	—
,,	,,	86,7	—	19,10	—	—	—	—
,,	,,	86,7	—	19,10	—	—	—	—
,,	,,	86,7	9,0	19,10	2,20	16,7	0.245	0.220

This same bar, on another day, was subjected to a new test; the measurement of the transverse expansion was made in a direction perpendicular to the original direction, and the loads were applied in steps, with each step held for 5 minutes; the results are set forth in the following table:

Table No. 2.

Load in kgf. On the machine	kg/cm², taking into account the error of the machine and the weight of the bar	Longitudinal compression per 1 cm length in \( \frac{1}{100000} \) cm, or \(e \cdot 10^5\)	Difference of successive compressions	Transverse expansion per 1 cm width in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Difference of transverse expansions	Temperature C°.	Poisson’s ratio. For the difference of longitudinal and transverse expansions	Poisson’s ratio. For full compression and expansion
500	7,884	—	—	—	—	—	—	—
5000	77,63	7,3	7,3	1,38	1,38	18,0	0.189	0.189
10.000	155,2	15,9	8,6	3,01	1,63	—	0.190	0.189
15.000	232,7	24,7	8,8	4,89	1,88	17,9	0.214	0.198
20.000	310,2	33,6	8,9	6,90	2,01	18,0	0.226	0.205
25.000	387,8	42,7	9,1	8,96	2,06	—	0.226	0.210
30.000	465,3	51,7	9,0	11,03	2,07	17,9	0.230	0.214
35.000	542,9	60,8	9,1	13,16	2,13	—	0.234	0.219
40.000	620,4	69,9	9,1	15,29	2,13	17,8	0.234	0.219
45.000	697,9	79,0	9,1	17,42	2,13	17,8	0.234	0.220

SPECIMEN No. 2.

Cross-sectional area \(\omega = 7.98 \times 7.99 = 63.76\ \mathrm{cm}^2\).
Total length \(l = 27.9\ \mathrm{cm}\).
Length for measuring elongations \(l = 15\ \mathrm{cm}\).
Own weight of specimen \(G = 12.53\ \mathrm{klgr.}\)

Table No. 3.

Load intervals, in klgr. — on the machine	Kg./cm², taking into account the error of the machine and own weight of the bar	Longitudinal elongation per 1 cm length, in 1/100000 cm, or \(10^5\)	Mean value for individual intervals	Transverse expansion per 1 cm length, in 1/100000 cm, or \(10^5\)	Mean value for individual intervals	Temperature C°.	Poisson’s ratio: for individual intervals	Poisson’s ratio: for whole load intervals
500—5.000	7.837—77.45	7.40	—	1.32	—	18,0	—	0.178
„	„	7.28	—	1.25	—	—	—	—
„	„	7.20	—	1.25	—	—	—	—
„	„	7.20	—	1.25	—	—	0.174	0.174
500—10.000	7.837—154.8	16.25	—	3.25	—	—	—	0.201
„	„	15.72	—	3.16	—	—	—	—
„	„	15.60	—	3.14	—	—	—	—
„	„	15.60	8.40	3.14	1,89	18,0	0.225	0.201
500—15.000	7.837—232.1	25.13	—	5.15	—	—	—	0.205
„	„	24.40	—	5.08	—	—	—	—
„	„	24.20	—	5.15	—	—	—	—
„	„	24.13	—	5.15	—	—	—	—
„	„	24.07	—	5.08	—	—	—	—
„	„	24.07	8.47	5.08	1,94	18,0	0.229	0.211
500—20.000	7.837—309.5	33.93	—	7.09	—	—	—	0.209
„	„	33.13	—	7.09	—	—	—	—
„	„	32.87	—	7.01	—	—	—	—
„	„	32.73	—	7.01	—	—	—	—
„	„	32.73	8.66	7.01	1,93	18,1	0.223	0.214
500—25.000	7.837—386.8	42.53	—	9.08	—	—	—	0.214
„	„	41.87	—	9.02	—	—	—	—
„	„	41.60	—	9.02	—	—	—	—
„	„	41.47	—	9.02	—	—	—	—
„	„	41.47	8.74	9.02	2,01	18,2	0.230	0.218
500—30.000	7.837—464.2	51.25	—	11.08	—	—	—	0.216
„	„	50.60	—	11.08	—	—	—	—
„	„	50.40	—	11.08	—	—	—	—
„	„	50.27	—	11.02	—	—	—	—
„	„	50.20	—	11.02	—	—	—	—
„	„	50.20	8.73	11.02	2,00	18,1	0.229	0.220
500—35.000	7.837—541.5	60.47	—	13.14	—	—	—	0.217
„	„	59.13	—	13.08	—	—	—	—
„	„	59.00	—	13.02	—	—	—	—
„	„	58.93	—	13.02	—	—	—	—
„	„	58.93	—	13.02	2,00	18,0	0.229	0.221
500—40.000	7.837—618.9	69.07	—	15.14	—	—	—	0.220

Load intervals in klgr	Load intervals in klgr	Longitudinal compression per 1 cm length, in \( \frac{1}{100000} \) cm or \(10^5\)	Difference between adjacent compressions when dividing the load interval	Transverse expansion per 1 cm length, in \( \frac{1}{100000} \) cm or \(10^5\)	Difference between transverse expansions when dividing the interval	Temperature C°	Poisson’s ratio	Poisson’s ratio
On the machine	Kg./cm², taking into account the error of the machine and the proper weight of the bar						For longitudinal intervals	For full intervals of loads
500—40.000	7.837—618,9	68,20	—	15,02	—	—	—	—
ditto	ditto	68,00	—	14,95	—	—	—	—
ditto	ditto	67,87	—	15,02	—	—	—	—
ditto	ditto	67,80	—	15,02	—	—	—	—
ditto	ditto	67,73	—	15,02	—	—	—	—
ditto	ditto	67,73	8,80	15,02	2,00	18,0	0,227	0,222
500—45.000	7.837—696,2	77,93	—	17,27	—	—	—	0,222
ditto	ditto	77,13	—	17,15	—	—	—	—
ditto	ditto	76,87	—	17,02	—	—	—	—
ditto	ditto	76,73	—	17,02	—	—	—	—
ditto	ditto	76,67	—	17,02	—	—	—	—
ditto	ditto	76,67	8,94	17,02	2,00	17,9	0,224	0,223
500—50.000	7.837—773,6	87,20	—	19,40	—	—	—	0,222
ditto	ditto	86,33	—	19,27	—	—	—	—
ditto	ditto	86,00	—	19,15	—	—	—	—
ditto	ditto	85,87	—	19,09	—	—	—	—
ditto	ditto	85,80	—	19,09	—	—	—	—
ditto	ditto	85,73	—	19,09	—	—	—	—
ditto	ditto	85,73	9,06	19,09	2,05	17,9	0,227	0,223

For the same bar, when measuring the transverse expansions in a direction perpendicular to the one just adopted, the following results were obtained:

Table No. 4.

Load in klgr.	Load in klgr.	Longitudinal compression per 1 cm length, in \( \frac{1}{100000} \) cm or \(10^5\)	Difference between longitudinal compressions	Transverse expansion per 1 cm length, in \( \frac{1}{100000} \) cm or \(10^5\)	Difference between transverse expansions	Temperature C°	Poisson’s ratio	Poisson’s ratio
On the machine	Kg./cm², taking into account the error of the machine and the proper weight of the bar						For differences of adjacent quantities	For full compressions and expansions
500	7.837	—	—	—	—	17,8	—	—
5.000	77,45	7,20	7,20	1,19	1,19	—	0,165	0,165
10.000	154,8	15,60	8,40	3,07	1,88	17,8	0,224	0,197
15.000	232,1	24,33	8,73	4,95	1,88	—	0,216	0,204
20.000	309,5	33,07	8,74	6,95	2,00	17,9	0,229	0,206
25.000	386,8	41,87	8,80	8,96	2,01	17,9	0,228	0,214
30.000	464,2	50,67	8,80	10,97	2,01	—	0,228	0,216
35.000	541,5	59,60	8,93	13,03	2,06	17,8	0,230	0,218
40.000	618,9	68,60	9,00	15,10	2,07	17,8	0,230	0,219
45.000	696,2	77,60	9,00	17,23	2,13	—	0,237	0,222

V. N. PIPETIN.

SPECIMEN No. 3.

Cross-sectional area \(\omega\)

\[ = \frac{\pi d^{2}}{4}=\frac{3.14\cdot 7.75^{2}}{4}=47.15\ \mathrm{cm}^{2} \]

Total length of the bar \(L=25\ \mathrm{cm}\).
Length for measuring longitudinal elongations \(l=10\ \mathrm{cm}\).
Own weight of the bar \(G=8.26\ \mathrm{kg}\).

Table No. 5.

Load intervals, kg — on the machine	kg/cm², taking into account the error of the machine and the own weight of the bar	Longitudinal compression per 1 cm of length, in \(1/10000\) cm, or \(10^5\)	Difference of adjacent states under different load intervals	Transverse expansion per 1 cm of length, in \(1/10000\) cm, or \(10^5\)	Difference of transverse expansion under adjacent load intervals	Temperature C°	Poisson’s coefficient — for difference of intervals	Poisson’s coefficient — for full load intervals
500—5.000	10.56—104.7	10.5	—	2.03	—	18.0	—	0.194
„	„	9.8	—	1.96	—	—	—	—
„	„	9.7	—	1.87	—	—	—	—
„	„	9.7	9.7	1.87	1.87	—	0.193	0.193
500—10.000	10.56—209.3	22.0	—	4.33	—	18.2	—	0.197
„	„	21.3	—	4.20	—	—	—	—
„	„	21.2	—	4.13	—	—	—	—
„	„	21.1	—	4.13	—	—	—	—
„	„	21.1	11.4	4.13	2.26	—	0.198	0.196
500—15.000	10.56—313.9	34.0	—	6.84	—	18.2	—	0.201
„	„	32.9	—	6.59	—	—	—	—
„	„	32.8	—	6.64	—	—	—	—
„	„	32.7	—	6.59	—	—	—	—
„	„	32.7	11.6	6.59	2.46	—	0.212	0.202
500—20.000	10.56—418.5	45.8	—	9.59	—	18.2	—	0.209
„	„	44.9	—	9.49	—	—	—	—
„	„	44.6	—	9.36	—	—	—	—
„	„	44.4	—	9.23	—	—	—	—
„	„	44.4	11.7	9.23	2.64	—	0.226	0.208
500—25.000	10.56—523.1	58.0	—	12.52	—	—	—	0.216
„	„	56.4	—	12.20	—	—	—	—
„	„	56.3	—	12.13	—	—	—	—
„	„	56.1	—	12.13	—	—	—	—
„	„	56.1	11.7	12.13	2.90	18.0	0.248	0.216
500—30.000	10.56—627.7	69.5	—	15.42	—	—	—	0.222
„	„	68.1	—	15.03	—	—	—	—
„	„	68.1	—	14.90	—	—	—	—
„	„	67.8	—	15.03	—	—	—	—
„	„	67.8	11.7	15.03	2.90	17.9	0.248	0.222
500—35.000	10.56—732.2	81.6	—	18.45	—	—	—	0.226
„	„	80.0	—	18.20	—	—	—	—
„	„	79.7	—	18.06	—	—	—	—
„	„	79.5	—	18.06	—	—	—	—
„	„	79.5	11.7	18.06	3.03	17.8	0.259	0.227
500—40.000	10.56—836.8	93.3	—	21.49	—	—	—	0.230
„	„	91.7	—	20.97	—	—	—	—

Load intervals in klgr. On the machine	Load intervals in klgr. Kg./cm², taking into account the machine error and the bar’s own weight	Longitudinal compression per 1 cm length, \( \frac{1}{100000}\) cm or \(q \cdot 10^5\)	Difference of longitudinal compressions, under difference of integrated loads	Transverse expansion per 1 cm length, \( \frac{1}{100000}\) cm or \(q_1 \cdot 10^5\)	Difference of transverse expansions, under difference of integrated loads	Temperature \(C^\circ\)	Poisson’s ratio. For the difference of longitudinal and transverse deformations	Poisson’s ratio. For the total integrated deformations
500—40,000	10,56—836,8	91,4	—	20,97	—	—	—	—
″	″	91,3	—	21,10	—	—	—	—
″	″	91,2	—	21,10	—	—	—	—
″	″	91,2	11,7	21,10	3,04	17,8	0,260	0,232
500—45,000	10,56—941,4	104,5	—	24,32	—	—	—	0,232
″	″	102,9	—	24,20	—	—	—	—
″	″	103,0	—	24,06	—	—	—	—
″	″	102,9	—	24,13	—	—	—	—
″	″	102,9	11,7	24,13	3,03	17,8	0,259	0,235
500—50,000	10,56—1046	117,2	—	27,54	—	—	—	0,235
″	″	115,4	—	27,41	—	—	—	—
″	″	115,0	—	27,38	—	—	—	—
″	″	114,9	—	27,35	—	—	—	—
″	″	114,8	—	27,35	—	—	—	—
″	″	114,7	—	27,35	—	—	—	—
″	″	114,7	11,8	27,35	3,22	17,8	0,273	0,238

S P E C I M E N No. 4.

Cross-sectional area \(\omega = 4,455 \cdot 5,02 = 22,364\ \mathrm{cm}^2\).

Total length of the bar \(L = 34\ \mathrm{cm}\).

Length for measuring longitudinal compressions \(l = 15\ \mathrm{cm}\).

Own weight of the bar \(G = 5,35\ \mathrm{klgr}\).

The bar had already previously been subjected to compression up to a load \(P = 51290\ \mathrm{kg}\ \left(2293\ \frac{\mathrm{kg}}{\mathrm{cm}^2}\right)\).

For measuring transverse expansions, the dimension \(5,02\ \mathrm{cm}\) was taken.

Table No. 6.

Load in klgr. On the machine	Load in klgr. Kg./cm², taking into account the machine error and the bar’s own weight	Longitudinal compression per 1 cm length, \( \frac{1}{100000}\) cm or \(q \cdot 10^5\)	Difference of longitudinal compressions	Transverse expansion per 1 cm length, \( \frac{1}{100000}\) cm or \(q_1 \cdot 10^5\)	Difference of transverse expansions	Temperature \(C^\circ\)	Poisson’s ratio. For the difference of longitudinal compressions and transverse expansions	Poisson’s ratio. For the total compressions and expansions
500	22,19	—	—	—	—	18,6	—	—
4.000	176,6	16,70	16,70	3,78	3,78	18,2	0,226	0,226
8.000	353,0	37,00	20,30	8,76	4,98	18,3	0,245	0,237
12.000	529,4	57,47	20,47	13,84	5,08	18,2	0,248	0,241
16.000	705,8	78,00	20,53	18,92	5,08	18,2	0,247	0,243
20.000	882,3	98,60	20,60	24,30	5,38	18,2	0,261	0,247
24.000	1059	119,20	20,60	29,88	5,58	18,1	0,271	0,251
28.000	1235	139,93	20,73	35,76	5,88	18,1	0,284	0,256
32.000	1412	160,73	20,80	41,83	6,07	18,1	0,291	0,260
36.000	1588	181,67	20,94	47,91	6,08	18,1	0,290	0,264
40.000	1764	203,13	21,46	54,18	6,27	18,1	0,292	0,267

The same bar, when the experiment was repeated, gave the following results:

Table No. 7.

Load in kg, on the machine	Load in kg/cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, divisions in 1 cm; line in 1/100000 cm	Difference of longitudinal compressions	Transverse expansion, divisions in 1 cm; line in 1/100000 cm	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for the difference of longitudinal compression and transverse expansion	Poisson’s ratio: for the total compressions and expansions
500	22,19	—	—	—	—	18,0	—	—
4.000	176,6	16,10	16,10	3,78	3,78	18,0	0,235	0,235
8.000	353,0	35,87	19,77	8,76	4,98	18,0	0,252	0,244
12.000	529,4	55,80	19,93	13,94	5,18	18,0	0,260	0,250
16.000	705,8	75,80	20,00	19,12	5,18	18,0	0,259	0,252
20.000	882,3	95,87	20,07	24,60	5,48	17,9	0,273	0,257
24.000	1059	115,94	20,07	30,08	5,48	17,9	0,273	0,259
28.000	1235	136,07	20,13	35,66	5,58	17,9	0,277	0,260
32.000	1412	156,40	20,33	41,54	5,88	17,9	0,289	0,265
36.000	1588	176,80	20,40	47,52	5,98	17,9	0,293	0,269
40.000	1764	197,40	20,60	53,50	5,98	17,8	0,290	0,271

After compression of the same bar for the 3rd time, the following was obtained:

Table No. 8.

Load in kg, on the machine	Load in kg/cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, divisions in 1 cm; line in 1/100000 cm	Difference of longitudinal compressions	Transverse expansion, divisions in 1 cm; line in 1/100000 cm	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for the difference of longitudinal compression and transverse expansion	Poisson’s ratio: for the total compressions and expansions
500	22,19	—	—	—	—	—	—	—
4.000	176,6	15,93	15,93	3,39	3,39	19,8	0,213	0,213
8 000	353,0	35,46	19,53	8,47	5,08	19,8	0,260	0,239
12.000	529,4	55,33	19,87	13,75	5,28	19,7	0,265	0,248
16.000	705,8	75,20	19,87	19,32	5,57	19,4	0,280	0,256
20.000	882,3	95,20	20,00	24,90	5,58	19,2	0,279	0,261
24.000	1059	115,20	20,00	30,58	5,68	19,1	0,284	0,265
28.000	1235	135,20	20,00	36,45	5,87	19,0	0,293	0,270
32.000	1412	155,40	20,20	42,33	5,88	19,0	0,291	0,272
36.000	1588	175,73	20,33	48,31	5,98	19,0	0,294	0,275
40.000	1764	196,13	20,40	54,38	6,07	19,0	0,297	0,277

Finally, for the same bar, when for measuring the transverse expansions the dimension 4.455 cm was taken, the following was obtained:

Table No. 9.

Load in kg: on the machine	Load in kg/cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, gauge length 1 cm, in 1/100000 cm, or ε·10⁵	Difference of longitudinal compressions	Transverse expansion, gauge length 1 cm, in 1/100000 cm, or q·10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for differences of longitudinal compressions and transverse expansions	Poisson’s ratio: for total compression and expansion
500	22.19	—	—	—	—	18.2	—	—
4,000	175.6	16.33	16.33	3.59	3.59	18.4	0.220	0.220
8,000	353.0	36.26	19.93	8.08	4.49	18.7	0.226	0.223
12,000	529.4	56.26	20.00	13.24	5.16	18.7	0.258	0.235
16,000	705.8	76.26	20.00	18.62	5.38	18.6	0.269	0.244
20,000	882.3	96.26	20.00	24.00	5.38	18.6	0.269	0.249
24,000	1059	116.19	19.93	29.39	5.39	18.6	0.271	0.253
28,000	1235	136.12	19.93	35.11	5.72	18.6	0.287	0.258
32,000	1412	156.12	20.00	40.95	5.84	18.5	0.291	0.262
36,000	1588	176.25	20.13	46.79	5.84	18.4	0.290	0.265
40,000	1764	196.45	20.20	52.96	6.17	18.3	0.305	0.269

SAMPLE No. 5.

Cross-sectional area of the specimen $\omega = 4.475 \times 5.02 = 22.46\ \mathrm{cm.^2}$.

Total length of the specimen $L = 54\ \mathrm{cm}$.

Length for measuring longitudinal compressions $l = 10\ \mathrm{cm}$.

Own weight of the bar $G = 5.37\ \mathrm{kg}$.

The bar had already previously been subjected to compression up to a load $P = 51.290\ \mathrm{kg}$ $(2.283\ \mathrm{kg/cm.^2})$; for measuring transverse expansions the dimension 5.02 cm was taken.

Table No. 10.

Load in kg: on the machine	Load in kg/cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, gauge length 1 cm, in 1/100000 cm, or ε·10⁵	Difference of longitudinal compressions	Transverse expansion, gauge length 1 cm, in 1/100000 cm, or q·10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for differences of longitudinal compressions and transverse expansions	Poisson’s ratio: for total compression and expansion
500	22.09	—	—	—	—	18	—	—
4,000	175.8	17.6	17.6	3.48	3.48	—	0.198	0.198
8,000	351.4	37.8	20.2	7.99	4.51	18.1	0.224	0.211
12,000	527.0	58.0	20.2	12.76	4.77	18.2	0.236	0.220
16,000	702.6	78.1	20.1	17.83	5.07	18.1	0.251	0.228
20,000	878.2	98.2	20.1	23.41	5.58	17.9	0.278	0.238
24,000	1054	118.4	20.2	28.99	5.58	17.9	0.276	0.245
28,000	1229	138.5	20.1	34.57	5.58	18.0	0.278	0.250
32,000	1405	159.0	20.5	39.88	5.31	18.0	0.260	0.251
36,000	1581	179.5	20.5	45.71	5.83	18.0	0.285	0.255
40,000	1757	200.4	20.9	51.54	5.83	18.0	0.279	0.257

After a fourfold repetition of the experiment, the following was obtained:

Table No. 11.

