Bridgman’s Investigations in the Field of High Pressures

Privatdozent A. V. Rakovsky.

PART I.

METHODOLOGY.

The latest investigations of the American physicist Bridgman in the field of high pressures constitute a major step forward in physics and physical chemistry. Before Bridgman we had only the most complete investigations of Amagat up to 3000 atmospheres and scattered investigations by a number of scientists, concerning narrow topics, up to 4000–4500 atmospheres. Bridgman’s work is remarkable in that he at once extended the range of accurately measurable pressures to 13,500, and of conditionally measurable ones to 20,000–30,000 atmospheres. The limits of the astonishing skill of the American physicist are determined by the very nature of the metal from which he built his apparatus. In Bridgman’s investigations the methodology is as important as the results he obtained; it will therefore not be superfluous to dwell in somewhat greater detail on the methodology of experiments in the field of high pressures.

I.

The first task of any physical investigation is to measure accurately the quantities that determine the phenomena under study. In our case the first task is the construction of a manometer necessary for determining high pressures. Among the various types of such manometers we shall briefly consider two: the manometers of Amagat and Bridgman.

Figure 1 gives a diagram of Amagat’s manometer, the so-called manometer with two free pistons. The pressure from the space under investigation is transmitted, by means of a liquid (a mixture of water + glycerin, water + glycerin + glucose), through channel \(a\) into chamber \(o\), filled with grease; the grease presses on the small piston \(p\), which in turn presses on the large piston \(P\). Beneath \(P\) there is a layer of liquid (water + glycerin) \(H\); still lower is a layer of mercury \(Hg\). Under the pressure of the descending piston \(P\), the mercury passes through channel \(bb\) into the manometric tube \(h\), open at its upper end. The pressure under the pist—

the height \(P\) by the same factor less than the pressure at \(o\) as the transverse section \(P\) is greater than the transverse section of the piston \(p\). Multiplying the found height of the mercury column in \(h\) by the ratio \(\frac{P}{p}\) and dividing by \(760\),1 we obtain the pressure at \(o\) (and, consequently, also in the space under investigation) in atmospheres. At high pressures the piston \(P\) can be lowered quite far. To avoid some inconveniences connected with such a large lowering of \(P\), Amagat produced a preliminary pressure on \(P\) from below by means of an additional pump through the channel \(dd\).

Fig. 1.

In Amagat’s experiments the diameters of the large pistons \(P\) ranged from 6 to 12 centimeters; there was a whole series of small pistons, the smallest having a diameter of 5.527 mm. At pressures up to 1000 atmospheres, Amagat, by selecting pistons, reduced one atmosphere to a height of 4.99 mm of mercury column in \(h\); at pressures up to 3000 atmospheres—to a height of 1.601 mm. In the latter case the mercury in tube \(h\) at 3000 atmospheres rose to 4.8 meters.

Amagat’s manometer belongs to the type of primary manometers, giving directly the value of the pressure in the chosen units. But this bulky manometer is not very convenient for frequent use in experiments, and therefore in practice the results of Amagat’s experiments were used for constructing a series of secondary manometers, in which changes are measured in some property of one or another substance, for example, the volume of water, the change in the form of a copper spiral tube, and so forth; knowing from Amagat’s experiments how these properties vary with pressure, we can judge the magnitude of the pressure from the magnitude of the property; the most commonly used secondary manometers are manometers of the Bourdon type.

Since Bridgman worked in regions of pressure considerably exceeding 3000 atmospheres, he had to construct a new primary manometer exclusively for high pressures. Bridgman could not follow in Amagat’s footsteps and increase the scale of the latter’s manometer, since at high pressures a very high column of mercury would be obtained in tube \(h\); reducing the height

of this column would have a strong effect on the accuracy of the pressure measurement, not to mention the enormous constructional difficulties.

Bridgman’s primary manometer has only one piston (Fig. 2).

The pressure is transmitted by means of a liquid through channel \(J\) into chamber \(A\). The same liquid (water + glycerin) fills both chamber \(A\) and the rubber bag \(H\). The liquid in \(H\), pressing on piston \(P\), makes it rise upward. Piston \(P\) moves in cylinder \(B\) and pushes rod \(D\) upward. On the upper end \(C\) of rod \(D\) there is suspended a stirrup (not shown in the drawing), which descends below the apparatus and carries below it a pan for weights. When, under the influence of the pressure from within, piston \(P\) and rod \(D\) rise upward, weights are placed on the pan until the piston descends to its former position. Knowing the weight of the weights used and the cross-section of piston \(P\), we can readily calculate the pressure in \(A\) (and, consequently, also in the space under investigation) in kg per sq. cm. In Bridgman’s experiments the diameter of the piston was \(1/16''\) (inch) \(= 0.159\) cm. A load on the piston of 130 kg corresponded to a pressure of 1800 kg/sq. cm.

