Instruments for the Rapid and Sufficiently Accurate Determination of the Specific Gravity of Ice and Its Resistance to Fracture.

B. P. Weinberg.

1. In the middle of March 1911, the commission for flood prevention under the Tomsk municipal public self-government appealed to me, in the person of its chairman, E. L. Zubashev, with a request to devise a program and methods of observation that could provide material for predictions of the time of onset of the ice drift and of its intensity and the floods caused by it. Owing to the scarcity of time remaining (presumably) before the ice drift of that year, I decided to use it only for developing methods that would make it possible to follow the successive—according to the approach of the ice drift—changes in certain physical properties of the ice, characterized in ordinary speech by the word “loosening.” Such properties of the ice seemed to me to be its specific gravity and its resistance to fracture,—and I made an attempt to devise methods and to construct simple instruments that would make it possible quickly and sufficiently accurately to determine these quantities for a series of pieces of ice taken at various distances from its free surface.

2. Since it could hardly be expected that changes in specific gravity would be considerable, it was natural to resort to a method of the variational type. Such a method seemed to me to be one that would be a combination of floating with the method of hydrostatic weighing: a liquid would be taken which does not act on the ice and is only slightly inferior to it in specific gravity, and in each experiment, besides the weight of the piece of ice, the small “apparent” weight that the tested piece would have in this liquid would be determined. This method¹ makes it possible to increase the accuracy arbitrarily far: if, for determining the small weight of the ice in the liquid, one uses scales more sensitive than those used for determining the weight of the piece itself, then the accuracy of determining the specific gravity of the piece of ice is almost equal to the accuracy of determining the specific gravity of the liquid.

In fact, denoting by \(x\) the specific gravity of the ice, by \(\Delta\) the specific gravity of the liquid, by \(\delta\) the specific gravity of air under the conditions—

¹ Described in detail in Journal of the Russian Physico-Chemical Society, vol. 43, 1911, pp. 338–339.

weighing experiment, through \(P\)—the weight of the piece of ice in air, and through \(p\)—the weight of the piece of ice in the liquid, we have:

\[ \frac{P}{P-p}=\frac{x-\delta}{\Delta-\delta}. \tag{1} \]

Hence, taking into account that \(p\) is small in comparison with \(P\), we find successively

\[ x=(\Delta-\delta)\frac{P}{P-p}+\delta=(\Delta-\delta)\frac{1}{1-\frac{p}{P}}+\delta=(\Delta-\delta)\left(1+\frac{p}{P}\right)+ \]

\[ +\delta=\Delta+\frac{p}{P}(\Delta-\delta). \tag{2} \]

A convenient liquid proved to be a mixture—of approximately equal parts by weight—of Russian turpentine (oleum terebenthinae rossicum) and linseed oil (oleum lini recens), but, since ice pieces from the upper layers, owing to abundant air bubbles, were lighter than this mixture, then, although loading them with additional weights does not present significant difficulties, it is perhaps better, for such pieces, to use a mixture of two parts linseed oil and one part turpentine.

Experience showed that even two adjacent pieces of one and the same layer can give differences in specific gravity sometimes reaching one thousandth. Therefore I considered an accuracy of 5 ten-thousandths sufficient—all the more so since a change in temperature by \(1^\circ\) produces a change in the specific gravity of the mixture of turpentine and linseed oil of approximately 7–8 ten-thousandths, and to maintain and measure the temperature under the presumed conditions of the experiment—on the river or near it—is hardly possible more accurately than to \(0^\circ.2\).

Such accuracy is easily attainable, and, consequently, it remained to fulfill the second condition: rapidity of measurement at this degree of accuracy. For this purpose I decided to use not lever balances but spring balances, whose accuracy—provided the difference in the specific gravity of the ice and of the chosen liquid is sufficiently small—is quite adequate.

1. Finally, I settled on the following set of instruments. For weighing the piece of ice in air, spring balances were used with a limiting load of 5 kg and divisions of 100 g, allowing readings with an error of 10–20 g (Fig. 1, left). From the ice a piece of square cross-section was cut out (side about 20 cm.)

throughout the entire thickness of the piece; this piece was sawn into pieces 12–15 centimeters thick, and they were given—by means of a Finnish knife—an approximately cylindrical shape (diameter—18 cm). Such a piece weighed 3–4 kg, and, consequently, a few dozen seconds were sufficient to determine its weight in air with an error, in any case, not exceeding 1%.

Fig. 1.

For weighing such a piece of ice in a mixture of turpentine and linseed oil, spring balances with a maximum load of 100 g and divisions of 5 g were used, allowing readings with an accuracy of about 1 g. The pan, both in these and in those balances, consisted of a ring-shaped strip of aluminum sheet (its weight in these balances, with wires, was 33 g). The specific gravity of the investigated pieces of ice ranged from 0.906 to 0.910, while the specific gravity of the liquid, whose temperature in the various experiments varied between 2° and 8°C, was about 0.909 at 0°, 0.903 at 8°; the weight in the liquid of a piece of 3–4 kg (i.e., with a volume of 3300–4400 cm³), with a difference in specific gravities of 0.001, is 3–4 g. Hence it is clear that the spring balances used gave an error of about 0.0002–0.0003 in the difference of the specific gravities of the ice and the liquid, which is quite sufficient for the intended purpose.

I note that, in the observations I carried out, this error exceeded the error in determining the specific gravity itself

liquid—because at that time there was no suitable areometer of sufficient sensitivity and because of the difficulty of using Mohr’s balance in the open air. Having, for example, an areometer with a scale of 0.880–0.940 and divisions of 0.0005, and testing pieces of ice 18 cm in diameter and 20 cm high—weighing about 4½ kg—one can easily, with our set of balances, determine the specific gravity of ice with an accuracy of up to 0.0002.