Load in kg	Load in kg/cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression at 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Difference of longitudinal compressions	Transverse expansion at 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Difference of transverse expansions	Temperature °C	Poisson’s ratio: for equal longitudinal compressions and transverse expansions	Poisson’s ratio: for total compression and expansion
500	22,09	—	—	—	—	18	—	—
4.000	175,8	16,4	16,4	3,19	3,19	—	0,195	0,195
8.000	351,4	36,3	19,9	7,44	4,25	18	0,214	0,205
12.000	527,0	56,3	20,0	12,21	4,77	18,1	0,239	0,217
16.000	702,6	76,3	20,0	17,52	5,31	18,1	0,265	0,229
20.000	878,2	96,3	20,0	23,10	5,58	18,1	0,279	0,240
24.000	1054	116,4	20,1	28,68	5,58	18,1	0,278	0,246
28.000	1229	136,4	20,0	34,26	5,58	18,0	0,279	0,251
32.000	1405	156,4	20,0	39,84	5,58	18,1	0,279	0,255
36.000	1581	176,6	20,2	45,67	5,83	18,0	0,289	0,259
40.000	1757	197,1	20,5	51,50	5,83	18,1	0,285	0,261

When, for measuring the transverse expansions, the dimension \(4,475\) cm was taken, the following was obtained:

Table No. 12.

Load in kg	Load in kg/cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression at 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Difference of longitudinal compressions	Transverse expansion at 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Difference of transverse expansions	Temperature °C	Poisson’s ratio: for equal longitudinal compressions and transverse expansions	Poisson’s ratio: for total compression and expansion
500	22,09	—	—	—	—	17,2	—	—
4.000	175,8	16,7	16,7	3,58	3,58	—	0,214	0,214
8.000	351,4	36,7	20,0	8,05	4,47	17,2	0,224	0,219
12.000	527,0	56,7	20,0	13,12	5,07	17,1	0,254	0,231
16.000	702,6	76,9	20,2	18,48	5,37	16,9	0,266	0,240
20.000	878,2	97,0	20,1	23,84	5,37	16,8	0,267	0,246
24.000	1054	117,0	20,0	29,20	5,37	17,0	0,268	0,250
28.000	1229	137,0	20,0	34,58	5,37	17,1	0,268	0,252
32.000	1405	157,0	20,0	40,23	5,67	17,3	0,283	0,256
36.000	1581	177,0	20,0	46,20	5,67	17,5	0,298	0,261

After repeating the experiment:

Table No. 13.

Load in klgr. On the machine	Kg./cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, per 1 cm length, in 1/100000 cm or \(e \cdot 10^5\)	Difference of longitudinal compressions \(e \cdot 10^5\)	Transverse expansion, per 1 cm length, in 1/100000 cm or \(q \cdot 10^5\)	Difference of transverse expansions \(q \cdot 10^5\)	Temperature \(C^\circ\)	Poisson’s ratio: for difference of longitudinal compression and transverse expansion	Poisson’s ratio: for total compression and expansion
500	22,09	—	—	—	—	19,2	—	—
4.000	175,8	16,6	16,6	3,28	3,28	—	0,198	0,198
8.000	351,4	36,5	19,9	7,75	4,47	19,2	0,225	0,212
12.000	527,0	56,5	20,0	12,37	4,62	19,3	0,231	0,219
16.000	702,6	76,5	20,0	16,99	4,62	19,3	0,231	0,222
20.000	878,2	96,5	20,0	22,36	5,37	19,2	0,268	0,232
24.000	1054	116,5	20,0	27,73	5,37	19,3	0,268	0,238
28.000	1229	136,4	19,9	33,10	5,37	19,4	0,270	0,242
32.000	1405	156,2	19,8	38,77	5,67	19,2	0,286	0,248
36.000	1581	176,1	19,9	44,44	5,67	19,3	0,285	0,253

SPECIMEN No. 6.

Cross-sectional area of the specimen \(\omega = 4{,}49 \times 5{,}02 = 22{,}54\ \text{cm}^2\).
Total length of the specimen \(L = 25\ \text{cm}\).
Length for measuring longitudinal compressions \(l = 10\ \text{cm}\).
Own weight of the bar \(G = 3{,}94\ \text{klgr}\).
The bar had already previously been subjected to compression up to a load of \(51.290\ \text{klgr}\) \(\left(2276\ \frac{\text{kg}}{\text{cm}^2}\right)\). In measuring the transverse expansions in the direction of the larger dimension \((5{,}02\ \text{cm})\), the following results were obtained:

Table No. 14.

Load intervals in klgr. On the machine	Kg./cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, per 1 cm length, in 1/100000 cm or \(e \cdot 10^5\)	Difference of longitudinal compressions, allowing for loading intervals	Transverse expansion, per 1 cm length, in 1/100000 cm or \(q \cdot 10^5\)	Difference of transverse expansions, allowing for loading intervals	Temperature \(C^\circ\)	Poisson’s ratio: for difference of intervals	Poisson’s ratio: for total intervals of loading
500—4.000	21,99—175,1	17,7	—	3,69	—	18,4	—	0,209
„	„	17,2	—	3,59	—	—	—	—
„	„	17,1	—	3,59	—	—	—	—
„	„	17,1	—	3,59	—	—	0,210	0,210
500—8.000	21,99—350,2	38,2	—	8,22	—	18,4	—	0,215
„	„	37,5	—	7,98	—	—	—	—
„	„	37,4	—	7,98	—	—	—	—
„	„	37,4	20,3	7,98	4,39	—	0,216	0,213

Load intervals in kg, on the machine	kg/cm², taking into account the error of the machine and the bar’s own weight	Divisions of the elongation scale per 1 cm length, in \(1/100000\) cm	Difference of scale readings at stretching, in scale divisions	Transverse-compression scale divisions per 1 cm length, in \(1/100000\) cm	Difference of readings at transverse compression, in scale divisions	Temperature, C°	Poisson’s ratio, for elastic deformations	Poisson’s ratio, for full load intervals
500—12.000	21,99—525,2	58,4	—	12,92	—	18,4	—	0,221
〃	〃	57,9	—	12,82	—	—	—	—
〃	〃	57,6	—	12,76	—	—	—	—
〃	〃	57,6	20,2	12,76	4,78	—	0,236	0,221
500—16.000	21,99—700,2	78,5	—	17,76	—	18,5	—	0,226
〃	〃	78,0	—	17,58	—	—	—	—
〃	〃	77,8	—	17,58	—	—	—	—
〃	〃	77,8	20,2	17,58	4,82	—	0,239	0,226
500—20.000	21,99—875,3	98,8	—	23,00	—	18,5	—	0,233
〃	〃	98,3	—	22,80	—	—	—	—
〃	〃	98,2	—	22,75	—	—	—	—
〃	〃	98,0	—	22,75	—	—	—	—
〃	〃	98,0	20,2	22,75	5,17	—	0,256	0,232
500—24.000	21,99—1050	118,9	—	28,59	—	18,6	—	0,240
〃	〃	118,4	—	28,39	—	—	—	—
〃	〃	118,3	—	28,29	—	—	—	—
〃	〃	118,2	—	28,29	—	—	—	—
〃	〃	118,2	20,2	28,29	5,54	—	0,275	0,240
500—28.000	21,99—1225	139,7	—	34,06	—	18,5	—	0,244
〃	〃	138,8	—	33,96	—	—	—	—
〃	〃	138,5	—	33,87	—	—	—	—
〃	〃	138,4	—	33,87	—	—	—	—
〃	〃	138,4	20,2	33,87	5,58	—	0,276	0,245
500—32.000	21,99—1400	159,9	—	39,64	—	18,5	—	0,248
〃	〃	159,0	—	39,54	—	—	—	—
〃	〃	158,8	—	39,44	—	—	—	—
〃	〃	158,7	—	39,44	—	—	—	—
〃	〃	158,6	—	39,44	—	—	—	—
〃	〃	158,6	20,2	39,44	5,57	—	0,276	0,248
500—36.000	21,99—1575	180,2	—	45,82	—	18,5	—	0,254
〃	〃	179,2	—	45,72	—	—	—	—
〃	〃	179,1	—	45,72	—	—	—	—
〃	〃	179,0	—	45,62	—	—	—	—
〃	〃	178,9	—	45,62	—	—	—	—
〃	〃	178,9	20,3	45,62	6,18	—	0,305	0,255

When measuring the transverse expansions in a direction perpendicular to the one taken earlier, the following was obtained:

Table No. 15.

Load in klgr., on the machine	Load in klgr., kg./cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, in 1 cm of length, in $\frac{1}{100000}$ cm, or $q \cdot 10^5$	Difference of longitudinal compressions	Transverse expansion, in 1 cm of length, in $\frac{1}{100000}$ cm, or $q \cdot 10^5$	Difference of transverse expansions	Temperature C°	Poisson’s ratio: from the difference of longitudinal compression and transverse expansion	Poisson’s ratio: from transverse compressions and expansions
500	21,99	—	—	—	—	17,8	—	—
4.000	175,1	17,2	17,2	3,67	3,67	17,9	0,214	0,214
8.000	350,2	37,6	20,4	8,13	4,46	17,9	0,219	0,215
12.000	525,2	57,8	20,2	13,25	5,12	18,0	0,254	0,230
16.000	700,2	78,1	20,3	18,37	5,12	17,9	0,253	0,235
20.000	875,3	98,4	20,3	23,83	5,46	17,9	0,269	0,242
24.000	1050	118,7	20,3	29,29	5,46	17,8	0,269	0,246
28.000	1225	139,4	20,7	33,86	5,57	17,8	0,269	0,250
32.000	1400	160,2	20,8	40,65	5,79	17,7	0,278	0,254
36.000	1575	181,1	20,9	46,78	6,13	17,7	0,294	0,259

Finally, when measuring the transverse expansions along the diagonal of the section, we obtained:

Table No. 16.

Load in klgr., on the machine	Load in klgr., kg./cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, in 1 cm of length, in $\frac{1}{100000}$ cm, or $q \cdot 10^5$	Difference of longitudinal compressions	Transverse expansion, in 1 cm of length, in $\frac{1}{100000}$ cm, or $q \cdot 10^5$	Difference of transverse expansions	Temperature C°	Poisson’s ratio: from the difference of longitudinal compression and transverse expansion	Poisson’s ratio: from transverse compressions and expansions
500	21,99	—	—	—	—	18,0	—	—
4.000	175,1	17,2	17,2	3,59	3,59	18,0	0,209	0,209
8.000	350,2	37,6	20,4	7,78	4,19	18,0	0,206	0,207
12.000	525,2	58,0	20,4	12,35	4,57	18,0	0,224	0,213
16.000	700,2	78,3	20,3	17,51	5,16	17,9	0,254	0,223
20.000	875,3	98,6	20,3	22,97	5,46	17,9	0,269	0,233
24.000	1050	119,0	20,4	28,43	5,46	18,0	0,268	0,239
28.000	1225	139,5	20,5	33,89	5,46	17,9	0,266	0,243
32.000	1400	160,1	20,6	39,35	5,46	17,9	0,265	0,246
36.000	1575	180,7	20,6	44,97	5,62	17,8	0,273	0,249
40.000	1750	201,8	21,1	51,19	6,22	17,8	0,295	0,254

SPECIMEN No. 7

The cross-sectional area of the specimen

\[ \omega=\frac{\pi d^2}{4}=\frac{\pi\cdot 4.69^2}{4}=17.29\ \mathrm{cm}^2. \]

Total length of the specimen \(L=34\) cm.
Length for measuring longitudinal compressions \(l=15\) cm.
Own weight of the bar \(G=4.25\) klgr.
The bar had already previously been subjected to compression up to a load \(Q=38.470\) klgr. \((2225\ \mathrm{klgr}/\mathrm{cm}^2)\).

Table No. 17.

Load on the machine, klgr.	kg/cm², taking into account the error of the machine and the own weight of the bar	Longitudinal compression, taking \(1\) cm length as unit, \( \frac{1}{100000}\) cm, or \(q\cdot 10^5\)	Difference of longitudinal compressions	Transverse expansion, taking \(1\) cm length as unit, \( \frac{1}{100000}\) cm, or \(q\cdot 10^5\)	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for difference of longitudinal and transverse expansions	Poisson’s ratio: for total expansions
500	28,67	—	—	—	—	—	—	—
3.000	171,4	15,67	15,67	3,20	3,20	17,4	0,204	0,204
6.000	342,5	35,67	20,00	8,21	5,01	—	0,251	0,230
9.000	513,7	56,07	20,40	13,32	5,11	17,7	0,251	0,237
12.000	684,8	76,40	20,33	18,43	5,11	17,4	0,251	0,241
15.000	855,9	96,73	20,33	23,75	5,32	17,6	0,261	0,246
18.000	1027	117,13	20,40	29,18	5,43	17,6	0,266	0,250
21.000	1198	137,47	20,34	34,82	5,64	17,5	0,277	0,254
24.000	1369	158,00	20,53	40,79	5,97	17,4	0,291	0,258
27.000	1540	178,93	20,93	46,97	6,18	17,4	0,295	0,262
30.000	1712	200,47	21,53	53,26	6,29	17,4	0,292	0,266

Then the bar was subjected to compression three more times; limiting ourselves to the last of these three experiments, we give its results:

Table No. 18.

Load on the machine, klgr.	kg/cm², taking into account the error of the machine and the own weight of the bar	Longitudinal compression, taking \(1\) cm length as unit, \( \frac{1}{100000}\) cm, or \(q\cdot 10^5\)	Difference of longitudinal compressions	Transverse expansion, taking \(1\) cm length as unit, \( \frac{1}{100000}\) cm, or \(q\cdot 10^5\)	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for difference of longitudinal and transverse expansions	Poisson’s ratio: for total expansions
500	28,67	—	—	—	—	—	—	—
3.000	171,4	15,47	15,47	3,84	3,84	16,0	0,248	0,248
6.000	342,5	35,40	19,93	8,95	5,11	15,9	0,256	0,253
9.000	513,7	55,33	19,93	14,06	5,11	15,8	0,256	0,254
12.000	684,8	75,27	19,93	19,17	5,11	15,8	0,256	0,255
15.000	855,9	95,20	19,93	24,60	5,43	15,8	0,273	0,258
18.000	1027	115,07	19,87	30,03	5,43	15,7	0,274	0,261
21.000	1198	134,94	19,87	35,67	5,64	15,7	0,284	0,265
24.000	1369	154,81	19,87	41,43	5,76	15,6	0,290	0,267
27.000	1540	174,74	19,93	47,19	5,76	15,5	0,289	0,270
30.000	1712	195,00	20,26	53,37	6,18	15,3	0,305	0,274

SPECIMEN No. 8.

Cross-sectional area of the specimen

\[ \omega=\frac{\pi d^2}{4}=\frac{\pi \cdot 5.995^2}{4}=28.21\ \text{cm}^2 . \]

Total length of the specimen \(L=34\) cm.
Length for measuring longitudinal compressions \(l=15\) cm.
Own weight of the bar \(G=6.76\) kg.
The bar had already previously been subjected to compression up to a load of \(P=79{,}000\) kg \((2800\ \text{kg}/\text{cm}^2)\).

Table No. 19.

Load, kg	Load, kg/cm², taking into account the error of the machine and the own weight of the bar	Longitudinal compression per 1 cm length, in \(1/100000\) cm	Difference of longitudinal compressions	Transverse expansion per 1 cm length, in \(1/100000\) cm	Difference of transverse expansions	Temperature C°	Poisson’s coefficient: for differences of longitudinal compressions and transverse expansions	Poisson’s coefficient: for complete compression and expansion
500	17.62	—	—	—	—	19.0	—	—
5,000	175.0	16.40	16.40	4.25	4.25	—	0.259	0.259
10,000	349.8	35.80	19.40	9.26	5.01	19.1	0.259	0.259
15,000	524.6	55.20	19.40	14.27	5.01	19.2	0.259	0.259
20,000	699.4	74.53	19.33	19.44	5.17	19.3	0.267	0.261
25,000	874.2	93.86	19.33	25.11	5.67	19.3	0.293	0.268
30,000	1049	113.13	19.27	30.78	5.67	19.7	0.294	0.272
35,000	1224	132.40	19.27	36.53	5.75	19.9	0.298	0.275
40,000	1399	151.60	19.20	42.28	5.75	19.9	0.300	0.280
45,000	1573	170.93	19.33	48.29	6.01	19.9	0.311	0.283
50,000	1748	190.46	19.53	54.63	6.34	19.8	0.325	0.286

On repeating the experiment, the following was obtained:

Table No. 20.

Load, kg	Load, kg/cm², taking into account the error of the machine and the own weight of the bar	Longitudinal compression per 1 cm length, in \(1/100000\) cm	Difference of longitudinal compressions	Transverse expansion per 1 cm length, in \(1/100000\) cm	Difference of transverse expansions	Temperature C°	Poisson’s coefficient: for differences of longitudinal compressions and transverse expansions	Poisson’s coefficient: for complete compression and expansion
500	17.62	—	—	—	—	20.6	—	—
5,000	175.0	16.47	16.47	2.75	2.75	20.7	0.167	0.167
10,000	349.8	35.54	19.07	7.59	4.84	20.7	0.254	0.213
15,000	524.6	54.61	19.07	13.01	5.42	20.5	0.284	0.238
20,000	699.4	73.61	19.00	18.43	5.42	20.8	0.285	0.251
25,000	874.2	92.68	19.07	23.93	5.50	20.8	0.288	0.258
30,000	1049	111.75	19.07	29.60	5.67	—	0.296	0.265
35,000	1224	130.68	18.93	35.10	5.50	20.9	0.291	0.269
40,000	1399	149.41	18.73	40.77	5.67	—	0.303	0.273
45,000	1573	168.14	18.73	46.78	6.01	20.8	0.321	0.278
50,000	1748	187.07	18.93	52.95	6.17	20.8	0.326	0.283

Finally, after the third loading, we have:

Table No. 21.

Load in klgr., on the machine	Load in kg/cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, at 1 cm length in 1/100000 cm or ε·10⁵	Difference of longitudinal compressions	Transverse expansion, at 1 cm length in 1/100000 cm or q·10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for difference of longitudinal and transverse expansions	Poisson’s ratio: for full compression and expansion
500	17,62	—	—	—	—	21,2	—	—
5.000	175,0	16,33	16,33	4,25	4,25	21,2	0,260	0,260
10.000	349,8	35,20	18,87	9,26	5,01	—	0,266	0,263
15.000	524,6	54,20	19,00	14,60	5,34	21,0	0,281	0,269
20.000	699,4	73,20	19,00	20,02	5,42	21,2	0,285	0,273
25.000	874,2	92,20	19,00	25,69	5,67	21,2	0,298	0,278
30.000	1049	111,07	18,87	31,44	5,75	21,1	0,304	0,283
35.000	1224	129,94	18,87	37,19	5,75	21,1	0,304	0,286
40.000	1399	148,81	18,87	43,03	5,84	21,0	0,309	0,289
45.000	1573	167,54	18,73	49,12	6,09	20,8	0,325	0,293
50.000	1748	186,47	18,93	55,29	6,17	20,8	0,326	0,296

SPECIMEN No. 9.

The cross-sectional area of the specimen is

\[ \omega=\frac{\pi d^2}{4}=\frac{\pi}{4}\,5{,}993^2=28{,}194\ \mathrm{cm}^2. \]

Total length of the specimen \(L=34\) cm.

Length for measuring longitudinal compressions \(l=15\) cm.

Own weight of the bar \(G=6.76\) klgr.

The bar had already previously been subjected to compression up to a load of \(P=64100\) klgr. \((2273\ \mathrm{klgr./cm.^2})\).

Table No. 22.

Load in klgr., on the machine	Load in kg/cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, at 1 cm length in 1/100000 cm or ε·10⁵	Difference of longitudinal compressions	Transverse expansion, at 1 cm length in 1/100000 cm or q·10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for difference of longitudinal and transverse expansions	Poisson’s ratio: for full compression and expansion
500	17,75	—	—	—	—	16,6	—	—
5.000	175,0	16,93	16,93	3,75	3,75	16,6	0,222	0,222
10.000	350,0	37,20	20,27	8,84	5,09	16,7	0,251	0,238
15.000	524,9	57,47	20,27	14,11	5,27	16,7	0,260	0,245
20.000	699,7	77,80	20,33	19,44	5,33	16,8	0,263	0,250
25.000	874,6	98,07	20,27	24,86	5,42	16,8	0,267	0,254
30.000	1050	118,33	20,26	30,62	5,76	16,8	0,284	0,259
35.000	1224	138,67	20,34	36,46	5,84	16,8	0,287	0,263
40.000	1399	159,13	20,46	42,47	6,01	16,8	0,295	0,266

On repeating the experiment, the following was obtained:

Table No. 23.