Fig. 2.

The whole difficulty in constructing apparatuses for high pressures with free pistons consists in the fact that it is necessary to achieve two mutually exclusive results: 1) the piston must move “freely” in the channel, i.e. the friction must not be significant, and 2) the liquid transmitting the pressure must not seep through the clearance, i.e. through the gap between the piston and the walls of the channel in which the piston moves. Meanwhile, the liquid that has entered the clearance presses on the piston from the outside, i.e. makes the piston contract; the same liquid presses on the channel from the inside, i.e. makes the channel expand. As a result, with increasing pressure the clearance increases, and leakage appears, the seepage of liquid through the clearance outward. Seepage is the bane of all experiments under the conditions described. The generally accepted method of combating seepage is, first, the arrangement of special kinds of gaskets, compressed by a screw before the experiment (gaskets \(F\) and \(g\), screw \(K\) in Fig. 2), and, second, the use, as the liquid transmit—

pressure of viscous liquids (water + glycerin, water + glycerin + glucose, castor oil). In Tammann’s experiments (up to 3000–4000 atm.), already at 2000 atm. the seepage of castor oil was so great that Tammann had to weigh the oil that had seeped through and introduce the corresponding correction.

Bridgman built all the apparatus himself, and he succeeded in bringing the size of the clearance down to \(0.0003''\) \((=0.00075\) cm). In one case the clearance proved equal to \(0.0001''\). Nevertheless seepage, though very small, did occur; the greatest seepage was observed at \(2000\) kg/cm²; at higher pressures, owing to the strong increase in the viscosity of the liquid, the seepage is less. The manometer described had a high sensitivity of 2 kg/cm² at 7000 kg/cm²; its accuracy was about \(0.1\%\).

The form of manometer described was the first in time; it proved of little use for pressures from 10000 to 20000 kg/cm². For high pressures Bridgman modified both the shape of the cylinder and the role of the packing (Fig. 3).

The essential innovations were the lengthening of the lower part of the cylinder \(AB\), so that the greater part of it was subjected to the pressure of the liquid not only from the clearance but also from outside, the introduction of a conical steel packing \(D\), and the construction of a slightly conical piston (the diameter of the piston below being \(0.0001''\) larger than above). In the new form of manometer the seepage proved quite negligible. In constructing pistons for manometers it is necessary to bear in mind that the piston must move without great friction; otherwise the sensitivity of the instrument is greatly reduced, and the correction for friction is increased; and for every method, the smaller the correction, the greater the accuracy of the work.

Fig. 3.

In apparatus in which the influence of pressure on the properties of substances was studied, the pistons had another function: by their position changes in the volume of the system were produced and measured; here one could sacrifice freedom of motion of the piston in favor of measures against seepage. The latest form of such a piston is a composite piston with an annular packing (Fig. 4).

Fig. 4.

The lower part of the piston \(AA\), the upper—\(P\). \(AA\) has the form of an inverted letter \(T\), and on its shoulders \(aa\) are put rings \(B\) (rubber), \(C\) and \(K\) (steel); \(AA\) is separated from \(P\) by an air space \(o\). The pressure experienced by the lower side of the piston \(AA\) from the side \(L\), trans-

is effected by the shoulders \(aa\), the area of which is less than the area \(AA\), through the packing of the upper part \(P\); consequently, the packing always experiences a pressure greater than the pressure in the liquid, and is always pressed tightly against the walls of the cylinder.

With such a construction of the piston, leakage of liquid is not observed at all, even when kerosene and gasoline are used as the liquid transmitting the pressure.

An extremely important role in the technique of experiments with high pressures is played by the material used in the construction of the apparatus. B r i d g m a n has noted that the various parts of one and the same apparatus should be made from different grades of steel; this applies especially to metal packings, and even one and the same part is usefully made from different grades of steel, depending on the magnitude of the pressure for which the apparatus is intended. Pistons for pressures up to \(15000\) kg/sq. cm should be made of carbon steel; for higher pressures, of chromium or silicon steel.