1. I shall give in Table I the results obtained in the spring of 1911 in the investigation of two pieces of ice (transverse dimensions about \(70 \times 70\) cm\(^2\)), which were taken from the Tom River on March 23 (thickness without the snow crust 70 cm) and on March 31 (thickness without the snow crust 55 cm), and which were subsequently kept in the laboratory yard under a layer of snow. Later it was no longer possible to cut out the ice, since its surface was under water, and on April 11 the ice broke up. The results referring to different days of measurement are poorly comparable with one another, because the composition of the mixture was not quite the same on different days, and measurements with Mohr’s balances—and at first with a crude areometer—do not permit one to vouch for more than 0.001.

In Table I are given the specific gravities of the pieces of ice, computed with an accuracy of 0.0001; the first row gives the day of testing, the first column—the serial number of the piece, if counted from the free surface (the upper one).

Table I.

These determinations can be regarded only as a trial of the method proposed by me, showing, among other things, the necessity of using a liquid cooled beforehand to \(0^\circ\): in our measurements the temperature of the liquid changed greatly—for example, on 2.4.11 from \(4^\circ.5\) at the beginning of the measurements to \(2^\circ.7\) at their end; moreover, the temperature of the liquid at the top of the vessel and at its bottom, despite mixing by raising and lowering the piece of ice being weighed, usually differed by \(1^\circ\)–\(2^\circ\). In any case it is clear that the first piece brought in had the same specific gravity throughout its whole thickness, but, after standing without sufficient protection in the air, dimin-

to determine the specific gravity of the upper layer. The second piece was kept more carefully, and in it, markedly inferior in specific gravity, both on the first and on the subsequent days, was the upper part; and, to the eye, it was more abundantly studded with air bubbles than the remaining thickness.

1. To determine the resistance of ice to fracture, it was necessary to construct an apparatus in which the penetration of the supporting parts into the piece being broken would be avoided. Since this penetration depends on the fact that, in ice, the melting temperature decreases with increasing pressure, the supports had to be made of a material with poor thermal conductivity. Therefore I decided to make the supporting platforms of wood, and moreover rotating in the plane in which the breaking force is applied. Fig. 2 shows the appearance of the constructed apparatus, which proved very convenient and required only the addition of a device that would allow the supporting platforms to be fixed immovably (in our experiments we, having moved them to the desired distance from the middle, then held them against the tendency to rise upward by pressing with the hand).

Fig. 2.

The apparatus consists of a wooden frame, on the upper board of which are placed spring balances (from Hopkins’s apparatus for determining the magnetic permeability of iron by pull-off), stretched-

… by means of rotation of the handle located at the top. From the ice a piece of prismatic form was cut out in such a way that its length was parallel to the free surface of the ice on the river, and it was given the proper shape first by planing with a knife, and then by melting on a small copper plate heated from below by water vapor. This piece was placed between a horizontal wooden plate, suspended from spring scales and pressing on the specimen being tested from below, and two wooden bearing pads pressing on the specimen from above. Then, by rotating the handle, the spring scales were stretched and the specimen was brought to fracture, while the stress at the moment of fracture could easily be read off with an accuracy of up to \(1/2\) English pound (the scale of the scales was divided into half-pounds). If, however, the limiting pull of the scales (25 English pounds) proved insufficient for fracture, the specimen was removed, once more brought into proper condition on the steam-heated copper plate, and the experiment was repeated.

The limiting stress \(T\) was calculated by the formula

\[ T = \frac{3}{2}\frac{Pl}{ah^2}, \tag{3} \]

where \(P\) is the pull of the scales at the moment of fracture, \(l\) is the distance between the points of support, taken as the distance between the axes of the bearing pads (from 23 to 30 cm), \(a\) is the width of the bar (from 2 to 4 cm), and \(h\) is its height (from 2 to \(3\frac{1}{3}\) cm). The quantities \(a\) and \(h\) were measured with a wooden stangen-circus compass at several places on the specimen.

1. From the first piece of ice it was possible to subject two specimens to experiment (the results were \(T = 8.0\) and \(9.9\) kg/cm\(^2\)), since the apparatus was ready only on the morning of March 31, and soon a second piece of ice was brought. From the second piece, on March 31, April 1, and April 2, four specimens were tested each day; these were cut from the upper layers, from the middle layers, and from the lower layers (two). The values of \(T\) calculated from the results of these experiments (in kg/cm\(^2\)) are collected in Table II.

Table II.

From this it is seen that three days’ standing in warm weather under snow did not affect the limiting stress experienced by…

ice, that the strongest are apparently the middle layers (on average \(T = 13\cdot0\)), to which, perhaps, the lower layers are somewhat inferior (on average \(T = 12\cdot7\)), but that the upper layers are in fact “looser” than the rest of the mass (on average \(T = 8\cdot3\)).

In the projected systematic observations it would be desirable, for each layer, to determine the rate of its formation and the temperature gradient of the flow of cold that caused its formation; then it will be possible to try to answer the question of how much the speed of formation of the river’s ice cover affects—ceteris paribus—its strength.

1. I have decided to publish even these fragmentary data, together with a description of the instruments by means of which they were obtained, in the hope that perhaps someone among those living near rivers will begin to carry out similar observations and determinations and thereby add new information on so little developed a question as the specific gravity and resistance to fracture of such a widespread material as river ice.

Tomsk, 7. 9. 11.