Load in klgr., on the machine	Load in klgr., kg/cm², taking into account the machine error and the beam’s own weight	Longitudinal compression, divisions per 1 cm, or cm × 10⁵	Difference of longitudinal compressions	Transverse expansion, divisions per 1 cm, or cm × 10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio, for differences of longitudinal compression and transverse expansion	Poisson’s ratio, for total compression and expansion
500	17,75	—	—	—	—	16,9	—	—
5.000	175,0	16,77	16,77	3,00	3,00	16,9	0,179	0,179
10.000	350,0	36,64	19,87	8,01	5,01	16,9	0,252	0,219
15.000	524,9	56,57	19,93	13,02	5,01	16,9	0,251	0,230
20.000	699,7	76,50	19,93	18,19	5,17	16,9	0,259	0,238
25.000	874,6	96,37	19,87	23,61	5,42	16,9	0,273	0,245
30.000	1050	116,24	19,87	29,12	5,51	16,9	0,277	0,251
35.000	1224	136,04	19,80	34,54	5,42	16,9	0,274	0,254
40.000	1399	155,91	19,87	40,38	5,84	16,9	0,294	0,259
45.000	1574	176,44	20,53	46,39	6,01	16,9	0,293	0,263
50.000	1749	197,17	20,73	52,56	6,17	16,9	0,297	0,266

After the fourth loading:

Table No. 24.

Load in klgr., on the machine	Load in klgr., kg/cm², taking into account the machine error and the beam’s own weight	Longitudinal compression, divisions per 1 cm, or cm × 10⁵	Difference of longitudinal compressions	Transverse expansion, divisions per 1 cm, or cm × 10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio, for differences of longitudinal compression and transverse expansion	Poisson’s ratio, for total compression and expansion
500	17,75	—	—	—	—	16,6	—	—
5.000	175,0	16,73	16,73	3,88	3,88	—	0,232	0,232
10.000	350,0	36,53	19,80	8,56	4,68	16,7	0,236	0,234
15.000	524,9	56,47	19,94	13,56	5,00	16,7	0,251	0,240
20.000	699,7	76,33	19,86	18,73	5,17	16,7	0,260	0,245
25.000	874,6	96,20	19,87	23,99	5,26	16,8	0,265	0,249
30.000	1050	115,93	19,73	29,41	5,42	16,8	0,275	0,254
35.000	1224	135,73	19,80	34,92	5,51	17,0	0,279	0,257
40.000	1399	155,59	19,86	40,59	5,67	17,0	0,285	0,261
45.000	1574	175,46	19,87	46,35	5,76	17,0	0,290	0,265

After the 5th repetition of the experiment, the following was obtained:

Table No. 25.

Load in klgr. — On the machine	Load in klgr. — Kg./cm², taking into account the machine error and the bar’s own weight	Longitudinal compression per 1 cm length in $1/100000$ cm, or $e \cdot 10^5$	Difference of longitudinal compressions	Transverse extension per 1 cm length in $1/100000$ cm, or $q \cdot 10^5$	Difference of transverse extensions	Temperature C°	Poisson’s ratio — for the difference of longitudinal compressions and transverse extensions	Poisson’s ratio — for the total compression and extension
500	17,75	—	—	—	—	17,0	—	—
5.000	175,0	17,07	17,07	4,01	4,01	17,0	0,235	0,235
10.000	350,0	36,93	19,86	8,84	4,83	17,0	0,243	0,240
15.000	524,9	56,80	19,87	14,02	5,17	17,0	0,260	0,246
20.000	699,7	76,67	19,87	19,27	5,26	17,0	0,265	0,251
25.000	874,6	96,53	19,86	24,61	5,34	17,0	0,269	0,255
30.000	1050	116,26	19,73	30,04	5,43	17,0	0,276	0,258
35.000	1224	135,99	19,73	35,62	5,58	17,0	0,282	0,262
40.000	1399	155,79	19,80	41,30	5,67	17,0	0,286	0,265
45.000	1749	175,66	19,87	46,97	5,68	16,9	0,285	0,268

SPECIMEN No. 10.

The cross-sectional area of the specimen

$$ \omega = \frac{\pi d^2}{4} = \frac{\pi}{4}\,4{,}70^2 = 17{,}32\ \text{cm.}^2 $$

Total length of the specimen $L = 34$ cm.
Length for measuring longitudinal compressions $l = 15$ cm.
Own weight of the specimen $G = 4{,}26$ klgr.

Like this specimen, the following specimen No. 11 was not subjected to direct tension, but was made from a part of a beam stretched during its bending.

Table No. 26.

Load in klgr. — On the machine	Load in klgr. — Kg./cm², taking into account the machine error and the bar’s own weight	Longitudinal compression per 1 cm length in $1/100000$ cm, or $e \cdot 10^5$	Difference of longitudinal compressions	Transverse extension per 1 cm length in $1/100000$ cm, or $q \cdot 10^5$	Difference of transverse extensions	Temperature C°	Poisson’s ratio — for the difference of longitudinal compressions and transverse extensions	Poisson’s ratio — for the total compression and extension
500	28,62	—	—	—	—	19,7	—	—
3.000	171,0	15,93	15,93	2,84	2,84	—	0,178	0,178
6.000	341,8	35,87	19,94	7,66	4,82	—	0,241	0,214
9.000	512,6	56,20	20,33	12,77	5,11	19,1	0,252	0,227
12.000	683,5	76,60	20,40	17,88	5,11	19,7	0,251	0,234
15.000	854,3	97,00	20,40	23,12	5,24	20,0	0,257	0,239
18.000	1025	117,40	20,40	28,37	5,25	20,1	0,257	0,241
21.000	1196	137,87	20,47	34,19	5,82	20,0	0,285	0,248
24.000	1367	158,40	20,53	40,15	5,96	19,9	0,290	0,253
27.000	1538	179,33	20,93	46,39	6,24	19,8	0,299	0,259
30.000	1708	200,93	21,60	52,91	6,52	19,8	0,302	0,263

After a fourfold repetition of the experiment, the following was obtained:

Table No. 27.

Load in kg: on the machine	Load in kg/cm², taking into account the error of the machine and the beam’s own weight	Longitudinal compression, total at 1 cm length in \( \frac{1}{100000}\) cm	Difference of longitudinal compressions	Transverse expansion, total at 1 cm length in \( \frac{1}{100000}\) cm	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for differences of longitudinal compressions and transverse expansions	Poisson’s ratio: for full compression and expansion
500	28,62	—	—	—	—	20,0	—	—
3.000	171,00	15,47	15,47	3,40	3,40	20,0	0,219	0,219
6.000	341,8	35,27	19,80	7,94	4,54	—	0,229	0,225
9.000	512,6	55,14	19,87	13,05	5,11	19,9	0,257	0,236
12.000	683,5	75,07	19,93	18,44	5,39	19,8	0,270	0,245
15.000	854,3	94,94	19,87	23,83	5,39	19,8	0,271	0,251
18.000	1025	114,81	19,87	29,22	5,39	20,0	0,271	0,255
21.000	1196	134,74	19,93	34,75	5,53	20,2	0,278	0,258
24.000	1367	154,74	20,00	40,28	5,53	20,7	0,276	0,260
27.000	1538	174,67	19,93	45,81	5,56	20,6	0,278	0,262
30.000	1708	194,87	20,20	51,77	5,96	20,5	0,295	0,265

Finally, in measuring the transverse expansions in a direction perpendicular to the preceding one, the following was obtained:

Table No. 28.

Load in kg: on the machine	Load in kg/cm², taking into account the error of the machine and the beam’s own weight	Longitudinal compression, total at 1 cm length in \( \frac{1}{100000}\) cm	Difference of longitudinal compressions	Transverse expansion, total at 1 cm length in \( \frac{1}{100000}\) cm	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for differences of longitudinal compressions and transverse expansions	Poisson’s ratio: for full compression and expansion
500	28,62	—	—	—	—	18,0	—	—
3.000	171,0	15,67	15,67	3,55	3,55	—	0,226	0,226
6.000	341,8	35,34	19,67	8,51	4,96	18,0	0,252	0,241
9.000	512,6	55,34	20,00	13,62	5,11	18,0	0,256	0,246
12.000	683,5	75,34	20,00	18,73	5,11	18,0	0,256	0,248
15.000	854,3	95,34	20,00	24,12	5,39	18,0	0,269	0,254
18.000	1025	115,27	19,93	29,80	5,68	17,8	0,285	0,259
21.000	1196	135,27	20,00	35,48	5,68	17,7	0,284	0,262
24.000	1367	155,27	20,00	41,29	5,81	17,7	0,290	0,266
27.000	1538	175,27	20,00	47,10	5,81	17,7	0,290	0,269
30.000	1708	195,40	20,13	53,20	6,10	17,4	0,303	0,273

SPECIMEN No. 11

Cross-sectional area of the specimen \(\omega=\dfrac{\pi d^2}{4}=\dfrac{\pi}{4}4.69^2=17.28\ \mathrm{cm}^2\).

Total length of the specimen \(L=25\ \mathrm{cm}\).
Length for measuring longitudinal contractions \(l=10\ \mathrm{cm}\).
Own weight of the specimen \(G=3.04\ \mathrm{kg}\).

Table No. 29

Load intervals, kg: on the machine	kg/cm², taking into account the error of the machine and the own weight of the bar	Longitudinal contraction, per 1 cm length, in \(1/100000\) cm, or \(10^5\)	Difference of longitudinal contractions, at equal or full load intervals	Transverse expansion, per 1 cm length, in \(1/100000\) cm, or \(10^5\)	Difference of transverse expansions, at equal or full load intervals	Temperature C°	Poisson’s coefficient: for equal intervals	Poisson’s coefficient: for full intervals
500—3,000	28.67—171.4	15.8	—	2.78	—	16.5	—	0.176
..	..	15.1	—	2.66	—	—	—	—
..	..	15.1	—	2.56	—	—	—	—
..	..	15.1	—	2.56	—	—	0.170	0.170
500—6,000	28.67—342.7	34.5	—	7.04	—	16.5	—	0.204
..	..	33.7	—	6.82	—	—	—	—
..	..	33.9	—	6.82	—	—	—	—
..	..	33.7	—	6.82	—	—	—	—
..	..	33.7	18.6	6.82	4.26	16.6	0.229	0.203
500—9,000	28.67—514.0	53.6	—	12.08	—	—	—	0.225
..	..	52.9	—	12.13	—	—	—	—
..	..	52.8	—	11.83	—	—	—	—
..	..	52.8	19.1	11.83	5.01	—	0.262	0.225
500—12,000	28.67—685.2	73.0	—	17.19	—	16.6	—	0.235
..	..	72.2	—	17.09	—	—	—	—
..	..	71.9	—	17.05	—	—	—	—
..	..	71.8	—	16.95	—	—	—	—
..	..	71.8	19.0	16.95	5.12	—	0.270	0.236
500—15,000	28.67—856.5	91.5	—	22.29	—	16.6	—	0.244
..	..	91.1	—	22.17	—	—	—	—
..	..	90.8	—	22.17	—	—	—	—
..	..	90.8	—	22.07	—	—	—	—
..	..	90.8	19.0	22.07	5.12	—	0.270	0.244
500—18,000	28.67—1028	110.5	—	27.82	—	16.6	—	0.251
..	..	109.9	—	27.72	—	—	—	—
..	..	109.8	—	27.51	—	—	—	—
..	..	109.8	—	27.40	—	—	—	—
..	..	109.8	19.0	27.40	5.33	—	0.281	0.249
500—21,000	28.67—1199	129.5	—	32.26	—	16.7	—	0.249
..	..	128.9	—	33.05	—	—	—	—
..	..	128.6	—	32.94	—	—	—	—
..	..	128.7	—	32.84	—	—	—	—
..	..	128.7	18.9	32.84	5.44	16.7	0.288	0.255

Load intervals in klgr. — on the machine	Kg./cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, increment per 1 cm length in 1/100000 cm, or q·10⁵	Difference of adjacent longitudinal compressions	Transverse expansion, increment per 1 cm length in 1/100000 cm, or q·10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for differences of intervals	Poisson’s ratio: for full intervals
500—24.000	28,67—1370	148,4	—	38,71	—	—	—	0,260
„	„	147,9	—	38,59	—	—	—	—
„	„	147,8	—	38,59	—	—	—	—
„	„	147,7	—	38,38	—	—	—	—
„	„	147,8	—	38,38	—	—	—	—
„	„	147,7	—	38,38	—	—	—	—
„	„	147,7	19,0	38,38	5,54	16,8	0,291	0,260
500—27.000	28,67—1542	167,7	—	44,37	—	—	—	0,265
„	„	167,1	—	44,26	—	—	—	—
„	„	167,0	—	44,20	—	—	—	—
„	„	166,9	—	44,16	—	—	—	—
„	„	166,9	—	44,14	—	—	—	—
„	„	166,9	19,2	44,14	5,76	16,8	0,300	0,265
500—30.000	28,67—1713	187,9	—	50,44	—	—	—	0,269
„	„	186,9	—	50,44	—	—	—	—
„	„	186,5	—	50,33	—	—	—	—
„	„	186,4	—	50,22	—	—	—	—
„	„	186,3	—	50,11	—	—	—	—
„	„	186,2	—	50,11	—	—	—	—
„	„	186,2	19,3	50,11	5,97	16,8	0,309	0,269

SPECIMEN No. 12.

Area of the transverse section of the specimen \(\omega = 5{,}01 \cdot 2{,}42 = 12{,}14\) cm.

Full length of the specimen \(L = 34\) cm.

Length for measuring longitudinal compressions \(l = 15\) cm.

Own weight of the specimen \(G = 2{,}87\) klgr.

The specimen had previously been subjected to tension up to a load of 13940 klgr.
\((1149\ \mathrm{klgr}/\mathrm{cm}^2.)\)

Table No. 30.

Load in klgr. — on the machine	Kg./cm², taking into account the error of the machine and the bar’s own weight	Longitudinal compression, increment per 1 cm length in 1/100000 cm, or q·10⁵	Difference of longitudinal compressions	Transverse expansion, increment per 1 cm length in 1/100000 cm, or q·10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for differences of longitudinal compression and transverse expansion	Poisson’s ratio: for full longitudinal compression and transverse expansion
500	40,78	—		—	—	14,6	—	—
2.000	162,7	15,60	15,60	2,99	2,99	—	0,192	0,192
4.000	325,2	37,87	22,27	7,18	4,19	14,6	0,188	0,189
6.000	487,8	63,14	25,27	11,87	4,69	14,6	0,186	0,188
8.000	650,3	93,54	30,40	17,35	5,48	—	0,180	0,186
10.000	812,8	124,67	31,13	23,13	5,78	14,5	0,185	0,186
12.000	975,4	155,27	30,60	29,31	6,18	14,3	0,202	0,189
14.000	1138	185,34	30,07	36,39	7,08	14,2	0,235	0,196
16.000	1300	215,87	30,53	43,97	7,58	14,2	0,248	0,204

On repeating the experiment, the following was obtained:

Table No. 31.

Load in klgr. on the machine	Kg./cm², taking into account the error of the machine and the beam’s own weight	Longitudinal strain per 1 cm length, in \(1/100000\) cm, or \(\varepsilon \cdot 10^5\)	Difference of longitudinal strains	Transverse strain per 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Difference of transverse strains	Temperature C°	Poisson’s ratio for the difference of longitudinal and transverse strains	Poisson’s ratio for the complete static strain
500	40,78	—	—	—	—	16,5	—	—
2.000	162,7	13,93	13,93	2,79	2,79	—	0,200	0,200
4.000	325,2	33,20	19,27	6,67	3,88	16,8	0,201	0,201
6.000	487,8	52,67	19,47	11,06	4,39	16,8	0,225	0,210
8.000	650,3	71,60	18,93	15,64	4,58	16,2	0,242	0,219
10.000	812,8	90,40	18,80	20,22	4,58	15,8	0,244	0,223
12.000	975,4	109,33	18,93	25,00	4,78	15,6	0,253	0,229
14.000	1138	128,40	19,07	29,88	4,88	15,5	0,256	0,232
16.000	1300	148,67	20,27	34,96	5,08	15,3	0,251	0,235
18.000	1462	176,87	28,20	42,54	7,58	15,3	0,269	0,240

On repeating the experiment for the 5th time, the following was obtained:

Table No. 32.

Load in klgr. on the machine	Kg./cm², taking into account the error of the machine and the beam’s own weight	Longitudinal strain per 1 cm length, in \(1/100000\) cm, or \(\varepsilon \cdot 10^5\)	Difference of longitudinal strains	Transverse strain per 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Difference of transverse strains	Temperature C°	Poisson’s ratio for the difference of longitudinal and transverse strains	Poisson’s ratio for the complete static strain
500	40,78	—	—	—	—	17,7	—	—
2.000	162,7	13,60	13,60	2,99	2,99	—	0,220	0,220
4.000	325,2	32,40	18,80	7,48	4,49	17,0	0,239	0,231
6.000	487,8	51,27	18,87	12,17	4,69	16,8	0,249	0,236
8.000	650,3	69,97	18,70	16,75	4,58	16,5	0,245	0,240
10.000	812,8	88,54	18,57	21,33	4,58	16,5	0,247	0,241
12.000	975,4	106,87	18,33	25,91	4,58	16,5	0,250	0,243
14.000	1138	125,10	18,33	30,50	4,59	16,4	0,251	0,245
16.000	1300	143,50	18,40	35,09	4,59	16,4	0,250	0,245
18.000	1462	162,63	19,13	39,97	4,88	16,3	0,255	0,246

The experiment, carried out for the sixth time, gave the following results:

Table No. 33.

Load, kg: on the machine	Load, kg/cm², taking into account the error of the machine and the beam’s own weight	Longitudinal compression per 1 cm of length, in 1/100000 cm, or \(a \cdot 10^5\)	Difference of longitudinal compressions	Transverse expansion per 1 cm of length, in 1/100000 cm, or \(q \cdot 10^5\)	Difference of transverse expansions	Temperature, °C	Poisson’s ratio: for equal longitudinal compression and transverse expansion	Poisson’s ratio: for total compression and expansion
500	40.78	—	—	—	—	16.1	—	—
2,000	162.7	13.67	13.67	2.79	2.79	16.0	0.204	0.204
4,000	325.2	32.54	18.87	7.18	4.39	16.0	0.232	0.220
6,000	487.8	51.41	18.87	11.57	4.39	16.0	0.232	0.225
8,000	650.3	70.28	18.87	15.96	4.39	16.0	0.232	0.227
10,000	812.8	88.95	18.67	20.54	4.58	16.0	0.245	0.230
12,000	975.4	107.28	18.33	25.13	4.59	16.0	0.250	0.235
14,000	1138	125.41	18.13	29.72	4.59	16.0	0.254	0.237
16,000	1300	143.94	18.53	34.31	4.59	15.9	0.248	0.239
18,000	1462	162.81	18.87	39.09	4.78	16.0	0.253	0.240

Then the instrument was moved to the broad faces of the specimen; consequently, the dimension serving for the measurement of the transverse expansions was equal to 2.42 cm; in the experiment with this arrangement of the instrument, the following was obtained:

Table No. 34.

Load, kg: on the machine	Load, kg/cm², taking into account the error of the machine and the beam’s own weight	Longitudinal compression per 1 cm of length, in 1/100000 cm, or \(a \cdot 10^5\)	Difference of longitudinal compressions	Transverse expansion per 1 cm of length, in 1/100000 cm, or \(q \cdot 10^5\)	Difference of transverse expansions	Temperature, °C	Poisson’s ratio: for equal longitudinal compression and transverse expansion	Poisson’s ratio: for total compression and expansion
500	40.78	—	—	—	—	16.0	—	—
2,000	162.7	14.20	14.20	2.89	2.89	16.0	0.204	0.204
4,000	325.2	33.27	19.07	7.02	4.13	16.1	0.216	0.211
6,000	487.8	52.47	19.20	11.57	4.55	16.1	0.237	0.220
8,000	650.3	71.40	18.93	16.11	4.54	16.2	0.240	0.226
10,000	812.8	90.20	18.80	20.86	4.75	16.2	0.253	0.231
12,000	975.4	108.67	18.47	25.61	4.75	16.2	0.257	0.235
14,000	1138	127.14	18.47	30.36	4.75	16.2	0.257	0.239
16,000	1300	145.54	18.40	35.11	4.75	16.1	0.258	0.241
18,000	1462	164.81	19.27	40.07	4.96	16.1	0.257	0.243

The experiment with this arrangement of the apparatus was repeated once more, and the following was obtained:

Table No. 35.