After the pistons, the most important part of the apparatus are the cylinders—the pressure chambers in which the substances to be studied are placed. Such cylinders are subjected to pressure only from the inside outward; consequently, under the influence of pressure the diameter of the chamber increases; it is necessary to introduce a correction for such widening of the channel. But such corrections have meaning only so long as the cylinder behaves as a perfectly elastic body.

Let us suppose that the internal diameter of the cylinder before the start of the experiments is \(9/16''\). Let us subject the channel of the cylinder to high pressure; its diameter will increase as the pressure rises. Let the curve \(AaB\) be the curve of the increase of the diameter with the growth of pressure (Fig. 5). With a gradual decrease of the pressure we may observe three cases. First, the curve of the reverse decrease of the diameter with the fall of pressure \(BaA\) may coincide with the curve of increase of the diameter; in this case we have to do with perfect elasticity. Second, the curve of decrease of the diameter \(BbA\), while not coinciding along the whole path with the curve of increase, coincides with the latter at the initial point; this is the case of “pure hysteresis,” an indication of imperfect elasticity. Third, the curve of decrease of the diameter with the fall of pressure \(Bb'C\) does not coincide with the curve \(AaB\), and at the end of its path, after the pressure has returned to normal, the diameter of the chamber remains enlarged; \(AC\) is the rema—

Fig. 5.

...an alteration of the diameter remains, an elastic after-effect. The magnitude \(AC\) may remain unchanged for a very long time, and may diminish over the course of days and weeks.

It is quite understandable that Bridgman’s experiments required such grades of steel which, even at high pressures, would give absolutely no residual changes and, as far as possible, no hysteresis. With the latter in some cases one can be reconciled, especially if the curves \(AaB\) and \(BbA\) diverge only slightly.

To increase the elasticity of steel it is necessary first to harden it and, under definite conditions, to temper it; in order that such steel be homogeneous, one must not work with very thick cylinders, since otherwise the hardening will not be uniform through the thickness of the metal. Besides the necessity of working with apparatus of small dimensions, such apparatus must also be accustomed to high pressures. By acclimatization one can raise the elastic limit of steel for a certain period. Let us give a few examples from Bridgman’s practice.

A cylinder was made of soft nickel steel. The internal diameter of the channel was \(d = \frac{5}{8}''\). The channel was filled with water; the latter was subjected to a pressure of \(28000\) kg/cm². After removal of the pressure, \(d\) proved to be equal to \(\frac{9}{8}''\). In the given case an enormous elastic after-effect appeared. Upon subsequent applications of pressures not exceeding \(15000\) kg/cm², the cylinder still continued to give residual changes of diameter, though, of course, considerably smaller in magnitude. Such steel is completely unsuitable for the construction of cylinders.

A cylinder was made of chrome-vanadium steel; the internal diameter of the channel was \(d = \frac{14}{32}''\). A pressure of \(30000\) kg/cm² was applied. After removal of the pressure,

\(d = \frac{15}{32}''\). The residual change was \(\frac{1}{32}''\). Upon subsequent applications of pressure up to \(20000\) kg/cm², during 6 months no residual changes of diameter were observed; the cylinder behaved as an entirely elastic body.

In another case a cylinder of the same steel was taken with \(d = \frac{6}{16}''\); after several applications of pressure of \(24000\) kg/cm², the diameter \(d\) became equal to \(\frac{9}{16}''\) and did not change further even under the same pressure of \(24000\) kg/cm².

The best steel for cylinders is chrome-vanadium; with small dimensions and uniform hardening, after acclimatization to high...

pressure, it greatly increases its elastic limit and permits precise work in the direction described here up to 20,000 atmospheres.

It is quite understandable that the high elastic limit attained by conditioning is rather unstable; it must be used at the very first opportunity (after a prolonged rest the cylinder must again be conditioned). Nor may rapid and sharp jumps in pressure be allowed in such a cylinder. These complications are especially unpleasant and considerable in thick-walled cylinders that have been nonuniformly hardened. Here one observes a whole series of irregularities in the behavior of the metal at high pressures, including, among other things, phenomena of metal fatigue and peculiar delays in the reaction. For example, in one such case, after the pressure was removed, a residual change in diameter was found. But in the first moments of the new application of pressure the diameter of the channel decreased as the pressure increased. It was as though, when the pressure was first removed, the molecules became stuck and did not return to their original position; the new increase in pressure shook up the molecules, and they went back and only then behaved properly.