Load, in klgr. — on the machine	Load, in klgr. — kg/cm², taking into account the machine error and the beam’s own weight	Longitudinal contraction, observed at 1 cm length in $1/100000$ cm, or $\varepsilon \cdot 10^5$	Difference of longitudinal contractions	Transverse expansion, observed at 1 cm length in $1/100000$ cm, or $q \cdot 10^5$	Difference of transverse expansions	Temperature C°	Poisson’s ratio — for the difference of longitudinal contractions and transverse expansions	Poisson’s ratio — for the complete contraction and expansion
500	40.78	—	—	—	—	15.9	—	—
2,000	162.7	13.87	13.87	2.89	2.89	—	0.208	0.208
4,000	325.2	32.54	18.67	7.02	4.13	15.8	0.221	0.216
6,000	487.8	51.61	19.07	11.36	4.34	15.7	0.227	0.220
8,000	650.3	70.41	18.80	15.91	4.55	15.7	0.242	0.226
10,000	812.8	88.74	18.33	20.87	4.96	15.3	0.271	0.235
12,000	975.4	107.07	18.33	25.83	4.96	15.3	0.271	0.241
14,000	1138	125.34	28.27	30.79	4.96	15.3	0.272	0.246
16,000	1300	143.61	18.27	35.75	4.96	15.3	0.272	0.250

Finally, in measuring the transverse expansions along the direction of the diagonal of the section, the following was obtained:

Table No. 36.

Load, in klgr. — on the machine	Load, in klgr. — kg/cm², taking into account the machine error and the beam’s own weight	Longitudinal contraction, observed at 1 cm length in $1/100000$ cm, or $\varepsilon \cdot 10^5$	Difference of longitudinal contractions	Transverse expansion, observed at 1 cm length in $1/100000$ cm, or $q \cdot 10^5$	Difference of transverse expansions	Temperature C°	Poisson’s ratio — for the difference of longitudinal contractions and transverse expansions	Poisson’s ratio — for the complete contraction and expansion
500	40.78	—	—	—	—	14.8	—	—
2,000	162.7	14.27	14.27	2.78	2.78	14.8	0.195	0.195
4,000	325.2	33.20	18.93	7.02	4.24	14.8	0.224	0.212
6,000	487.8	52.53	19.33	11.26	4.24	14.8	0.220	0.215
8,000	650.3	71.40	18.87	15.59	4.33	14.8	0.230	0.218
10,000	812.8	90.17	18.77	20.19	4.60	14.8	0.245	0.224
12,000	975.4	108.80	18.63	24.88	4.69	14.8	0.252	0.229
14,000	1138	127.13	18.33	29.57	4.69	14.8	0.256	0.233
16,000	1300	145.46	18.33	34.35	4.78	14.8	0.261	0.236

The experiment was repeated once more, and this time the following was obtained:

Table No. 37.

Load in kg	Load in kg/cm², taking into account the error of the machine and the beam’s own weight	Longitudinal compression, in 1 cm of length, in hundred-thousandths of a cm, or a·10⁵	Difference of longitudinal compressions	Transverse expansion, in 1 cm of length, in hundred-thousandths of a cm, or q·10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for equal longitudinal compressions and transverse expansions	Poisson’s ratio: for longitudinal compression and transverse expansion
500	40,78	—	—	—	—	14,5	—	—
2.000	162,7	14,00	14,00	2,78	2,78	14,6	0,198	0,198
4.000	325,2	32,93	18,93	6,84	4,06	—	0,215	0,208
6.000	487,8	51,86	18,93	10,99	4,15	14,6	0,220	0,213
8.000	650,3	70,73	18,87	15,41	4,42	14,6	0,234	0,218
10.000	812,8	89,53	18,80	19,92	4,51	14,6	0,240	0,223
12.000	975,4	107,93	18,40	24,52	4,60	14,6	0,250	0,227
14.000	1138	126,33	18,40	29,03	4,51	14,6	0,245	0,230
16.000	1300	144,80	18,47	33,72	4,69	14,6	0,254	0,228
18.000	1462	164,07	19,27	38,59	4,87	14,8	0,253	0,235

SPECIMEN No. 13.

Cross-sectional area of the specimen $\omega = 5{,}01 \times 2{,}42 = 12{,}124\ \text{cm}^2$.

Total length of the specimen $L = 34\ \text{cm}$.

Length for measuring longitudinal compressions $l = 15\ \text{cm}$.

Own weight of the specimen $G = 2{,}88\ \text{kg}$.

The specimen had previously been subjected to tension up to a load of 14.770 kg (1.218 kg/cm²). For measuring transverse expansions, first take the dimension 5,01 cm.

Table No. 38.

Load in kg	Load in kg/cm², taking into account the error of the machine and the beam’s own weight	Longitudinal compression, in 1 cm of length, in hundred-thousandths of a cm, or a·10⁵	Difference of longitudinal compressions	Transverse expansion, in 1 cm of length, in hundred-thousandths of a cm, or q·10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for equal longitudinal compressions and transverse expansions	Poisson’s ratio: for longitudinal compression and transverse expansion
500	40,83	—	—	—	—	17,0	—	—
2.000	162,9	15,07	15,07	2,99	2,99	16,8	0,198	0,198
4.000	325,7	36,27	21,20	7,18	4,19	16,8	0,198	0,198
6.000	488,4	58,73	22,46	11,47	4,29	16,8	0,191	0,196
8.000	651,0	84,60	25,87	16,27	4,80	16,8	0,186	0,193
10.000	813,7	114,00	29,40	22,55	6,28	16,8	0,214	0,198
12.000	976,4	144,53	30,53	29,14	6,59	16,8	0,216	0,202
14.000	1139	173,83	29,30	35,93	6,79	16,8	0,231	0,207
16.000	1302	202,76	28,93	42,92	6,99	16,8	0,242	0,212

When the experiment was repeated, the following was obtained:

Table No. 39.

Load in kgf: on the machine	Load in kg/cm², taking into account the error of the machine and the specimen’s own weight	Longitudinal compression, taken on 1 cm of length, in 1/100000 cm, or q.10⁵	Difference of longitudinal compressions	Transverse expansion, taken on 1 cm of length, in 1/100000 cm, or q.10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for the difference of longitudinal and transverse compressions	Poisson’s ratio: for the total compression and expansion
500	40.83	—	—	—	—	—	—	—
2,000	162.9	13.27	13.27	2.59	2.59	16.3	0.195	0.195
4,000	325.7	32.14	18.87	6.38	3.79	16.3	0.201	0.198
6,000	488.4	51.21	19.07	10.77	4.39	16.2	0.230	0.210
8,000	651.0	69.94	18.73	14.96	4.19	16.2	0.224	0.214
10,000	813.7	88.61	18.67	19.25	4.29	16.1	0.230	0.217
12,000	976.4	107.28	18.67	23.64	4.39	16.1	0.235	0.220
14,000	1139	125.75	18.47	28.03	4.39	16.0	0.238	0.223
16,000	1302	146.08	20.33	32.82	4.79	16.0	0.236	0.225

In measuring the transverse expansions in a direction (dimension 2.42 cm) perpendicular to the preceding one, we obtained:

Table No. 40.

Load in kgf: on the machine	Load in kg/cm², taking into account the error of the machine and the specimen’s own weight	Longitudinal compression, taken on 1 cm of length, in 1/100000 cm, or q.10⁵	Difference of longitudinal compressions	Transverse expansion, taken on 1 cm of length, in 1/100000 cm, or q.10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for the difference of longitudinal and transverse compressions	Poisson’s ratio: for the total compression and expansion
500	40.83	—	—	—	—	15.8	—	—
2,000	162.9	13.53	13.53	2.69	2.69	15.8	0.199	0.199
4,000	325.7	32.33	18.80	7.03	4.34	15.8	0.231	0.218
6,000	488.4	51.00	18.67	11.57	4.54	15.8	0.243	0.226
8,000	651.0	69.47	18.47	15.91	4.34	15.8	0.235	0.229
10,000	813.7	87.80	18.33	20.25	4.34	15.8	0.237	0.231
12,000	976.4	106.07	18.27	24.59	4.34	15.8	0.238	0.232
14,000	1139	124.14	18.07	28.93	4.34	15.8	0.240	0.233
16,000	1302	142.74	18.60	33.87	4.96	15.8	0.267	0.237

When measuring the transverse expansions along the diagonal of the section, the following was obtained:

Table No. 41.

Load in klgr. — on the machine	Load in klgr. — kg/cm², taking into account the error of the machine and the specimen’s own weight	Longitudinal compression, per 1 cm of length, in 1/100000 cm, or ε·10⁵	Difference of longitudinal compressions	Transverse expansion, per 1 cm of length, in 1/100000 cm, or q·10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio — for difference of longitudinal compressions and transverse expansions	Poisson’s ratio — for complete compression and expansion
500	40,83	—	—	—	—	16,0	—	—
2.000	162,9	13,80	13,80	3,08	3,08	16,0	0,223	0,223
4.000	325,7	32,90	19,10	7,34	4,26	15,0	0,223	0,223
6.000	488,4	51,83	18,93	11,60	4,26	16,0	0,225	0,224
8.000	651,0	70,56	18,73	16,03	4,43	16,0	0,236	0,227
10.000	813,7	89,09	18,53	20,56	4,53	16,0	0,245	0,231
12.000	976,4	107,42	18,33	25,07	4,53	16,0	0,247	0,234
14.000	1139	125,62	18,20	29,50	4,43	15,9	0,244	0,235
16.000	1302	143,82	18,20	34,03	4,53	15,9	0,249	0,236

SPECIMEN No. 14.

Area of the transverse section of the specimen, \( \omega = 5,02 \cdot 2,43 = 12,17\ \mathrm{cm.^2} \).

Total length of the specimen \( L = 25\ \mathrm{cm.} \)

Length for measuring longitudinal compressions \( l = 10\ \mathrm{cm.} \)

Own weight of the specimen \( G = 2,11\ \mathrm{klgr.} \)

The specimen had previously been subjected to tension up to a load of \( 13.430\ \mathrm{klgr.} \)
\((1103\ \mathrm{klgr.}/\mathrm{cm.^2})\).

For measuring the transverse expansions, the dimension \(5,02\ \mathrm{cm.}\) was first taken.

Table No. 42.

Load in klgr. — on the machine	Load in klgr. — kg/cm², taking into account the error of the machine and the specimen’s own weight	Longitudinal compression, per 1 cm of length, in 1/100000 cm, or ε·10⁵	Difference of longitudinal compressions	Transverse expansion, per 1 cm of length, in 1/100000 cm, or q·10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio — for difference of longitudinal compressions and transverse expansions	Poisson’s ratio — for complete compression and expansion
500	40,65	—	—	—	—	14,8	—	—
2.000	162,2	19,30	19,30	2,79	2,79	—	0,145	0,145
4.000	324,2	51,80	32,50	7,17	4,38	14,8	0,135	0,138
6.000	486,3	96,40	44,60	12,85	5,68	14,7	0,127	0,134
8.000	648,3	145,10	48,70	19,03	6,18	14,7	0,127	0,131
10.000	810,3	193,00	47,90	26,50	7,47	14,7	0,156	0,137
12.000	972,4	235,40	42,40	34,37	7,87	14,7	0,186	0,146
14.000	1134	274,10	38,70	42,34	7,97	14,6	0,206	0,154
16.000	1296	320,40	46,30	50,91	8,57	14,5	0,185	0,158

When the experiment was repeated, the following was obtained:

Table No. 43.

Load in klgr. — on the machine	Load in klgr. — Kg./cm², taking into account the machine error and the bar’s own weight	Longitudinal deformation, increment per 1 cm length in \( \frac{1}{100000} \) cm, or \(e \cdot 10^5\)	Difference of longitudinal deformations	Transverse deformation, increment per 1 cm length in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Difference of transverse deformations	Temperature C°.	Poisson’s ratio — for difference of longitudinal and transverse deformations	Poisson’s ratio — for complete longitudinal and transverse deformation
500	40,65	—	—	—	—	16,6	—	—
2.000	162,2	16,3	16,3	2,69	2,69	16,5	0,165	0,165
4.000	324,2	39,1	22,8	7,07	4,38	16,4	0,192	0,181
6.000	486,3	61,4	22,3	11,75	4,68	16,2	0,210	0,192
8.000	648,3	83,1	21,7	16,73	4,98	16,0	0,230	0,201
10.000	810,3	104,6	21,5	21,71	4,98	15,8	0,232	0,207
12.000	972,4	125,9	21,3	26,89	5,18	15,8	0,243	0,214
14.000	1134	147,2	21,3	31,87	4,98	15,6	0,234	0,216
16.000	1296	171,0	23,8	37,45	5,58	15,6	0,235	0,219

In the fourth trial the result proved to be as follows:

Table No. 44.

Load in klgr. — on the machine	Load in klgr. — Kg./cm², taking into account the machine error and the bar’s own weight	Longitudinal deformation, increment per 1 cm length in \( \frac{1}{100000} \) cm, or \(e \cdot 10^5\)	Difference of longitudinal deformations	Transverse deformation, increment per 1 cm length in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Difference of transverse deformations	Temperature C°.	Poisson’s ratio — for difference of longitudinal and transverse deformations	Poisson’s ratio — for complete longitudinal and transverse deformation
500	40,65	—	—	—	—	15,1	—	—
2.000	162,2	16,4	16,4	2,69	2,69	15,2	0,164	0,164
4.000	324,2	39,1	22,7	7,07	4,38	15,2	0,193	0,181
6.000	486,3	61,2	22,1	11,55	4,48	15,2	0,203	0,189
8.000	648,3	82,7	21,5	16,13	4,58	15,2	0,213	0,195
10.000	810,3	103,9	21,2	20,81	4,68	15,2	0,221	0,200
12.000	972,4	124,6	20,7	25,69	4,88	15,2	0,236	0,206
14.000	1134	145,2	20,6	30,57	4,88	15,2	0,237	0,211
16.000	1296	166,7	21,5	35,65	5,08	15,3	0,236	0,214

Then, for measuring the transverse expansions, a direction (dimension 2.43 cm) perpendicular to the preceding one was adopted, and the following was obtained:

Table No. 45.

Load in kg: on the machine	Load in kg: kg/cm², taking into account the error of the machine and the specimen’s own weight	Longitudinal compression, dial divisions per 1 cm, or cm · 10⁵	Difference of longitudinal compressions	Transverse expansion, dial divisions per 1 cm, or cm · 10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for difference of longitudinal compressions and transverse expansions	Poisson’s ratio: for total compressions and expansions
500	40.65	—	—	—	—	15.2	—	—
2,000	162.2	17.4	17.4	2.89	2.89	15.2	0.166	0.166
4,000	324.2	40.9	23.5	7.22	4.33	15.2	0.185	0.177
6,000	486.3	63.8	22.9	11.76	4.54	15.2	0.198	0.184
8,000	648.3	85.9	22.1	16.71	4.95	15.2	0.224	0.194
10,000	810.3	107.4	21.5	21.86	5.15	15.2	0.240	0.203
12,000	972.4	128.7	21.3	27.01	5.15	15.2	0.242	0.210
14,000	1134	149.9	21.2	32.16	5.15	15.2	0.243	0.215
16,000	1296	172.5	22.6	37.52	5.36	15.1	0.238	0.217

And on repetition:

Table No. 46.

Load in kg: on the machine	Load in kg: kg/cm², taking into account the error of the machine and the specimen’s own weight	Longitudinal compression, dial divisions per 1 cm, or cm · 10⁵	Difference of longitudinal compressions	Transverse expansion, dial divisions per 1 cm, or cm · 10⁵	Difference of transverse expansions	Temperature C°	Poisson’s ratio: for difference of longitudinal compressions and transverse expansions	Poisson’s ratio: for total compressions and expansions
500	40.65	—	—	—	—	15.4	—	—
2,000	162.2	16.6	16.6	2.89	2.89	15.4	0.174	0.174
4,000	324.2	39.5	22.9	7.22	4.33	15.4	0.190	0.183
6,000	486.3	61.6	22.1	11.76	4.54	15.4	0.205	0.191
8,000	648.3	83.1	21.5	16.71	4.95	15.3	0.230	0.201
10,000	810.3	104.3	21.2	21.75	4.74	15.3	0.224	0.205
12,000	972.4	125.1	20.8	26.40	4.95	15.3	0.238	0.211
14,000	1134	145.8	20.7	31.76	5.36	15.3	0.259	0.218
16,000	1296	166.9	21.1	37.12	5.36	15.3	0.254	0.222

In measuring the transverse expansions along the diagonal of the section, the following was obtained:

Table No. 47.

Load in klgr. on the machine	Kg./cm², taking into account the error of the machine and the specimen’s own weight	Longitudinal compression, per 1 cm of length, \(\frac{1}{100000}\) cm, or \(e \cdot 10^5\)	Difference of longitudinal compressions	Transverse expansion, per 1 cm of length, \(\frac{1}{100000}\) cm, or \(q \cdot 10^5\)	Difference of transverse expansions	Temperature C°.	Poisson’s ratio for the differences of longitudinal compression and transverse expansion	Poisson’s ratio for total compression and expansion
500	40,65	—	—	—	—	—	—	—
2 000	162,2	16,8	16,8	2,71	2,71	18,2	0,161	0,161
4 000	324,2	39,4	22,6	6,51	3,80	18,3	0,168	0,165
6 000	486,3	61,9	22,5	10,67	4,16	18,3	0,185	0,173
8 000	648,3	83,5	21,6	15,10	4,43	18,3	0,205	0,181
10 000	810,3	104,4	20,9	19,71	4,61	18,3	0,221	0,188
12 000	972,4	125,0	20,6	24,41	4,70	18,4	0,228	0,195
14 000	1134	145,5	20,5	29,20	4,79	18,5	0,234	0,201
16 000	1296	166,8	21,3	34,08	4,88	18,5	0,230	0,204

Such are the results obtained from compression tests of bars of various shapes. We have given the values of Poisson’s ratio both for various magnitudes of loads and for their differences. Even a single glance at the data presented in the tables is sufficient to see that Poisson’s ratio, for different magnitudes of load in one and the same experiment, is a quantity that is not constant; it increases with increasing load; but the same data of the tables show that the differences in the increase of Poisson’s ratio with increasing load diminish, and thus the magnitude of this ratio tends, as it were, toward a certain limit. Literally the same may be said of the variation of this ratio also in the case when the entire experiment is repeated or when only the loading in a given interval is repeated; with every such repetition there occurs an increase of the ratio up to a certain limit. But in this case this limit, and the initial values of the ratio (at small stresses), are not the same for different states of the cast iron: they depend on whether the bar had previously, before compression, been stretched, compressed, or had not been subjected in advance to any deformations; in order to present more clearly this dependence of the coefficient on the load on the specimen and on the state of the material, the giv-

the above tables are represented graphically (Drawings 3, 4). In this graphical representation, the stresses of the specimens are laid off along the axis of abscissas, and along the axis of ordinates the values of Poisson’s ratio corresponding to these stresses; the scale adopted for the stresses is: \(1\ \mathrm{m}/\mathrm{m} \sim 5\ \mathrm{kg}/\mathrm{cm}^{2}\), and for the coefficient \(1\ \mathrm{m}/\mathrm{m} \sim 0.002\).

In the appended drawing (Drawings 3, 4) the curves of Poisson’s ratio obtained in this way are also given; only the curves for specimens No. 10 and No. 11 are not plotted on it, since these specimens, in earlier tests, had already been strongly compressed after tension (after they had been cut from the beams), and therefore the data for these specimens do not correspond to the initial state of the material.

It is sufficient now to glance at the plotted curves to see that the curves of Poisson’s ratio obtained from specimens that had not previously been subjected to any deformations occupy a middle position between the curves from specimens previously compressed or stretched; moreover, the curves of the coefficient obtained from specimens previously compressed lie higher, the values of the coefficient, consequently, being greater, while the curves of the coefficient obtained from specimens previously stretched lie lower, the values of the coefficient, consequently, being smaller than for specimens that had not previously been subjected to any deformations. If one calculates the mean values of the coefficient for these three kinds of specimens, it appears that for the three most characteristic loads the following values of the coefficient are obtained:

Table No. 48.

Load per sq. cm.	Coefficient for specimens previously subjected to compression.	Coefficient for specimens not previously subjected to any deformations.	Coefficient for specimens previously subjected to tension.
175	0.227 (0.220)	0.193 (0.198)	0.188 (0.178)
650	0.247 (0.241)	0.220 (0.219)	0.208 (0.170)
1300	0.265 (0.258)	—	0.223 (0.191)

Here the figures not in parentheses correspond to the mean values of the coefficient obtained after repeated repetitions of the experiment (the specimens’ “settled state”).

The figures in parentheses correspond to the initial tests (the “unsettled state”).

The same diagrams show that, for bars previously subjected to tension, Poisson’s ratio at first decreases up to a load somewhat greater than half the preliminary tensile force, and then begins to increase and, at a load somewhat less than the tensile force, becomes equal to the value it had at the initial loads, and thereafter continues to increase. But even the very first repetition of the experiment changes the picture completely, and Poisson’s ratio, as for the other specimens, increases steadily with increasing load.

The limit toward which Poisson’s ratio tends with increasing load and with repeated loading may be taken as equal to 0.3; at least, the values of the coefficient obtained by us for specimens that had previously been strongly compressed are very close to this value. For specimens that had previously been stretched, and for those that had not been subjected to any deformations, this limit, according to our experiments, is below 0.3 and above 0.21.

As regards the question whether the direction in which the transverse expansions are measured, for a given form of specimen, influences the magnitude of Poisson’s ratio, our experiments did not show any sharp difference in the magnitude of the transverse expansions for different directions of the section: if there is some difference, it is so insignificant that it does not exceed the limits of the observational errors possible in the experiments. Thus, it seems to us, in summary of what has been said, that we may establish the following propositions:

1) Poisson’s ratio for cast iron under compression is a variable quantity, depending on the magnitude of the load and on the number of repetitions of the load.

2) Poisson’s ratio under compression increases with increasing load and with the number of repetitions of the load, approaching a certain limit close to 0.3.

3) In general, Poisson’s ratio is larger for bars previously subjected to compression and smaller for bars previously subjected to tension than for bars not previously subjected to any deformations.

4) The direction in which the transverse expansions are measured, for a given section, has no noticeable influence on the magnitude of the coefficient.

I now turn to the experiments on the investigation of Poisson’s ratio under tension of cast-iron bars, and also to the investigation of the variation of this ratio with variable loading.

For these experiments, as I have already said above, I had at my disposal 4 specimens, Nos. 15, 16, 17, 18, shown in drawing 2.

With two of these bars, Nos. 16 and 17, tensile experiments were begun, and with the other two, Nos. 15 and 18, compression experiments.

In both cases the experiments were conducted with repeated loading within a certain interval until the bar had been fully brought into the “established state.”

In view of the fact that it was desirable to preserve the bars for several experiments, the load was brought approximately only to 650 klg/cm². After the first series of experiments the bars changed their roles, and experiments in tension were conducted with bars Nos. 15 and 18, and experiments in compression with bars Nos. 16 and 17; after the second series of experiments, again bars Nos. 16 and 17 were stretched, and bars Nos. 15 and 18 were compressed, etc.; in all, with bars Nos. 16 and 17 there were carried out 4 tensile experiments and 3 compression experiments, and with bars Nos. 15 and 18, 3 compression experiments and 2 tensile experiments.

The experiments were carried out on the same machines and with the same precautions as those described above; likewise, the corrections in the readings of loads and deformations were made in the same way, except that, because these experiments were performed six months after the compression experiments, and during that time Werder’s machine had been carefully checked and set up, the error it gave proved to be extremely small (less than 1%), for which reason it was not considered necessary to introduce a correction when computing the load per cm² of cross-section of the specimens in the tensile experiments; Pohlmeyer’s machine gave its former error of 1.37%. A graphical representation of the data of the tables is given only for the “established state” of the specimens, when the experimental data are the most reliable; for this reason, the calculations of Poisson’s ratio have been made only for this state.

The results of these experiments are given in the following tables.

TENSION TESTS.

SPECIMEN No. 17.

Cross-sectional area of the specimen \(\omega = 2.396 \times 4.96 = 11.88\ \mathrm{cm.^2}\).

Length for measuring longitudinal extensions and contractions \(P = 15\ \mathrm{cm}\).

Dimension for measuring transverse contractions and extensions taken as \(a = 4.96\ \mathrm{cm}\).

Table No. 49.

Load intervals in kg: on the machine	Load intervals in kg/cm², taking the machine error into account	Longitudinal extension readings on 1 cm length, in \(1/1000\) cm, or \(e \cdot 10^5\)	Difference of longitudinal extensions during the considered loading interval	Transverse compression readings on 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Difference of transverse compressions during the considered loading interval	Poisson’s coefficient: for different intervals	Poisson’s coefficient: for half-intervals
500—2.000	42,09—168,4	12,27	—	2,92	—	—	—
„	„	11,47	—	2,02	—	—	—
„	„	11,47	—	1,92	—	—	—
„	„	11,47	11,47	1,92	1,92	0,168	0,168
500—4.000	42,09—336,7	29,53	—	6,95	—	—	—
„	„	27,60	—	4,84	—	—	—
„	„	27,47	—	4,64	—	—	—
„	„	27,40	—	4,64	—	—	—
„	„	27,40	15,93	4,64	2,72	0,171	0,169
500—6.000	42,09—505,1	48,13	—	9,58	—	—	—
„	„	46,13	—	8,06	—	—	—
„	„	46,00	—	7,56	—	—	—
„	„	45,87	—	7,46	—	—	—
„	„	45,87	—	7,36	—	—	—
„	„	45,87	18,47	7,36	2,72	0,147	0,161
500—8.000	42,09—673,4	72,93	—	12,20	—	—	—
„	„	67,67	—	10,60	—	—	—
„	„	67,27	—	10,28	—	—	—
„	„	67,27	—	10,08	—	—	—
„	„	67,20	—	10,08	—	—	—
„	„	67,20	—	10,08	—	—	—
„	„	67,20	21,33	10,08	2,72	0,128	0,150

SPECIMEN No. 16

Cross-sectional area of the specimen \(\omega = 2,40 \times 4,97 = 11,92\ \mathrm{cm.^2}\).

Length for measuring longitudinal extensions and compressions \(l = 15\ \mathrm{cm.}\)

Dimension for measuring transverse compressions and expansions \(a = 4,97\).

Table No. 50.

Load intervals in kg, on the machine	kg/cm², taking into account the error of the machine	Longitudinal extension, per 1 cm length, in \(1/1000\) cm, or \(e \cdot 10^5\)	Difference of longitudinal extensions over the load interval	Transverse compression, per 1 cm width, in \(1/100000\) cm, or \(\alpha \cdot 10^5\)	Difference of transverse compressions over the load interval	Poisson’s ratio: for extension intervals	Poisson’s ratio: for transverse intervals
500—2.000	41,95—167,8	12,13	—	2,72	—	—	—
500—2.000	41,95—167,8	11,63	—	2,62	—	—	—
500—2.000	41,95—167,8	11,53	—	2,62	—	—	—
500—2.000	41,95—167,8	11,60	—	2,52	—	—	—
500—2.000	41,95—167,8	11,53	—	2,52	—	—	—
500—2.000	41,95—167,8	11,53	11,53	2,52	2,52	0,219	0,219
500—4.000	41,95—335,6	29,93	—	6,64	—	—	—
500—4.000	41,95—335,6	28,73	—	6,43	—	—	—
500—4.000	41,95—335,6	28,73	—	6,34	—	—	—
500—4.000	41,95—335,6	28,67	—	6,34	—	—	—
500—4.000	41,95—335,6	28,67	—	6,34	—	—	—
500—4.000	41,95—335,6	28,60	—	6,34	—	—	—
500—4.000	41,95—335,6	28,60	17,07	6,34	3,82	0,224	0,222
500—6.000	41,95—503,4	49,47	—	10,46	—	—	—
500—6.000	41,95—503,4	47,27	—	10,36	—	—	—
500—6.000	41,95—503,4	47,27	—	10,26	—	—	—
500—6.000	41,95—503,4	47,27	—	10,26	—	—	—
500—6.000	41,95—503,4	47,20	—	10,26	—	—	—
500—6.000	41,95—503,4	47,07	—	10,26	—	—	—
500—6.000	41,95—503,4	47,07	18,47	10,26	3,92	0,212	0,218
500—8.000	41,95—671,1	67,73	—	14,48	—	—	—
500—8.000	41,95—671,1	67,60	—	14,38	—	—	—
500—8.000	41,95—671,1	67,47	—	14,29	—	—	—
500—8.000	41,95—671,1	67,47	—	14,29	—	—	—
500—8.000	41,95—671,1	67,33	—	14,29	—	—	—
500—8.000	41,95—671,1	67,27	—	14,29	—	—	—
500—8.000	41,95—671,1	67,27	20,20	14,29	4,03	0,200	0,212

Compression.

SPECIMEN No. 16.

Table No. 51.

Load intervals in kg	Load intervals in kg/cm², taking into account the machine error	Longitudinal strain, per 1 cm length in \( \frac{1}{100000} \) cm or \(10^5\)	Elastic longitudinal strain, according to the equation for different loads	Transverse strain, per 1 cm length in \( \frac{1}{100000} \) cm or \(10^5\)	Elastic transverse strain, according to the equation for different loads	Poisson’s ratio: for different intervals	Poisson’s ratio: for complete intervals
500—2.000	41,37—165,5	14,40	—	3.22	—	—	—
”	”	11,93	—	2.72	—	—	--
”	”	11,80	—	2.62	—	—	—
”	”	11,67	—	2.62	—	—	—
”	”	11,60	—	2.62	—	—	—
”	”	11,60	11.60	2.62	2.62	0,226	0,226
500—4.000	41,37—331,0	31,07	—	7.04	—	—	—
”	”	28,20	—	6.54	—	—	—
”	”	28,00	—	6.54	—	—	—
”	”	27,93	—	6.54	—	—	—
”	”	27,93	16.33	6.54	3.92	0.240	0.234
500—6.000	41.37—496,4	47,33	—	11.08	—	—	—
”	”	44,60	—	10,77	—	—	—
”	”	44,47	—	10,66	—	—	—
”	”	44,40	—	10,66	—	—	—
”	”	44,33	—	10,66	—	—	—
”	”	44,33	16.40	10,66	4.12	0.251	0.240
500—8.000	41.37—661,9	64,00	—	15,29	—	—	—
”	”	61,27	—	14,89	—	—	—
”	”	60,93	—	14,79	—	—	—
”	”	60,73	—	14,79	—	—	—
”	”	60,67	—	14,79	—	—	—
”	”	60,67	16.34	14,79	4.13	0.253	0,244

SPECIMEN No. 17.

Table No. 52.

Load intervals in kg	Load intervals in kg/cm², taking into account the machine error	Longitudinal strain, per 1 cm length in \( \frac{1}{100000} \) cm or \(10^5\)	Elastic longitudinal strain, according to the equation for different loads	Transverse strain, per 1 cm length in \( \frac{1}{100000} \) cm or \(10^5\)	Elastic transverse strain, according to the equation for different loads	Poisson’s ratio: for different intervals	Poisson’s ratio: for complete intervals
500—2.000	41,51—166,0	14,33	—	3.02	—	—	—
”	”	12,00	—	2.82	—	—	—
”	”	12,00	—	2.72	—	—	—
”	”	12,00	—	2.62	—	—	—
”	”	12,00	12,00	2.62	2,62	0,219	0,219
500—4.000	41,51—332,1	31,93	—	6.96	—	—	—
”	”	28,80	—	6.55	—	—	—
”	”	28,67	—	6,45	—	—	—

Load intervals in klgr. — On the machine.	Load intervals in klgr. — kg/cm², taking into account machine error.	Longitudinal compression, per 1 cm length, in \( \frac{1}{100000}\) cm, or \(q \cdot 10^5\).	Difference of longitudinal compressions in the interval under load.	Transverse expansion, per 1 cm length, in \( \frac{1}{100000}\) cm, or \(q_1 \cdot 10^5\).	Difference of transverse expansions in the interval under load.	Poisson’s ratio — for equal intervals.	Poisson’s ratio — for complete intervals.
500—4.000	41,51—332,1	28,53	—	6,55	—	—	—
〃	〃	28,53	16.53	6,55	3.93	0.238	0,230
500—6.000	41,51—498,1	48,80	—	11,29	—	—	—
〃	〃	45,73	—	11,09	—	—	—
〃	〃	54,53	—	10,99	—	—	—
〃	〃	45,40	—	10,79	—	—	—
〃	〃	45,27	—	10,69	—	—	—
〃	〃	45,27	16.74	10,69	4.14	0.248	0,236
500—8.000	41.51—664,0	65,27	—	15,52	—	—	—
〃	〃	62,87	—	15,12	—	—	—
〃	〃	62,33	—	15,02	—	—	—
〃	〃	62,07	—	14,92	—	—	—
〃	〃	62,00	—	14,92	—	—	—
〃	〃	62,00	16.73	14,92	4.23	0.253	0,241

Tension.

SPECIMEN No. 16.

Table No. 53.

Load intervals in klgr. — On the machine.	Load intervals in klgr. — kg/cm², taking into account machine error.	Longitudinal extension, per 1 cm length, in \( \frac{1}{100000}\) cm, or \(q \cdot 10^5\).	Difference of longitudinal extensions in the interval under load.	Transverse compression, per 1 cm length, in \( \frac{1}{100000}\) cm, or \(q_1 \cdot 10^5\).	Difference of transverse compressions in the interval under load.	Poisson’s ratio — for equal intervals.	Poisson’s ratio — for complete intervals.
500 - 2.000	41.95—167,8	12,73	—	3.12	—	—	—
〃	〃	11,73	—	2.82	—	—	—
〃	〃	11,73	—	2.82	—	—	—
〃	〃	11,73	11.73	2.82	2.82	0.240	0.240
400—4.000	41,95—335,6	31,27	—	7,04	—	—	—
〃	〃	29,67	—	6.74	—	—	—
〃	〃	29,53	—	6.64	—	—	—
〃	〃	29,53	—	6.74	—	—	—
〃	〃	29,47	—	6.74	—	—	—
〃	〃	29,47	17.74	6.74	3.92	0.221	0.229
500—6.000	41.95—503,4	50,47	—	11,28	—	—	—
〃	〃	48,67	—	10,76	—	—	—
〃	〃	48,80	—	10,66	—	—	—
〃	〃	48,73	—	10,66	—	—	—
〃	〃	48,53	—	10,66	—	—	—
〃	〃	48,53	19.06	10,66	3.92	0.206	0,220

Load intervals in kg	Load intervals in kg: kg/cm², taking into account the error of the machine	Longitudinal extension per 1 cm of length in \( \frac{1}{10000} \) cm, or \(q \cdot 10^5\)	Difference of longitudinal extensions corresponding to the difference of loads	Transverse contraction per 1 cm of length in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Difference of transverse contractions corresponding to the difference of loads	Poisson’s ratio: for increments of intervals	Poisson’s ratio: for complete intervals
500—8.000	41,95—671,1	70,67	—	14,79	—	—	—
„	„	69,13	—	14,69	—	—	—
„	„	68,87	—	14,69	—	—	—
„	„	68,87	—	14,59	—	—	—
„	„	68,80	—	14,69	—	—	—
„	„	68,80	20,27	14,69	4,03	0,199	0,213

SAMPLE No. 17.

Table No. 54.

Load intervals in kg	Load intervals in kg: kg/cm², taking into account the error of the machine	Longitudinal extension per 1 cm of length in \( \frac{1}{10000} \) cm, or \(q \cdot 10^5\)	Difference of longitudinal extensions corresponding to the difference of loads	Transverse contraction per 1 cm of length in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Difference of transverse contractions corresponding to the difference of loads	Poisson’s ratio: for increments of intervals	Poisson’s ratio: for complete intervals
500—2.000	42,09—168,4	14,67	—	3,02	—	—	—
„	„	12,53	—	2,82	—	—	—
„	„	12,33	—	2,72	—	—	—
„	„	12,33	—	2,62	—	—	—
„	„	12,33	—	2,72	—	—	—
„	„	12,33	12,33	2,72	2,72	0,221	0,221
500—4.000	42,09—336,7	32,53	—	6,95	—	—	—
„	„	30,67	—	6,65	—	—	—
„	„	30,27	—	6,55	—	—	—
„	„	30,27	—	6,55	—	—	—
„	„	30,27	17,94	6,55	3,83	0,214	0,216
500—6.000	42,09—505,1	51,47	—	10,48	—	—	—
„	„	49,87	—	10,48	—	—	—
„	„	49,67	—	10,48	—	—	—
„	„	49,53	—	10,38	—	—	—
„	„	49,47	—	10,38	—	—	—
„	„	49,47	19,20	10,38	3,83	0,199	0,210
500—8.000	42,09—673,4	71,93	—	14,62	—	—	—
„	„	70,33	—	14,21	—	—	—
„	„	70,13	—	14,21	—	—	—
„	„	70,07	—	14,21	—	—	—
„	„	69,87	—	14,21	—	—	—
„	„	69,87	20,40	14,21	3,83	0,188	0,203

Compression.

Specimen No. 16.

Table No. 55.

Load intervals in kg: on the machine	kg/cm², taking into account the machine error	Longitudinal contraction, in 1 cm length, in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Continued contraction, in conditional state, at different load differences	Transverse expansion, in 1 cm length, in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Expansion, in conditional state, at different load differences	Poisson’s ratio: for different intervals	Poisson’s ratio: for full intervals
500—2.000	41,37—165,5	13,67	—	3,32	—	—	—
500—2.000	41,37—165,5	12,00	—	2,72	—	—	—
500—2.000	41,37—165,5	11,80	—	2,62	—	—	—
500—2.000	41,37—165,5	11,80	—	2,62	—	—	—
500—2.000	41,37—165,5	11,80	11,80	2,62	2,62	0,222	0,222
500—4.000	41,37—331,0	30,20	—	7,04	—	—	—
500—4.000	41,37—331,0	27,87	—	6,54	—	—	—
500—4.000	41,37—331,0	27,87	—	6,44	—	—	—
500—4.000	41,37—331,0	27,93	—	6,44	—	—	—
500—4.000	41,37—331,0	27,80	—	6,44	—	—	—
500—4.000	41,37—331,0	27,80	16,00	6,44	3,82	0,239	0,232
500—6.000	41,37—496,4	46,07	—	10,86	—	—	—
500—6.000	41,37—496,4	44,53	—	10,66	—	—	—
500—6.000	41,37—496,4	44,47	—	10,66	—	—	—
500—6.000	41,37—496,4	44,20	—	10,46	—	—	—
500—6.000	41,37—496,4	44,20	16,40	10,46	4,02	0,245	0,237
500—8.000	41,37—661,9	62,33	—	14,89	—	—	—
500—8.000	41,37—661,9	61,07	—	14,69	—	—	—
500—8.000	41,37—661,9	60,93	—	14,69	—	—	—
500—8.000	41,37—661,9	60,60	—	14,69	—	—	—
500—8.000	41,37—661,9	60,67	—	14,59	—	—	—
500—8.000	41,37—661,9	60,60	—	14,59	—	—	—
500—8.000	41,37—661,9	60,60	16,40	14,59	4,13	0,252	0,241

Specimen No. 17.

Table No. 56.

Load intervals in kg: on the machine	kg/cm², taking into account the machine error	Longitudinal contraction, in 1 cm length, in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Continued contraction, in conditional state, at different load differences	Transverse expansion, in 1 cm length, in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Expansion, in conditional state, at different load differences	Poisson’s ratio: for different intervals	Poisson’s ratio: for full intervals
500—2.000	41,51—166,0	13,87	—	2,82	—	—	—
500—2.000	41,51—166,0	12,07	—	2,62	—	—	—
500—2.000	41,51—166,0	11,93	—	2,52	—	—	—
500—2.000	41,51—166,0	12,00	—	2,52	—	—	—
500—2.000	41,51—166,0	12,00	12,00	2,52	2,52	0,210	0,210

Load intervals in kg	Load intervals in kg	Longitudinal contraction, direct per 1 cm length in \(\frac{1}{100000}\) cm, or \(q \cdot 10^5\)	Difference of longitudinal contractions in the given load interval	Transverse expansion, direct per 1 cm length in \(\frac{1}{100000}\) cm, or \(q \cdot 10^5\)	Difference of transverse expansions in the given load interval	Poisson’s ratio	Poisson’s ratio
On the machine	kg/cm², taking into account the error of the machine					For the calculation intervals	For the half-intervals
500—4.000	41,51—332,1	30,66	—	6,76	—	—	—
500—4.000	41,51—332,1	28,67	—	6,55	—	—	—
500—4.000	41,51—332,1	28,58	—	6,55	—	—	—
500—4.000	41,51—332,1	28,40	—	6,45	—	—	—
500—4.000	41,51—332,1	28,27	—	6,35	—	—	—
500—4.000	41,51—332,1	28,27	—	6,45	—	—	—
500—4.000	41,51—332,1	28,27	16,27	6,45	3,93	0,242	0,228
500—6.000	41,51—498,1	46,80	—	11,09	—	—	—
500—6.000	41,51—498,1	45,53	—	10,79	—	—	—
500—6.000	41,51—498,1	45,33	—	10,79	—	—	—
500—6.000	41,51—498,1	45,07	—	10,69	—	—	—
500—6.000	41,51—498,1	45,00	—	10,58	—	—	—
500—6.000	41,51—498,1	45,01	16,73	10,58	4,13	0,247	0,235
500—8.000	41,51—664,2	63,27	—	15,12	—	—	—
500—8.000	41,51—664,2	62,00	—	14,92	—	—	—
500—8.000	41,51—664,2	61,73	—	14,82	—	—	—
500—8.000	41,51—664,2	61,73	—	14,72	—	—	—
500—8.000	41,51—664,2	61,77	—	14,82	—	—	—
500—8.000	41,51—664,2	61,77	16,67	14,82	4,24	0,254	0,240

Tension.

SPECIMEN No. 16.

Table No. 57.