As regards the thickness of the cylinder walls, experiment has shown that the outer diameter \(d\) of the cylinder must exceed the inner diameter \(d'\) by 6–10 times. If \(d\) is more than \(d'\) by a factor of 4, then the cylinders, as a rule, produce cracks after conditioning1.

In general, it should be noted that not every piece, even one that upon careful inspection proves to be good, will yield a satisfactory cylinder; about 20% of cylinders produce the finest cracks, through which the liquid transmitting the pressure leaks out (see below).

A very difficult matter in constructing complex instruments consisting of 2–3 cylinders is the selection and arrangement of the tubes connecting the cylinders. Up to 1000 kg/sq. cm copper tubes may be used; from 1000 to 7000 kg/sq. cm, commercial steel ones; from 7000 to 12–13,000 kg/sq. cm, one must make the tubes oneself. At still higher pressures no tubes withstand the test; the entire instrument has to be constructed in the form of a single cylinder. For specialists, the details of the connection of the tubes, the type of gasket, the size of the threaded end, the thickness of the tubes, and so on are very interesting. We shall indicate only that tubes with an outer diameter \(d = \frac{1}{4}''\) and an inner diameter \(d' = \frac{1}{16}''\), with a thread of 32 threads over a length of \(\frac{5}{16}''\), withstand pressure excellently up to

12000 kg/cm² at room temperature, and at 200° already at 7000 kg/cm², develop cracks and burst. For higher temperatures one has to prepare tubes with \(d=\frac{3}{4}''\) and with special gaskets. Of interest is an attempt, ending in failure, to construct an apparatus from two cylinders with a tube connecting them, made from one solid piece of steel and with subsequent boring of the tube. Such apparatuses invariably developed cracks at 200°.

Bridgman works in a virgin region of high pressures; it is therefore quite understandable that he has to discover entirely new phenomena, often only incidentally. In reading his works one sees that much was noticed by him, but far from studied, and much was investigated only for the immediate purpose of constructing apparatuses. Among such questions that were little studied is the question of the behavior of liquids transmitting high hydrostatic pressure. For transmitting low pressures a mixture of water and glycerin is very convenient; at somewhat higher pressures glucose is added to this mixture in order to reduce the rate at which viscosity increases with pressure. In rare cases viscous oils are resorted to in order to reduce seepage. Under Bridgman’s pressures it was necessary to resort to readily mobile liquids, kerosene and gasoline. The viscosity of these liquids at high pressures can be judged from the rate of transmission of hydrostatic pressure. Kerosene and gasoline, at pressures above 12–15000 kg/cm², transmit pressure through tubes with an internal diameter of \(\frac{1}{16}''\) within 1–3 hours; apparently their consistency under such pressures resembles the consistency of Vaseline under ordinary conditions.

The question naturally arises whether pressure can be transmitted with the aid of mercury. After all, mercury does not form an amalgam with iron when these metals are in direct contact. The answer to this question was already given by Amagat’s experiments. Namely, Amagat observed the interesting phenomenon of mercury seeping through solid cylinder walls; in some cases mercury passed through the walls in little streams, and nevertheless no crack could be detected in such a wall even under the microscope. Bridgman observed phenomena of this kind not only at comparatively low pressures, but also at high ones.

The behavior of mercury in steel cylinders depends very substantially on the type of steel, in particular on its hardening. We must distinguish steels with a low elastic limit (soft grades) and with a high one (hard grades). In cylinders made of soft grades ...

steel, water and mercury began to behave in the same way1. Matters stand quite differently in the case of cylinders made of hard grades of steel (tool and nickel steel). Such cylinders withstand perfectly a pressure above 20,000 kg per sq. cm if the pressure is transmitted by water; when, however, the pressure is transmitted by mercury, these cylinders invariably develop cracks and burst already at 3,000–4,000 kg per sq. cm.

The explanation of this phenomenon lies in the conditions of amalgamation. Before Bridgman we knew that, when perfectly pure iron (or steel) is brought into direct contact with mercury, amalgamation does not occur; an amalgam of iron could be obtained only by electrolytic means. Bridgman’s experiments showed that pieces of any kind of steel, thrown into mercury and kept under mercury, do not amalgamate either at elevated temperatures or at high pressures. In these experiments the pieces of steel experienced a uniform pressure over the whole surface.