Load intervals in kg	Load intervals in kg	Longitudinal contraction, direct per 1 cm length in \(\frac{1}{100000}\) cm, or \(q \cdot 10^5\)	Difference of longitudinal contractions in the given load interval	Transverse expansion, direct per 1 cm length in \(\frac{1}{100000}\) cm, or \(q \cdot 10^5\)	Difference of transverse expansions in the given load interval	Poisson’s ratio	Poisson’s ratio
On the machine	kg/cm², taking into account the error of the machine					For the calculation intervals	For the half-intervals
500—2.000	41,95—167,8	12,80	—	3,02	—	—	—
500—2.000	41,95—167,8	11,20	—	2,82	—	—	—
500—2.000	41,95—167,8	11,13	—	2,82	—	—	—
500—2.000	41,95—167,8	11,13	—	2,82	—	—	—
500—2.000	41,95—167,8	11,13	11,13	2,82	2,82	0,253	0,253
500—4.000	41,95—335,6	30,00	—	6,84	—	—	—
500—4.000	41,95—335,6	28,47	—	6,74	—	—	—
500—4.000	41,95—335,6	28,40	—	6,64	—	—	—
500—4.000	41,95—335,6	28,40	—	6,74	—	—	—
500—4.000	41,95—335,6	28,40	—	6,74	—	—	—
500—4.000	41,95—335,6	28,40	17,27	6,74	3,92	0,227	0,237

Load intervals in kg	Load intervals in kg/cm², taking into account the machine error	Longitudinal extension, in 1 cm of length, in \( \frac{1}{100000} \) cm, or \( \varepsilon \cdot 10^5 \)	Difference of longitudinal extensions, in conventional units, upon decompression	Transverse contraction, in 1 cm of length, in \( \frac{1}{100000} \) cm, or \( q \cdot 10^5 \)	Difference of transverse contractions, in conventional units, upon decompression	Poisson’s ratio for various intervals	Poisson’s ratio for complete intervals
500—6.000	41,95—503,4	48,53	—	10,96	—	—	—
ditto	ditto	46,93	—	10,76	—	—	—
ditto	ditto	46,93	—	10,76	—	—	—
ditto	ditto	46,87	—	10,66	—	—	—
ditto	ditto	45,87	—	10,66	—	—	—
ditto	ditto	46,87	18,27	10,66	3,92	0,215	0,227
500—8.000	41,95—671,1	68,40	—	14,79	—	—	—
ditto	ditto	66,87	—	14,69	—	—	—
ditto	ditto	66,67	—	14,58	—	—	—
ditto	ditto	66,60	—	14,58	—	—	—
ditto	ditto	66,67	—	14,58	—	—	—
ditto	ditto	66,67	19,80	14,58	3,92	0,198	0,219

SPECIMEN No. 17.

Table No. 58.

Load intervals in kg	Load intervals in kg/cm², taking into account the machine error	Longitudinal extension, in 1 cm of length, in \( \frac{1}{100000} \) cm, or \( \varepsilon \cdot 10^5 \)	Difference of longitudinal extensions, in conventional units, upon decompression	Transverse contraction, in 1 cm of length, in \( \frac{1}{100000} \) cm, or \( q \cdot 10^5 \)	Difference of transverse contractions, in conventional units, upon decompression	Poisson’s ratio for various intervals	Poisson’s ratio for complete intervals
500—2.000	42,09—168,4	14,80	—	3,03	—	—	—
ditto	ditto	12,53	—	3,03	—	—	—
ditto	ditto	12,40	—	2,93	—	—	—
ditto	ditto	12,33	—	2,82	—	—	—
ditto	ditto	12,33	12,33	2,82	2,82	0,229	0,22[[unclear: digit]]
500—4.000	42,09—336,7	32,40	—	7,06	—	—	—
ditto	ditto	30,53	—	6,95	—	—	—
ditto	ditto	30,47	—	6,75	—	—	—
ditto	ditto	30,40	—	6,75	—	—	—
ditto	ditto	30,47	—	6,75	—	—	—
ditto	ditto	30,47	18,14	6,75	3,93	0,216	0,222
500—6.000	42,09—505,1	51,40	—	11,19	—	—	—
ditto	ditto	49,73	—	10,89	—	—	—
ditto	ditto	49,60	—	10,79	—	—	—
ditto	ditto	49,60	—	10,68	—	—	—
ditto	ditto	49,60	19,13	10,68	3,93	0,205	0,215
500—8.000	42,09—673,4	71,40	—	15,02	—	—	—
ditto	ditto	70,13	—	14,82	—	—	—
ditto	ditto	70,00	—	14,72	—	—	—
ditto	ditto	69,87	—	14,62	—	—	—
ditto	ditto	69,87	—	14,62	—	—	—
ditto	ditto	69,87	20,27	14,62	3,94	0,194	0,209

Compression.

SPECIMEN No. 16.

Table No. 59.

Load intervals in kg	kg/cm², taking into account the error of the machine	Longitudinal strain per 1 cm length in \( \frac{1}{100000}\) cm, or \(q \cdot 10^5\)	Difference of longitudinal strains in percent of load difference	Transverse strain per 1 cm length in \( \frac{1}{100000}\) cm, or \(q \cdot 10^5\)	Difference of transverse strains in percent of load difference	Poisson’s ratio for different intervals	Poisson’s ratio for complete intervals
500—2.000	41,37—165,5	13,60	—	3,32	—	—	—
„	„	11,87	—	2,72	—	—	—
„	„	11,87	—	2,72	—	—	—
„	„	11,87	—	2,62	—	—	—
„	„	11,87	11,87	2,62	2,62	0,221	0,221
400—4.000	41,37—331,0	29,87	—	6,84	—	—	—
„	„	28,13	—	6,54	—	—	—
„	„	28,00	—	6,44	—	—	—
„	„	28,00	16,13	6,44	3,82	0,237	0,230
500—6.000	41,37—496,4	45,67	—	10,87	—	—	—
„	„	44,47	—	10,66	—	—	—
„	„	44,33	—	10,56	—	—	—
„	„	54,33	—	10,56	—	—	—
„	„	44,27	—	10,46	—	—	—
„	„	44,27	16,27	10,46	4,02	0,247	0,236
500—8.000	41,37—661,9	61,80	—	14,99	—	—	—
„	„	61,00	—	14,79	—	—	—
„	„	60,67	—	14,69	—	—	—
„	„	60,67	—	14,69	—	—	—
„	„	60,67	16,40	14,79	4,23	0,258	0,242
500—10.000	41,37—827,4	79,60	—	19,32	—	—	—
„	„	77,53	—	19,01	—	—	—
„	„	77,33	—	19,01	—	—	—
„	„	77,13	—	18,91	—	—	—
„	„	77,00	—	19,01	—	—	—
„	„	77,00	16,33	19,01	4,32	0,265	0,247
500—12.000	41,37—992,9	96,07	—	23,94	—	—	—
„	„	94,33	—	23,74	—	—	—
„	„	93,87	—	23,54	—	—	—
„	„	93,67	—	23,54	—	—	—
„	„	93,53	—	23,54	—	—	—
„	„	93,47	—	23,54	—	—	—
„	„	93,47	16,47	23,54	4,53	0,275	0,252
500—14.000	41,37—1158	113,40	—	28,77	—	—	—
„	„	111,13	—	28,27	—	—	—
„	„	111,07	—	28,17	—	—	—
„	„	110,47	—	28,07	—	—	—
„	„	110,40	—	28,07	—	—	—
„	„	110,27	—	28,07	—	—	—

Load intervals in klgr. — on the machine	Kg./cm², taking into account the machine error	Increment of compression, longitudinal, per 1 cm length, in \( \frac{1}{100000}\) cm, or q. \(10^5\)	Difference of longitudinal compressions, in conventional units, occurring with the load difference interval	Increment of transverse extension per 1 cm length, in \( \frac{1}{100000}\) cm, or q. \(10^5\)	Difference of transverse extensions, in conventional units, occurring with the load difference interval	Poisson’s ratio for various intervals	Poisson’s ratio for full intervals
500—14.000	41,37—1158	110,13	—	28,07	—	—	—
〃	〃	110,00	—	28,07	—	—	—
〃	〃	110,00	16,53	28,07	4,53	0,274	0,255
500—16.000	41,37—1324	130,27	—	33,40	—	—	—
〃	〃	127,67	—	32,80	—	—	—
〃	〃	127,33	—	32,70	—	—	—
〃	〃	127,20	—	32,70	—	—	—
〃	〃	126,80	—	32,70	—	—	—
〃	〃	126,67	—	32,70	—	—	—
〃	〃	126,73	—	32,70	—	—	—
〃	〃	126,73	16,73	32,70	4,63	0,277	0,258

SAMPLE No. 17.

Table No. 60.

Load intervals in klgr. — on the machine	Kg./cm², taking into account the machine error	Increment of compression, longitudinal, per 1 cm length, in \( \frac{1}{100000}\) cm, or q. \(10^5\)	Difference of longitudinal compressions, in conventional units, occurring with the load difference interval	Increment of transverse extension per 1 cm length, in \( \frac{1}{100000}\) cm, or q. \(10^5\)	Difference of transverse extensions, in conventional units, occurring with the load difference interval	Poisson’s ratio for various intervals	Poisson’s ratio for full intervals
500—2.000	41,51—166,0	13,80	—	2,92	—	—	—
〃	〃	12,13	—	2,82	—	—	—
〃	〃	12,07	—	2,62	—	—	—
〃	〃	12,07	—	2,52	—	—	—
〃	〃	12,07	12,07	2,52	2,52	0,209	0,209
500—4.000	41,51—332,1	30,47	—	6,85	—	—	—
〃	〃	28,67	—	6,75	—	—	—
〃	〃	28,53	—	6,55	—	—	—
〃	〃	28,53	—	6,45	—	—	—
〃	〃	28,53	16,46	6,45	3,93	0,239	0,226
500—6.000	41,51—498,1	46,80	—	10,79	—	—	—
〃	〃	45,40	—	10,79	—	—	—
〃	〃	45,20	—	10,68	—	—	—
〃	〃	45,13	—	10,58	—	—	—
〃	〃	45,13	16,60	10,58	4,13	0,249	0,234
500—8.000	41,51—664,2	63,40	—	15,22	—	—	—
〃	〃	62,33	—	15,22	—	—	—
〃	〃	62,00	—	15,02	—	—	—
〃	〃	61,80	—	14,82	—	—	—
〃	〃	61,80	16,67	14,82	4,24	0,254	0,240

Load intervals in kg	Load intervals in kg	Longitudinal strain, divisions per 1 cm of length, in $\frac{1}{100000}$ cm, or $e \cdot 10^5$	Difference of longitudinal strains in conventional units under different loads	Transverse strain, divisions per 1 cm of length, in $\frac{1}{100000}$ cm, or $q \cdot 10^5$	Difference of transverse strains in conventional units under different loads	Poisson’s ratio	Poisson’s ratio
On the machine	Kg./cm², taking into account the error of the machine					For different intervals	For half-intervals
500—10.000	41,51—830,2	81,73	—	19,56	—	—	—
500—10.000	41,51—830,2	79,33	—	19,45	—	—	—
500—10.000	41,51—830,2	78,87	—	19,45	—	—	—
500—10.000	41,51—830,2	78,67	—	19,35	—	—	—
500—10.000	41,51—830,2	78,47	—	19,25	—	—	—
500—10.000	41,51—830,2	78,47	16,67	19,25	4,43	0,266	0,246
500—12.000	41,51—996,4	99,07	—	24,60	—	—	—
500—12.000	41,51—996,4	96,80	—	24,19	—	—	—
500—12.000	41,51—996,4	96,00	—	24,09	—	—	—
500—12.000	41,51—996,4	95,87	—	24,09	—	—	—
500—12.000	41,51—996,4	95,53	—	23,99	—	—	—
500—12.000	41,51—996,4	95,47	—	23,89	—	—	—
500—12.000	41,51—996,4	95,47	17,00	23,89	4,64	0,273	0,251
500—14.000	41,51—1162	115,60	—	29,33	—	—	—
500—14.000	41,51—1162	113,07	—	28,63	—	—	—
500—14.000	41,51—1162	112,87	—	28,63	—	—	—
500—14.000	41,51—1162	112,33	—	28,53	—	—	—
500—14.000	41,51—1162	112,07	—	28,43	—	—	—
500—14.000	41,51—1162	112,07	—	28,43	—	—	—
500—14.000	41,51—1162	112,07	16,60	28,43	4,54	0,274	0,254
500—16.000	41,51—1328	132,00	—	34,06	—	—	—
500—16.000	41,51—1328	129,87	—	33,16	—	—	—
500—16.000	41,51—1328	129,53	—	33,16	—	—	—
500—16.000	41,51—1328	129,27	—	33,16	—	—	—
500—16.000	41,51—1328	129,20	—	33,06	—	—	—
500—16.000	41,51—1328	129,00	—	33,06	—	—	—
500—16.000	41,51—1328	128,73	—	33,06	—	—	—
500—16.000	41,51—1328	128,73	16,66	33,06	4,63	0,278	0,257

Tension.

SPECIMEN No. 17.

Table No. 61.

Load intervals in kg	Load intervals in kg	Longitudinal strain, divisions per 1 cm of length, in $\frac{1}{100000}$ cm, or $e \cdot 10^5$	Difference of longitudinal strains in conventional units under different loads	Transverse strain, divisions per 1 cm of length, in $\frac{1}{100000}$ cm, or $q \cdot 10^5$	Difference of transverse strains in conventional units under different loads	Poisson’s ratio	Poisson’s ratio
On the machine	Kg./cm², taking into account the error of the machine					For different intervals	For half-intervals
500—2.000	42,09—168,4	15,40	—	3,33	—	—	—
500—2.000	42,09—168,4	12,47	—	2,82	—	—	—
500—2.000	42,09—168,4	12,33	—	2,72	—	—	—

Load intervals, in kg	Load intervals, in kg/cm², taking into account the error of the machine	Longitudinal extension, per 1 cm length, in 1/100000 cm, or q·10⁶	Difference of longitudinal extensions in the load-interval	Transverse contraction, per 1 cm length, in 1/100000 cm, or q·10⁶	Difference of transverse contractions in the load-interval	Poisson’s ratio: for the load-intervals	Poisson’s ratio: for the half-intervals
500—2.000	42,09—168,4	12,97	—	2,82	—	—	—
500—2.000	42,09—168,4	12,27	12,27	2,82	2,82	0,230	0,230
500—4.000	42,09—336,7	34,53	—	7,46	—	—	—
500—4.000	42,09—336,7	31,07	—	6,95	—	—	—
500—4.000	42,09—336,7	30,67	—	6,75	—	—	—
500—4.000	42,09—336,7	30,27	—	6,75	—	—	—
500—4.000	42,09—336,7	30,27	18,00	6,75	3,93	0,218	0,223
500—6.000	42,09—505,1	54,00	—	11,19	—	—	—
500—6.000	42,09—505,1	50,67	—	10,79	—	—	—
500—6.000	42,09—505,1	50,00	—	10,79	—	—	—
500—6.000	42,09—505,1	49,73	—	10,79	—	—	—
500—6.000	42,09—505,1	49,73	19,46	10,79	4,04	0,208	0,217
500—8.000	42,09—673,4	75,20	—	15,22	—	—	—
500—8.000	42,09—673,4	72,20	—	14,92	—	—	—
500—8.000	42,09—673,4	70,93	—	14,82	—	—	—
500—8.000	42,09—673,4	70,80	—	14,82	—	—	—
500—8.000	42,09—673,4	70,67	—	14,82	—	—	—
500—8.000	42,09—673,4	70,67	20,84	14,82	4,03	0,194	0,210

SPECIMEN No. 16.

Table No. 52.

Load intervals, in kg	Load intervals, in kg/cm², taking into account the error of the machine	Longitudinal extension, per 1 cm length, in 1/100000 cm, or q·10⁶	Difference of longitudinal extensions in the load-interval	Transverse contraction, per 1 cm length, in 1/100000 cm, or q·10⁶	Difference of transverse contractions in the load-interval	Poisson’s ratio: for the load-intervals	Poisson’s ratio: for the half-intervals
500—2.000	41,95—167,8	14,80	—	3,02	—	—	—
500—2.000	41,95—167,8	11,93	—	2,82	—	—	—
500—2.000	41,95—167,8	11,80	—	2,82	—	—	—
500—2.000	41,95—167,8	11,73	—	2,82	—	—	—
500—2.000	41,95—167,8	11,73	11,73	2,82	2,82	0,240	0,240
500—4.000	41,95—335,6	33,73	—	7,14	—	—	—
500—4.000	41,95—335,6	30,20	—	6,84	—	—	—
500—4.000	41,95—335,6	30,00	—	6,74	—	—	—
500—4.000	41,95—335,6	29,73	—	6,84	—	—	—
500—4.000	41,95—335,6	29,73	18,00	6,84	4,02	0,223	0,230

Load intervals in kg	Load intervals in kg	Longitudinal elongation in tension, per 1 cm of length, in $\frac{1}{10000}$ cm, or $q \cdot 10^5$	Difference of longitudinal elongations in tension, with increasing load	Transverse compression in tension, per 1 cm of length, in $\frac{1}{10000}$ cm, or $q \cdot 10^5$	Difference of transverse compressions in tension, with increasing load	Poisson’s ratio	Poisson’s ratio
On the machine	kg/cm², taking into account the machine error					For unlike intervals	For full intervals
500—6,000	41,95—503,4	53,33	—	11,37	—	—	—
500—6,000	41,95—503,4	50,00	—	11,07	—	—	—
500—6,000	41,95—503,4	49,53	—	10,97	—	—	—
500—6,000	41,95—503,4	49,40	—	10,87	—	—	—
500—6,000	41,95—503,4	49,07	—	10,87	—	—	—
500—6,000	41,95—503,4	48,80	—	10,87	—	—	—
500—6,000	41,95—503,4	48,67	—	10,87	—	—	—
500—6,000	41,95—503,4	48,67	18,94	10,87	4,03	0,213	0,224
500—8,000	41,95—671,1	73,67	—	15,29	—	—	—
500—8,000	41,95—671,1	70,00	—	15,09	—	—	—
500—8,000	41,95—671,1	69,87	—	15,09	—	—	—
500—8,000	41,95—671,1	69,47	—	14,99	—	—	—
500—8,000	41,95—671,1	69,27	—	14,99	—	—	—
500—8,000	41,95—671,1	69,00	—	14,99	—	—	—
500—8,000	41,95—671,1	68,87	—	14,99	—	—	—
500—8,000	41,95—671,1	68,87	20,20	14,99	4,12	0,204	0,218

The data of these tables are again presented graphically (drawings 5, 6), retaining the former scales for Poisson’s ratio and for the stresses. The numbers 1, 2, 3, 4 denote on these diagrams the successive order of the tensile tests alternating with compression tests: 1—2, 2—3, 3—4.

Considering the curves obtained, we may immediately observe that Poisson’s ratio is not a constant quantity in tension either; during the first stretching of the bar, as the load is increased, the coefficient at first increases up to a load of approximately 340 kg/cm², and then, with further increase of the load, decreases; the curve expressing the relation of the coefficient to the load has in this case a convex form; in subsequent extensions it changes its form: from convex it becomes concave, passing through a straight line; at the same time, with increasing load the curvature gradually diminishes, and the curve approaches a horizontal straight line: a sign that Poisson’s ratio, as the load increases, tends toward a certain limit.

Compression following tension changes the position of the curve, namely: each new curve of Poisson’s ratio in tension of the specimen after its compression is located higher.

curve obtained from tension to compression, i.e., compression of the specimen increases Poisson’s ratio during subsequent tension; but in this, as is evident from the diagrams, this successive increase has a certain limit, which is reached after as few as 4–5 compressions following tensions.

The limit toward which Poisson’s ratio tends in these successive tensions, as is evident from the diagrams, lies between 0.22 and 0.21 (at a load of \(675\ \mathrm{kg/cm.^2}\)).

Together with the curves of Poisson’s ratio for tensions of the specimen, there are also plotted the curves of Poisson’s ratio for compressions of the same specimen—those compressions with which the tensions alternate; these curves confirm the previously indicated properties of the ratio under compression: its increase with increasing load and its decrease from prior tension; the curves for the present case, as before, curve upward with gradually decreasing curvature and approach the horizontal—an indication of the tendency of Poisson’s ratio toward a certain limit.

Of all the curves presented, only one appears not to correspond to the foregoing: this is the curve of specimen No. 16 for the fourth tension after compression of the specimen by a force twice as large as the tensile force; although, nevertheless, the value of the ratio in this tension is greater than the values of the ratio in the second tension, and at the final load of \(675\ \mathrm{kg/cm.^2}\) it even almost coincides with the values of the ratio in the 3rd tension.

It remains for us now only to present the results of the experiments with specimens Nos. 15 and 18, which were subjected to compression with intermediate tension. These results are given in the following tables.

Compression.

SPECIMEN No. 15.

Cross-sectional area of the specimen \(\omega = 2.40 \times 4.98 = 11.95\ \text{cm}^2\);
Length for measuring longitudinal compressions and elongations \(l = 15\ \text{cm}\).
Dimension for measuring transverse expansions \(a = 4.98\ \text{cm}\).

Table No. 63.

Load intervals in kg	Load intervals in kg	Longitudinal compression per 1 cm of length in \(1/10000\) cm, or \(q \cdot 10^5\)	Difference of longitudinal compressions, taking account of load increments	Transverse expansion per 1 cm of length in \(1/10000\) cm, or \(q \cdot 10^5\)	Difference of transverse expansions, taking account of load increments	Poisson’s ratio: for increasing intervals	Poisson’s ratio: for complete intervals
On the machine	kg/cm², taking into account the machine error
500—2,000	41.27—165.1	11.53	—	3.22	—	—	—
500—2,000	41.27—165.1	11.40	—	2.81	—	—	—
500—2,000	41.27—165.1	11.27	—	2.81	—	—	—
500—2,000	41.27—165.1	11.33	—	2.81	—	—	—
500—2,000	41.27—165.1	11.33	—	2.71	—	—	—
500—2,000	41.27—165.1	11.33	11.33	2.71	2.71	0.239	0.239
500—4,000	41.27—330.1	28.47	—	6.93	—	—	—
500—4,000	41.27—330.1	27.27	—	6.73	—	—	—
500—4,000	41.27—330.1	27.13	—	6.63	—	—	—
500—4,000	41.27—330.1	27.13	—	6.63	—	—	—
500—4,000	41.27—330.1	27.13	15.80	6.63	3.92	0.248	0.244
500—6,000	41.27—495.2	45.27	—	11.06	—	—	—
500—6,000	41.27—495.2	43.73	—	10.96	—	—	—
500—6,000	41.27—495.2	43.27	—	10.85	—	—	—
500—6,000	41.27—495.2	43.20	—	10.85	—	—	—
500—6,000	41.27—495.2	43.20	—	10.85	—	—	—
500—6,000	41.27—495.2	43.20	16.07	10.85	4.22	0.263	0.251
500—8,000	41.27—660.3	61.40	—	15.38	—	—	—
500—8,000	41.27—660.3	59.93	—	15.28	—	—	—
500—8,000	41.27—660.3	59.80	—	15.28	—	—	—
500—8,000	41.27—660.3	59.40	—	15.18	—	—	—
500—8,000	41.27—660.3	59.33	—	15.18	—	—	—
500—8,000	41.27—660.3	59.33	—	15.18	—	—	—
500—8,000	41.27—660.3	59.33	16.13	15.18	4.33	0.268	0.256

SPECIMEN No. 18

Cross-sectional area of the specimen: \(\omega = 2.40 \times 4.98 = 11.95\ \mathrm{cm.^2}\)
Length for measuring longitudinal compressions and extensions: \(l = 15\ \mathrm{cm.}\)
Dimension for measuring transverse extensions and compressions: \(a = 4.98\ \mathrm{cm.}\)

Table No. 64.

Load intervals in kg. On the machine.	kg./cm.^2, taking into account the machine error.	Longitudinal compression, per 1 cm of length, in \(\frac{1}{100000}\) cm, or \(q \cdot 10^5\).	Difference of longitudinal compressions in the conventional state, under different loads.	Transverse extension, per 1 cm of length, in \(\frac{1}{100000}\) cm, or \(q \cdot 10^5\).	Difference of transverse extensions in the conventional state, under different loads.	Poisson’s ratio, for increasing intervals.	Poisson’s ratio, for complete intervals.
500—2,000	41.27—165.1	11.93	—	2.91	—	—	—
500—2,000	41.27—165.1	11.27	—	2.81	—	—	—
500—2,000	41.27—165.1	11.27	—	2.71	—	—	—
500—2,000	41.27—165.1	11.07	—	2.71	—	—	—
500—2,000	41.27—165.1	11.07	11.07	2.71	2.71	0.245	0.245
500—4,000	41.27—330.1	27.93	—	7.03	—	—	—
500—4,000	41.27—330.1	26.53	—	6.73	—	—	—
500—4,000	41.27—330.1	26.47	—	6.63	—	—	—
500—4,000	41.27—330.1	26.47	—	6.63	—	—	—
500—4,000	41.27—330.1	26.47	15.40	6.63	3.92	0.255	0.250
500—6,000	41.27—495.2	44.20	—	10.95	—	—	—
500—6,000	41.27—495.2	42.47	—	10.85	—	—	—
500—6,000	41.27—495.2	42.47	—	10.85	—	—	—
500—6,000	41.27—495.2	42.20	—	10.75	—	—	—
500—6,000	41.27—495.2	42.07	—	10.75	—	—	—
500—6,000	41.27—495.2	42.07	15.60	10.75	4.12	0.264	0.256
500—8,000	41.27—660.3	60.13	—	15.08	—	—	—
500—8,000	41.27—660.3	58.53	—	14.97	—	—	—
500—8,000	41.27—660.3	58.27	—	14.97	—	—	—
500—8,000	41.27—660.3	58.20	—	14.77	—	—	—
500—8,000	41.27—660.3	58.13	—	14.87	—	—	—
500—8,000	41.27—660.3	57.93	—	14.87	—	—	—
500—8,000	41.27—660.3	57.93	15.86	14.87	4.12	0.260	0.257

Extension.

SPECIMEN No. 15.

Table No. 65.

Load intervals in kg. On the machine.	kg./cm.^2, taking into account the machine error.	Longitudinal extension, per 1 cm of length, in \(\frac{1}{100000}\) cm, or \(q \cdot 10^5\).	Difference of longitudinal extensions in the conventional state, under different loads.	Transverse compression, per 1 cm of length, in \(\frac{1}{100000}\) cm, or \(q \cdot 10^5\).	Difference of transverse compressions in the conventional state, under different loads.	Poisson’s ratio, for increasing intervals.	Poisson’s ratio, for complete intervals.
500—2,000	41.91—167.6	15.27	—	2.91	—	—	—
500—2,000	41.91—167.6	13.27	—	2.81	—	—	—
500—2,000	41.91—167.6	13.00	—	2.81	—	—	—

Load intervals in klgr. — On the machine	Load intervals in klgr. — Kg./cm², taking into account the error of the machine	Longitudinal elongation, occurring over 1 cm length, in \( \frac{1}{100000}\) cm, or \(e \cdot 10^5\)	Difference of longitudinal elongations in the established state for different loads	Transverse contraction, occurring over 1 cm length, in \( \frac{1}{100000}\) cm, or \(q \cdot 10^5\)	Difference of transverse contractions in the established state for different loads	Poisson’s coefficient — For differences of intervals	Poisson’s coefficient — For complete intervals
500—2.000	41,91—167,6	13,00	—	2,81	—	—	—
”	”	13,00	13,00	2,81	2,81	0,216	0,216
500—4.000	41,91—335,3	33,93	—	7,23	—	—	—
”	”	31,40	—	6,93	—	—	—
”	”	31,20	—	6,83	—	—	—
”	”	31,07	—	6,83	—	—	—
”	”	31,00	—	6,73	—	—	—
”	”	31,00	18,00	6,73	3,92	0,218	0,217
500—6.000	41,91—502,9	53,60	—	11,06	—	—	—
”	”	50,93	—	10,85	—	—	—
”	”	50,40	—	10,85	—	—	—
”	”	50,27	—	10,75	—	—	—
”	”	50,27	—	10,65	—	—	—
”	”	50,27	19,27	10,65	3,92	0,203	0,212
500—8.000	41,91—670,6	74,80	—	15,07	—	—	—
”	”	71,67	—	14,77	—	—	—
”	”	71,60	—	14,67	—	—	—
”	”	71,27	—	14,67	—	—	—
”	”	71,07	—	14,67	—	—	—
”	”	71,00	—	14,67	—	—	—
”	”	70,00	20,73	14,67	4,02	0,194	0,207

SAMPLE No. 18.

Table No. 66.

Load intervals in klgr. — On the machine	Load intervals in klgr. — Kg./cm², taking into account the error of the machine	Longitudinal elongation, occurring over 1 cm length, in \( \frac{1}{100000}\) cm, or \(e \cdot 10^5\)	Difference of longitudinal elongations in the established state for different loads	Transverse contraction, occurring over 1 cm length, in \( \frac{1}{100000}\) cm, or \(q \cdot 10^5\)	Difference of transverse contractions in the established state for different loads	Poisson’s coefficient — For differences of intervals	Poisson’s coefficient — For complete intervals
500—2.000	41,84—167,4	14,13	—	3,22	—	—	—
”	”	12,53	—	2,81	—	—	—
”	”	12,47	—	2,71	—	—	—
”	”	12,40	—	2,71	—	—	—
”	”	12,40	12,40	2,71	2,71	0,219	0,219
500—4.000	41,84—334,7	32,00	—	6,93	—	—	—
”	”	30,67	—	6,83	—	—	—
”	”	30,13	—	6,73	—	—	—
”	”	30,13	—	6,73	—	—	—
”	”	30,00	—	6,63	—	—	—
”	”	30,00	17,60	6,63	3,92	0,223	0,221

Load intervals in klgr. On the machine	Load intervals in klgr. kg/cm², taking into account the error of the machine	Longitudinal elongation, readings over a length of 1 cm in units of 1/100000 cm, or q·10⁵	Difference of longitudinal elongations in the elastic state under different loads	Transverse elongation, readings over a length of 1 cm in units of 1/100000 cm, or q·10⁵	Difference of transverse elongations in the elastic state under different loads	Poisson’s ratio. For different intervals	Poisson’s ratio. For complete intervals
500—6.000	41,84—502,1	50,33	—	10,76	—	—	—
〃	〃	48,67	—	10,65	—	—	—
〃	〃	48,47	—	10,65	—	—	—
〃	〃	48,40	—	10,55	—	—	—
〃	〃	48,33	—	10,55	—	—	—
〃	〃	48,33	18,33	10,55	3,92	0,214	0,218
500—8.000	41,84—669,5	70,20	—	14,78	—	—	—
〃	〃	68,47	—	14,57	—	—	—
〃	〃	68,20	—	14,47	—	—	—
〃	〃	68,07	—	14,47	—	—	—
〃	〃	68,00	—	14,47	—	—	—
〃	〃	68,00	—	14,47	—	—	—
〃	〃	68,00	19,67	14,47	3,92	0,199	0,213

Compression.

SPECIMEN No. 15.

Table No. 67.

Load intervals in klgr. On the machine	Load intervals in klgr. kg/cm², taking into account the error of the machine	Longitudinal compression, readings over a length of 1 cm in units of 1/100000 cm, or q·10⁵	Difference of longitudinal compression in the elastic state under different loads	Transverse expansion, readings over a length of 1 cm in units of 1/100000 cm, or q·10⁵	Difference of transverse expansion in the elastic state under different loads	Poisson’s ratio. For different intervals	Poisson’s ratio. For complete intervals
500—2.000	41,27—165,1	13,13	—	2,71	—	—	—
〃	〃	11,67	—	2,61	—	—	—
〃	〃	11,60	—	2,61	—	—	—
〃	〃	11,60	—	2,61	—	—	—
〃	〃	11,60	11,60	2,61	2,61	0,225	0,225
500—4.000	41,27—330,1	29,60	—	6,63	—	—	—
〃	〃	27,93	—	6,53	—	—	—
〃	〃	27,60	—	6,53	—	—	—
〃	〃	27,60	—	6,53	—	—	—
〃	〃	27,60	16,00	6,53	3,92	0,245	0,237
500—6.000	41,27—495,2	45,67	—	10,95	—	—	—
〃	〃	44,07	—	10,85	—	—	—
〃	〃	43,95	—	10,75	—	—	—
〃	〃	43,80	—	10,75	—	—	—
〃	〃	43,80	—	10,75	—	—	—
〃	〃	43,80	16,20	10,75	4,22	0,260	0,245

Load intervals in kg	Load intervals in kg	Longitudinal compression per 1 cm length, in \(1/100000\) cm, or \(c \cdot 10^5\)	Mean longitudinal compression, in conventional units, for the load interval	Transverse extension per 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Mean transverse extension, in conventional units, for the load interval	Poisson’s ratio	Poisson’s ratio
On the machine	kg/cm², taking into account the machine error	Longitudinal compression per 1 cm length, in \(1/100000\) cm, or \(c \cdot 10^5\)	Mean longitudinal compression, in conventional units, for the load interval	Transverse extension per 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Mean transverse extension, in conventional units, for the load interval	For increasing intervals	For full intervals
500—8.000	41,27—660,3	61,67	—	15,28	—	—	—
500—8.000	41,27—660,3	60,20	—	15,07	—	—	—
500—8.000	41,27—660,3	60,07	—	14,97	—	—	—
500—8.000	41,27—660,3	60,00	—	14,97	—	—	—
500—8.000	41,27—660,3	60,00	—	14,97	—	—	—
500—8.000	41,27—660,3	60,00	16,20	14,97	4,22	0,260	0,250

SAMPLE No. 18.

Table No. 68.

Load intervals in kg	Load intervals in kg	Longitudinal compression per 1 cm length, in \(1/100000\) cm, or \(c \cdot 10^5\)	Mean longitudinal compression, in conventional units, for the load interval	Transverse extension per 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Mean transverse extension, in conventional units, for the load interval	Poisson’s ratio	Poisson’s ratio
On the machine	kg/cm², taking into account the machine error	Longitudinal compression per 1 cm length, in \(1/100000\) cm, or \(c \cdot 10^5\)	Mean longitudinal compression, in conventional units, for the load interval	Transverse extension per 1 cm length, in \(1/100000\) cm, or \(q \cdot 10^5\)	Mean transverse extension, in conventional units, for the load interval	For increasing intervals	For full intervals
500—2.000	41,27—165,1	13,47	—	3,01	—	—	—
500—2.000	41,27—165,1	11,33	—	2,61	—	—	—
500—2.000	41,27—165,1	11,20	—	2,61	—	—	—
500—2.000	41,27—165,1	11,20	—	2,61	—	—	—
500—2.000	41,27—165,1	11,20	11,20	2,61	2,61	0,233	0,233
500—4.000	41,27—330,1	28,67	—	7,03	—	—	—
500—4.000	41,27—330,1	26,93	—	6,73	—	—	—
500—4.000	41,27—330,1	26,80	—	6,63	—	—	—
500—4.000	41,27—330,1	26,73	—	6,63	—	—	—
500—4.000	41,27—330,1	26,80	—	6,63	—	—	—
500—4.000	41,27—330,1	26,80	15,60	6,63	4,02	0,258	0,247
500—6.000	41,27—495,2	44,67	—	11,06	—	—	—
500—6.000	41,27—495,2	43,33	—	10,95	—	—	—
500—6.000	41,27—495,2	42,67	—	10,75	—	—	—
500—6.000	41,27—495,2	42,47	—	10,75	—	—	—
500—6.000	41,27—495,2	42,67	—	10,65	—	—	—
500—6.000	41,27—495,2	42,47	—	10,65	—	—	—
500—6.000	41,27—495,2	42,47	15,67	10,65	4,02	0,257	0,251
500—8.000	41,27—660,3	59,87	—	14,87	—	—	—
500—8.000	41,27—660,3	58,60	—	14,77	—	—	—
500—8.000	41,27—660,3	58,60	—	14,77	—	—	—
500—8.000	41,27—660,3	58,53	—	14,67	—	—	—
500—8.000	41,27—660,3	58,53	—	14,77	—	—	—
500—8.000	41,27—660,3	58,47	—	14,67	—	—	—
500—8.000	41,27—660,3	58,40	—	14,67	—	—	—
500—8.000	41,27—660,3	58,40	15,93	14,67	4,02	0,252	0,251

Tension.

SPECIMEN No. 15.

Table No. 69.

Load intervals in kgf — on machine	Load intervals in kg/cm², taking into account the error of the machine	Longitudinal elongation of the prism per 1 cm length, in hundred-millionths of a cm, or \(e \cdot 10^5\)	Difference of longitudinal elongations, in hundred-millionths of a cm, for a load difference	Transverse contraction of the prism per 1 cm length, in hundred-millionths of a cm, or \(q \cdot 10^5\)	Difference of transverse contractions, in hundred-millionths of a cm, for a load difference	Poisson’s ratio — for load differences	Poisson’s ratio — for full intervals
500—2,000	41,91—167,6	15,40	—	3,01	—	—	—
″	″	13,13	—	2,91	—	—	—
″	″	12,87	—	2,81	—	—	—
″	″	12,87	—	2,91	—	—	—
″	″	12,87	—	2,91	—	—	—
″	″	12,87	12,87	2,91	2,91	0,226	0,226
500—4,000	41,91—333,3	33,33	—	6,93	—	—	—
″	″	31,67	—	6,83	—	—	—
″	″	31,53	—	6,73	—	—	—
″	″	31,47	—	6,83	—	—	—
″	″	31,33	—	6,83	—	—	—
″	″	31,33	18,56	6,83	3,92	0,211	0,218
500—6,000	41,91—502,9	52,33	—	10,95	—	—	—
″	″	51,07	—	10,85	—	—	—
″	″	50,80	—	10,75	—	—	—
″	″	50,60	—	10,75	—	—	—
″	″	50,40	—	10,75	—	—	—
″	″	50,40	18,97	10,75	3,92	0,207	0,213
500—8,000	41,91—670,6	72,20	—	14,87	—	—	—
″	″	70,93	—	14,77	—	—	—
″	″	70,67	—	14,77	—	—	—
″	″	70,33	—	14,67	—	—	—
″	″	70,27	—	14,67	—	—	—
″	″	70,13	—	14,67	—	—	—
″	″	70,13	19,73	14,67	3,92	0,199	0,209

SPECIMEN No. 18.

Table No. 70.

Load intervals in kgf — on machine	Load intervals in kg/cm², taking into account the error of the machine	Longitudinal elongation of the prism per 1 cm length, in hundred-millionths of a cm, or \(e \cdot 10^5\)	Difference of longitudinal elongations, in hundred-millionths of a cm, for a load difference	Transverse contraction of the prism per 1 cm length, in hundred-millionths of a cm, or \(q \cdot 10^5\)	Difference of transverse contractions, in hundred-millionths of a cm, for a load difference	Poisson’s ratio — for load differences	Poisson’s ratio — for full intervals
500—2,000	41,84—167,4	15,40	—	3,22	—	—	—
″	″	12,67	—	2,91	—	—	—
″	″	12,60	—	2,81	—	—	—
″	″	12,40	—	2,81	—	—	—
″	″	12,40	12,40	2,81	2,81	0,227	0,227

Load intervals in kg	Load intervals in kg	Longitudinal shortening per 1 cm length in \( \frac{1}{10000} \) cm, or \(\varphi \cdot 10^5\)	Difference of longitudinal shortening, in conventional units, under the various loads	Transverse contraction per 1 cm length in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Difference of transverse contraction in conventional units under the various loads	Poisson’s ratio	Poisson’s ratio
On the machine	kg/cm², taking into account the machine error	Longitudinal shortening per 1 cm length in \( \frac{1}{10000} \) cm, or \(\varphi \cdot 10^5\)	Difference of longitudinal shortening, in conventional units, under the various loads	Transverse contraction per 1 cm length in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Difference of transverse contraction in conventional units under the various loads	For increasing intervals	For decreasing intervals
500—4.000	41,84—334,7	32,60	—	7,03	—	—	—
"	"	30,40	—	6,83	—	—	—
"	"	30,40	—	6,73	—	—	—
"	"	30,07	—	6,73	—	—	—
"	"	30,07	17,67	6,73	3,92	0,222	0,224
500—6.000	41,84—502,1	50,80	—	10,85	—	—	—
"	"	49,13	—	10,85	—	—	—
"	"	48,93	—	10,75	—	—	—
"	"	48,73	—	10,65	—	—	—
"	"	48,67	—	10,65	—	—	—
"	"	48,53	—	10,65	—	—	—
"	"	48,53	18,46	10,65	3,92	0,212	0,219
500—8.000	41,84—669,5	70,33	—	14,67	—	—	—
"	"	69,00	—	14,67	—	—	—
"	"	68,60	—	14,57	—	—	—
"	"	68,40	—	14,57	—	—	—
"	"	68,33	—	14,57	—	—	—
"	"	68,33	19,80	14,57	3,92	0,198	0,213

Compression.

SPECIMEN No. 15.

Table No. 71.