It turned out, however, that steel of every kind is instantaneously amalgamated if it is broken under mercury; but if the steel is quickly broken above the mercury and the broken pieces are immediately thrown into mercury, amalgamation does not occur. Insignificant traces of air on the surface of the steel completely deprive it of the capacity to form an amalgam. If now a piece of steel amalgamated on the surface of the fracture (under mercury) is placed in mercury and subjected either to the action of an elevated temperature (up to 180°) or to the action of a high pressure (up to 6000 kg per sq. cm), then the process of amalgamation continues inward; in some grades the whole piece is amalgamated through and through, while in other grades the amalgamation proceeds sluggishly and not deeply.

The study of the fractures of cylinders that had burst when pressure was transmitted by mercury showed that inside the wall of the cylinder, in separate and irregular regions, the process of amalgamation had occurred, and that the crack had passed through one of these regions. The process of amalgamation precedes the formation of the crack. How, then, is the difference in the behavior of cylinders made of soft steel and of hard steel to be explained?

Here we must briefly set forth the results of another (also incidental) work of Bridgman’s on the change in the dimensions of cylinders subjected to one-sided pressure through the internal cavity (from the inside outward). Bridgman’s theory and experiments showed that the volume of the cylinder wall increases with increasing pressure inside the cavity up to the point at which the deformation of the cylinder is completely elastic;

this volume decreases if the pressure is above a certain limit, beyond which the deformations become inelastic.

As the volume increases, the pores of the metal, the spaces between the molecules, increase, “open up.” As the volume decreases, these pores “close.”

In order for the process of amalgamation of the steel to begin in the walls of the cylinder, a certain size of pores is necessary, through which mercury molecules can pass under pressure. In the case of soft steel, the pores begin to close too early (at sufficiently low pressures). In the case of hard steels with a high elastic limit, the pores reach the necessary size at pressures below the limiting ones, owing to which the mercury is drawn into the steel, where the process of amalgamation begins, very rapidly weakening the steel.

II.

Secondary manometers.

Primary manometers are inconvenient for constant use; Bridgman therefore, immediately after constructing the primary manometer, set himself the aim of constructing a secondary manometer. The latter must satisfy several conditions, chiefly allowing pressure readings to be taken accurately, without error, and quickly. The idea of a secondary manometer consists in the fact that we measure some property of the system chosen by us; the dependence of this property on pressure must be precisely determined once and for all, and from the magnitude of this property we judge the magnitude of the pressure. In the so-called Bourdon manometers, with pressure the position of the upper end of a spirally coiled metal tube, filled with air and connected with the pressure chamber, changes; the lower end of such a tube is fixed immovably. Bridgman’s experiments showed that the Bourdon manometer can be used up to 2000 atmospheres; at higher pressures hysteresis phenomena begin to appear in the readings of the manometer, and in the manometer studied by Bridgman the error in the readings reached as much as 4% in the range up to 4000 kg/cm² and up to 40% in the range up to 8000 kg/cm². It is quite understandable that by careful selection of the material for the tube the error can be reduced, but it can hardly be brought to nothing. Furthermore, the influence of the time during which the manometer is kept at high pressure must also make itself felt here. In a word, the Bourdon manometer is altogether

...is completely unreliable for pressures above 3000 atmospheres in more or less precise experiments1.

Bridgman rejected the Bourdon manometer by virtue of yet another secondary consideration, which had guided him in his first investigations of the secondary manometer. The Bourdon manometer must be graduated, i.e., with the aid of a primary manometer the values of its readings must be determined. Meanwhile Bridgman set himself the high goal of constructing such a secondary manometer whose readings, once determined by Bridgman for one specimen, would be fully suitable for any other. An investigator working after Bridgman in this field would not need to construct a primary manometer; it would be sufficient to construct a secondary one and to make use of the tables of values determined by Bridgman. For such a purpose the most suitable, it seemed, would be the electrical resistance of a mercury column, but not of metallic wires. The fact is that metallic wires are not uniform in their properties; the properties of different parts of one and the same piece of wire, throughout and side by side, may differ within measurable limits; and wires of one and the same metal, prepared at different times, especially by different factories, may even differ very noticeably. A different matter was a mercury column. There can be no doubt that different investigators can prepare pure mercury with completely identical properties. If the dependence between pressure and the electrical resistance of mercury were precisely known, then it would be sufficient to construct an instrument in which the resistance of a mercury column could be determined; from the magnitude of such a resistance we could calculate the pressure, without resorting to the aid of a primary manometer, complex and difficult to construct.