Load intervals in kg	Load intervals in kg	Longitudinal shortening per 1 cm length in \( \frac{1}{10000} \) cm, or \(\varphi \cdot 10^5\)	Difference of longitudinal shortening, in conventional units, under the various loads	Transverse contraction per 1 cm length in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Difference of transverse contraction in conventional units under the various loads	Poisson’s ratio	Poisson’s ratio
On the machine	kg/cm², taking into account the machine error	Longitudinal shortening per 1 cm length in \( \frac{1}{10000} \) cm, or \(\varphi \cdot 10^5\)	Difference of longitudinal shortening, in conventional units, under the various loads	Transverse contraction per 1 cm length in \( \frac{1}{100000} \) cm, or \(q \cdot 10^5\)	Difference of transverse contraction in conventional units under the various loads	For increasing intervals	For decreasing intervals
500—2.000	41,27—165,1	13,77	—	3,11	—	—	—
"	"	11,87	—	2,61	—	—	—
"	"	11,73	—	2,61	—	—	—
"	"	11,73	—	2,61	—	—	—
"	"	11,73	11,73	2,61	2,61	0,223	0,223
500—4.000	41,27—330,1	30,13	—	6,93	—	—	—
"	"	28,07	—	6,73	—	—	—
"	"	28,07	—	6,63	—	—	—
"	"	27,87	—	6,63	—	—	—
"	"	27,87	16,14	6,63	4,02	0,249	0,236

Load intervals in kg	Load intervals in kg/cm², taking into account the machine errors	Longitudinal compression strains per 1 cm length, in \(1/100000\) cm, or \(\varphi \cdot 10^5\)	Difference of longitudinal compressions, incl. residual, for load intervals	Transverse expansion strains per 1 cm length, in \(1/100000\) cm, or \(\psi \cdot 10^5\)	Difference of transverse expansions, incl. residual, for load intervals	Poisson’s ratio for increasing intervals	Poisson’s ratio for complete intervals
500—6.000	41,27—495,2	45,60	—	11,16	—	—	—
„	„	44,27	—	10,95	—	—	—
„	„	43,93	—	10,85	—	—	—
„	„	44,00	—	10,75	—	—	—
„	„	44,00	—	10,75	—	—	—
„	„	44,00	16,13	10,75	4,12	0,256	0,244
500—8.000	41,27—660,3	61,60	—	15,48	—	—	—
„	„	60,40	—	15,28	—	—	—
„	„	60,30	—	15,18	—	—	—
„	„	60,20	—	15,18	—	—	—
„	„	60,20	—	15,08	—	—	—
„	„	60,20	—	15,08	—	—	—
„	„	60,20	16,20	15,08	4,33	0,267	0,250
500—10.000	41,27—825,4	78,53	—	19,70	—	—	—
„	„	76,93	—	19,50	—	—	—
„	„	76,73	—	19,40	—	—	—
„	„	76,53	—	19,50	—	—	—
„	„	76,53	—	19,50	—	—	—
„	„	76,53	16,33	19,50	4,42	0,271	0,254
500—12.000	41,27—990,4	96,00	—	24,62	—	—	—
„	„	93,80	—	24,22	—	—	—
„	„	93,33	—	24,12	—	—	—
„	„	92,93	—	23,92	—	—	—
„	„	92,93	—	23,92	—	—	—
„	„	92,93	16,40	23,92	4,42	0,270	0,257
500—14.000	41,27—1155	112,33	—	29,05	—	—	—
„	„	110,67	—	28,54	—	—	—
„	„	109,87	—	28,44	—	—	—
„	„	109,87	—	28,44	—	—	—
„	„	109,60	—	28,44	—	—	—
„	„	109,53	—	28,44	—	—	—
„	„	109,53	16,60	28,44	4,52	0,272	0,260
500—16.000	41,27—1321	129,33	—	33,77	—	—	—
„	„	127,80	—	33,37	—	—	—
„	„	126,87	—	33,27	—	—	—
„	„	126,33	—	33,37	—	—	—
„	„	126,27	—	33,27	—	—	—
„	„	126,27	—	33,17	—	—	—
„	„	126,27	16,74	33,17	4,73	0,283	0,263

SAMPLE No. 18.

Table No. 72.

Load intervals in kg: on the machine	kg/cm², taking into account the machine error	Longitudinal contraction, observed on 1 cm length, in 1/100000 cm, or α·10⁵	Difference of longitudinal contractions, increasing with difference of intervals	Transverse expansion, observed on 1 cm length, in 1/100000 cm, or q·10⁵	Difference of transverse expansions, increasing with difference of intervals	Poisson’s ratio: for differences of all intervals	Poisson’s ratio: for differences of full intervals
500—2.000	41,27—165,1	12,67	—	2,71	—	—	—
〃	〃	11,40	—	2,61	—	—	—
〃	〃	11,27	—	2,51	—	—	—
〃	〃	11,27	—	2,61	—	—	—
〃	〃	11,27	11,27	2,61	2,61	0,232	0,232
500—4.000	41,27—330,1	28,73	—	6,73	—	—	—
〃	〃	27,13	—	6,63	—	—	—
〃	〃	26,93	—	6,53	—	—	—
〃	〃	26,87	—	6,53	—	—	—
〃	〃	26,87	15,60	6,53	3,92	0,251	0,243
500—6.000	41,27—495,2	44,67	—	11,06	—	—	—
〃	〃	42,93	—	10,65	—	—	—
〃	〃	42,67	—	10,55	—	—	—
〃	〃	42,60	—	10,55	—	—	—
〃	〃	42,60	—	10,55	—	—	—
〃	〃	42,60	15,73	10,55	4,02	0,256	0,248
500—8.000	41,27—660,3	59,67	—	14,97	—	—	—
〃	〃	58,67	—	14,97	—	—	—
〃	〃	58,47	—	14,87	—	—	—
〃	〃	58,40	—	14,87	—	—	—
〃	〃	58,33	—	14,77	—	—	—
〃	〃	58,33	—	14,77	—	—	—
〃	〃	58,33	15,73	14,77	4,22	0,268	0,253
500—10.000	41,27—825,4	76,00	—	19,30	—	—	—
〃	〃	74,87	—	19,20	—	—	—
〃	〃	74,80	—	19,10	—	—	—
〃	〃	74,40	—	19,10	—	—	—
〃	〃	74,20	—	19,10	—	—	—
〃	〃	74,20	15,87	19,10	4,33	0,273	0,257
500—12.000	41,27—990,4	92,53	—	23,72	—	—	—
〃	〃	91,00	—	23,62	—	—	—
〃	〃	90,73	—	23,52	—	—	—
〃	〃	90,53	—	23,52	—	—	—
〃	〃	90,20	—	23,42	—	—	—
〃	〃	90,13	—	23,42	—	—	—
〃	〃	90,13	—	23,42	—	—	—
〃	〃	90,13	15,93	23,42	4,32	0,271	0,260
500—14.000	41,27—1155[[unclear: decimal part cut off]]	108,47	—	28,24	—	—	—
〃	〃	107,13	—	28,04	—	—	—
〃	〃	106,60	—	27,94	—	—	—
〃	〃	106,47	—	27,94	—	—	—

Load intervals, kg: on the machine	Load intervals, kg/cm², taking into account the machine error	Longitudinal compression per 1 cm of length, in 1/100000 cm, or $\varepsilon \cdot 10^5$	Difference of longitudinal comp., taking into account the initial correction	Transverse expansion per 1 cm of length, in 1/100000 cm, or $q \cdot 10^5$	Difference of transverse expansion, taking into account the initial correction	Poisson’s ratio: for the difference intervals	Poisson’s ratio: for complete intervals
500—14,000	41.27—1155	106.33	—	27.94	—	—	—
„	„	106.33	—	27.94	—	—	—
„	„	106.33	16.20	27.94	4.52	0.279	0.263
500—16,000	41.27—1321	125.33	—	32.97	—	—	—
„	„	123.60	—	32.66	—	—	—
„	„	123.13	—	32.66	—	—	—
„	„	122.73	—	32.56	—	—	—
„	„	122.67	—	32.46	—	—	—
„	„	122.67	—	32.56	—	—	—
„	„	122.67	16.34	32.56	4.62	0.283	0.265

The diagrams (drawings 7, 8), constructed (figures 1, 2, 3—the consecutive numbers of the compression experiments, alternating with tensile experiments: 1—2, 2—3) on the basis of the data of these tables, fully confirm the propositions already stated by us above: in compression of the specimen, Poisson’s ratio increases with increasing load per cm² of cross-sectional area; the curve expressing the dependence between the coefficient and the load is convex, with gradually decreasing curvature, and gradually approaches a certain horizontal line—an indication of the existence of a limit for the magnitude of the coefficient; the tension following compression reduces Poisson’s ratio in the new compression: the curves expressing the dependence between the coefficient and the load are situated, in the new compression after tension, below the curves obtained in the preceding compression, although the differences of the ordinates of the successive curves decrease—an indication of approach to the limit; in tension of the specimen, Poisson’s ratio during the first tension up to a load of approximately 340 kg/cm² increases, and then decreases with increasing load per cm² of cross-sectional area; in subsequent tensions following compression, the coefficient decreases all the time; the curve of the coefficient during the first tension is convex, while in subsequent tensions it is concave, with gradually decreasing curvature and slope toward the horizontal line—an indication of approach to the limit; the compression following tension increases Poisson’s ratio—the curve of the coefficient during

with a new tension after compression is located above the curve obtained in the preceding tension.

In conclusion of this article I shall point out the following modification of the original construction (drawing 1) of the apparatus for determining transverse deformations. The matter is that, when considering the apparatus of the first construction, the thought may arise that, when the prism-shaped mirror carriers are pressed against the rods \(b,b\) by the clamping plates \(f,f\) (although, it must be noted, this pressure is extremely slight), friction appears on the side surfaces of the rods, impeding their free motion. This thought occurred to me as well during the performance of the experiments described above; after long reflection, on the advice of Prof. Meyer, it was decided, in order to clarify this doubt, to make a certain modification in the apparatus which would already completely eliminate the above-mentioned one-sided pressure of the mirror carriers on the rods \(b,b\). As may be seen in the appended drawing (see drawing 9), this modification consisted in the following: by means of frame \(A\), entirely analogous to the frame in drawing 1, pressure was produced, in the same manner as in the first construction, on the rods \(b,b\) against the test body \(B\); but these rods \(b,b\) were now embraced on both sides by \(\Pi\)-shaped steel plates \(\pi,\pi\), having at one end points \(c,c\), similar to how the steel plates in Martens’s apparatus have them, and at the other end obtuse-angled recesses for placing the prism-shaped mirror carriers \(p,p\), as is shown in the appended drawing. The pressure of the \(\Pi\)-shaped plates \(\pi,\pi\) was produced by means of clamp \(k\), and the entire arrangement of the apparatus on the test specimen is visible in the drawing. With such a construction, the pressure of the mirrors on the rods in no way affects the freedom of motion of the latter; the transverse deformations are indicated entirely by the mirrors, and are not divided between two mirrors, as in the first construction; and, finally, the indications of two mirrors on the two sides of rod \(b\) guard against the possibility of error owing to skewing of the rods. Therefore it was very important to compare the indications of these two apparatuses and, in this way, to determine the qualities of the first apparatus.

For this purpose I carried out, with this and the other apparatus, compression experiments on a cast-iron specimen of rectangular cross-section \(\omega = 2.425 \times 5.01 = 12.149\ \mathrm{cm.^2}\) and length \(l = 34\ \mathrm{cm.}\); this specimen, in the previous tensile experiments, had been stretched to a load of \(1149\ \mathrm{kg}/\mathrm{cm.^2}\).

To obtain comparable results from these two apparatuses, I brought the specimen, by repeated compression, to a “settled” state, and then made first the determination of Poisson’s ratio with the apparatus of the first design, and then with the apparatus of the new design. The results of these experiments are given in the following two tables:

Table No. 73.

Load, in klgr. On the machine	Load, in klgr. Kg./cm², taking into account the error of the machine	Longitudinal compression, taken over 1 cm of length in $\frac{1}{100000}$ cm or $q \cdot 10^5$	Difference of longitudinal compressions	Transverse expansion, taken over 1 cm of length in $\frac{1}{100000}$ cm or $q \cdot 10^5$	Difference of transverse expansions	Poisson’s ratio. For differences of longitudinal and transverse expansions	Poisson’s ratio. For total longitudinal and transverse expansions
500	41,15	—	—	—	—	—	—
2.000	164,6	13,67	13,67	2,49	2,49	0,182	0,182
4.000	329,2	32,60	18,93	6,09	3,60	0,190	0,187
6.000	493,8	51,60	19,00	10,38	4,29	0,226	0,201
8.000	658,4	70,60	19,00	14,77	4,39	0,231	0,209
10.000	823,0	89,33	18,73	19,36	4,59	0,245	0,216
12.000	987,7	107,67	18,34	23,95	4,59	0,250	0,223
14.000	1152	126,20	18,53	28,54	4,59	0,248	0,226
16.000	1317	144,93	18,73	33,13	4,59	0,245	0,229

Table No. 74.

Load, in klgr. On the machine	Load, in klgr. Kg./cm², taking into account the error of the machine	Longitudinal compression, taken over 1 cm of length in $\frac{1}{100000}$ cm or $q \cdot 10^5$	Difference of longitudinal compressions	Transverse expansion, taken over 1 cm of length in $\frac{1}{100000}$ cm or $q \cdot 10^5$	Difference of transverse expansions	Poisson’s ratio. For differences of longitudinal and transverse expansions	Poisson’s ratio. For total longitudinal and transverse expansions
500	41,15	—	—	—	—	—	—
2.000	164,6	13,93	13,93	2,59	2,59	0,186	0,186
4.000	329,2	33,67	19,74	6,38	3,79	0,192	0,189
6.000	493,8	52,87	19,20	10,77	4,39	0,229	0,204
8.000	658,4	71,74	18,87	15,16	4,39	0,234	0,211
10.000	823,0	90,47	18,73	19,75	4,59	0,245	0,216
12.000	987,7	108,67	18,20	24,34	4,59	0,252	0,224
14.000	1152	127,27	18,60	28,93	4,59	0,247	0,227
16.000	1317	146,27	19,00	33,62	4,69	0,247	0,230

Comparing the results of the last two experiments, we see that these results differ from one another very little; if there is any difference, in any case it does not exceed the errors of observation. Thus, the apparently obvious advantages of the new apparatus, of which we spoke above, in fact proved to have little influence on the results of the experiments; meanwhile, the first design has its own substantial advantage over the second design—namely, convenience of handling and ease of mounting on the specimen being tested, qualities which the second design does not possess, since it requires the expenditure of a rather considerable amount of time for setting up the apparatus.

Nevertheless, for greater confidence in the correctness of the results, all the experiments with the last four specimens, Nos. 15, 16, 17, and 18, were carried out with the apparatus of the latest design; but, as we have already seen, the results obtained were entirely identical with the former ones.

Noticed misprints

Page	Line	Printed	Should be
10	12 from bottom	7,783—464,2	7,837—464,2
19	18 from top (5th column from left)	33,86	34,8
19	13 from top (1st column from right)	0,215	0,216
25	19 from top (6th column from left)	5,56	5,53
26	24 from top (5th column from left)	12,13	12,03
30	18 from top (4th column from left)	28,27	18,27
37	12 from top	for that reason	because
38	14 from top	equal to 0,3	close to 0,3
38	14 from bottom	establish such positions	establish such positions, correct for the present within the limits of the experiments carried out:
46	23 from top (3rd column from left)	61,77	61,67
46	24 from top (3rd column from left)	61,77	61,67
52	19 from bottom	Figures	figures
63	26 from top	figures	figures

Drawing 3. The solid curve—3, intersecting the solid curve marked 1, should be designated by the number 2.

Drawing 3. The upper tensile curve (dotted -----) should be marked with the number 13.

Drawing 6. The lower tensile curve (solid line, marked with the number 7) should be marked with the number 1.

Drawing 9. The letters \(\pi\pi\) were omitted for the \(\parallel\)—shaped plates.

Drawing 1.

Technical drawing of the experimental apparatus and its components, with dimensions indicated.

Drawing 2.

Visible dimension labels: 350; 30; 24; 30; 45; 5; 15; 25; 10; 200; 30; 25; 15; 5; 50.

Drawing 3.

Curves of the relative transverse change in volume during the testing of cast-iron specimens.

Legend:

— solid lines denote the transverse changes of the specimens;
— dashed lines represent the longitudinal changes of the specimens.

Curve labels visible on the drawing: No. 1, No. 2, No. 3, No. 4, No. 5, No. 6, No. 8, No. 9, No. 14.

Scale markings visible along the axes: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400.

Drawing 1.

Curves of the ratio of transverse compression to longitudinal elongation of specimens of ordinary treated cast iron.

Curve labels visible on the drawing:
No. 1, No. 2, No. 3, No. 4, No. 5, No. 6, No. 7, No. 8, No. 9, No. 10, No. 11, No. 12, No. 13.

Vertical scale: values from approximately 0.02 to 0.30.

Horizontal scale: values from approximately 200 to 1500.

Legend:

— Solid lines: specimens of ordinary treatment, not subjected to artificial [[unclear: aging/seasoning]].

– – – Dashed lines: specimens subjected to artificial [[unclear: aging/seasoning]].

– · – Dash-dot lines: [[unclear: third category of specimens]].

Drawing 5.

Specimen No. 16. Arrangement of relative compressions [[unclear: handwritten word]].

Vertical scale: relative deformation values from \(0\) to \(0.30\).

Horizontal scale: stresses, in \(\mathrm{kg}/\mathrm{cm}^2\), from \(100\) to \(1400\).

Curve labels visible on the drawing: \(1\), \(2\), \(3\), \(1_0\), \(2_0\), \(3_0\), \(3 \tfrac{1}{2}\).

Handwritten note along the stress scale: magnitudes of relative transverse [[unclear: deformations/compressions]] under tensile stresses.

Fig. 6.

Specimen No. 17.

Distances, taken from the middle of the specimen

Graph labels:

• Vertical axis: \(\mu\)
• Lower horizontal scale: scale divisions of Peters’ micrometer
• Upper/right horizontal scale: units of load of the tensile apparatus, \(\mathrm{kg}/\mathrm{mm}^2\)

Visible numerical scale marks:

• Vertical scale: 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18, 0.20, 0.22, 0.24, 0.26
• Horizontal scale: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300

Curve labels visible on the drawing: 1, 2, 3, 4.

Specimen No. 15

Compression of cast iron under tension

Drawing 2.

Visible labels in the drawing:

• Magnitude of relative elongation
• Relative compression under tension
• kg/mm²

Graph markings include the curve labels: \(A\), \(B\), \(b_1\), \(b_2\), \(\varphi\).

Drawing 8.

Specimen No. 18

[[unclear: handwritten caption beneath “Specimen No. 18”]]

Magnitude of the relative elongation
(micrometer)

Magnitude of the relative transverse expansion
(micrometer)

kg/cm²

Drawing 9.

[Engineering drawing of the apparatus with dimensional annotations and lettered parts.]

1. O. Berner. Untersuchungen über den Einfluss der Art und der Wechsels der Belastung auf die elastischen und bleibenden Formänderungen. 1903. ↩↩↩↩

2. Wertheim, Mémoire sur l’équilibre des corps solides homogènes. Ann. de Chimie et de Physik. 1848. T. 23, p. 53. ↩

3. N. Götz u. A. Kurz. Messungen der durch Anspannen von Drähten bewirkten Quercontraction.
   Repertorium der Physik. Herausgegeben von Dr. Exner. 22 Bd. 1886. S. 9, 274, 511. ↩

4. P. Cardani. Ueber die directe Bestimmung des Poissonischen Koefficienten an Drähten. Phil. Zeitschrift. Bd. 4. S. 144, 449. 1903. ↩

5. Röntgen. Ueber das Verhältnis der Quercontraction zur Längendilatation bei Kautschuk. Pogg. Ann. Bd. 159. S. 601. u. ff. ↩

6. Bauschinger. Ueber die Quercontraction und—Dilatation bei der Längenausdehnung und—Zusammendrückung prismatischer Körper. Der Civilingenieur. Bd. XXV, 1879. S. 81—124. ↩

7. J. Morrow. On an Instrument for Measuring the Lateral Contraction of Tie-bars and on the Determination of Poisson’s Ratio. Phil. Mag. (Ser. 6) Vol. 6 (1903) S. 417. ↩

8. Kirchhoff. Über das Verhältniss der Quercontraction zur Längendilatation bei Stäben von federhartem Stahle. Pogg. Ann. Bd. 108 (1859). S. 369—392. ↩

9. Okatov. Über das Verhältniss der Quercontraction zur Längendilatation bei Stahlstäben. Pogg. Ann. Bd. 119 (1863) S. 11, or in Russian: Theory of Equilibrium and Motion of an Elastic Wire. St. Petersburg, 1867. ↩

10. Cornu. Méthode optique pour l’étude de la déformation de la surface extérieure des solides élastiques. C. R. t. 69 (1869). ↩

11. Schneebelli. Über das Verhältniss der Quercontraction zur Längendilatation. Pogg. Ann. Bd. 140 (1870) S. 598—621. ↩

12. A. Mallock. The Measurement of the Ratio of Lateral Contraction to Longitudinal Extension in a Body under Strain. Proc. Royl. Soc. Vol. 29 (1879). ↩

13. Straubel. Ueber die Elasticitätszahlen und Elasticitätsmoduln des Glases. Wied. Ann. Bd. 68 (1899). ↩

14. References to the literature may be found in Khvolson: Course of Physics, vol. I, p. 632. ↩