Bridgman’s experiments in this direction were not crowned with success. The first major difficulties—the construction of the pressure chamber in which the mercury column and the electrodes are placed, and the construction of the insulating bolt through which the wire from one of the electrodes is led out—were solved by him brilliantly. Especially much labor was required by the construction of the insulating bolt for high pressures. However, the stumbling block proved to be the construction of glass instruments for mercury. Figure 6 shows the final and most successful form of such an instrument. A—glass pro-

Fig. 6.

a vessel filled with mercury, \(B\)—a glass capillary, terminating at the top in an expansion into which the electrode \(b\) is inserted, \(a\)—the second electrode. Correct filling of the capillary is very troublesome, but quite feasible. The electrical resistance which is observed when an electric current passes from \(a\) to \(b\), as is quite understandable, can be attributed wholly to the resistance of the mercury column in \(ii\) (the diameter of the capillary is \(0.1\) mm). The experiments described by Bridgman provided abundant numerical material on the electrical resistance of liquid and solid mercury at different temperatures and pressures, and made it possible to determine very accurately the freezing temperatures of mercury at different pressures; but at the same time it turned out that the electrical resistance of mercury cannot be used for the purposes of a secondary manometer. The dependence of electrical resistance on pressure is very complex; of course, this circumstance cannot serve as an obstacle for manometric purposes, since one could compute very detailed tables for practical needs. The principal obstacle is the enormous fragility of glass capillaries at high pressures, while the decisive obstacle proves to be the fact that mercury freezes at ordinary temperature if the pressure is greater than \(7000\) kg/cm\(^2\).

After the failure, thus revealed, of constructing a secondary mercury manometer, Bridgman returned to the idea of determining pressure from the magnitude of the electrical resistance of metallic wires. Manganin wire proved the most convenient. According to Liseell’s experiments, the electrical resistance of manganin wire varies linearly with pressure up to \(4200\) atmospheres. Bridgman found a strictly linear dependence up to \(13000\) kg/cm\(^2\). At the same time it turned out that, up to \(30000\) atmospheres, the electrical resistance exhibits neither hysteresis phenomena nor after-effect phenomena. The effect of temperature on the electrical resistance of manganin wire is insignificant; if \(\Delta R\) is the increase in electrical resistance when the pressure is raised by \(1\) kg/cm\(^2\), \(R_0\) is the resistance at ordinary pressure, and \(p\) is the pressure, then for manganin wire the coefficient \(\dfrac{\Delta R}{pR_0}\) at \(0^\circ\)—\(12^\circ\) is equal to \(2301 \cdot 10^{-9}\), and at \(50^\circ\)—\(2295 \cdot 10^{-9}\). A manometer made of manganin wire is extremely convenient not only because of the ease and speed of determining the electrical resistance of the wire, the simplest dependence of resistance on pressure, and the small temperature coefficient, but also because of its portability. The entire part of the manometer which is located in the pressure chamber consists of a piece of wire \(3\)—\(4\) meters long, wound in the form of a toroid and consequently requiring very little space in the cavity of the cylinder. One end of the wire is soldered

to the outer side of the insulating bolt, while the other is led through the bolt.

Since the electrical resistance of the wire varies somewhat from piece to piece, each secondary manometer that is constructed must be graduated and checked against a primary manometer. After Bridgman had studied the properties of water at high pressures, he succeeded in finding three points that are easily reproducible experimentally and whose coordinates he determined exactly, namely: the freezing point of water at \(0^\circ\) and ordinary pressure; the transition point of ice I into ice III at \(2120\ \mathrm{kg}/\mathrm{sq.\ cm}\) and at a temperature of \(-22^\circ\) (this pressure does not change when the temperature varies from \(22^\circ\) to \(-30^\circ\), and keeping the thermostat accurate to within a few degrees presents no difficulty); and the freezing point of water into ice VI at \(0^\circ\) and \(6370\ \mathrm{kg}/\mathrm{sq.\ cm}\). Having determined the electrical resistance of a given piece of wire at these three points, and knowing the linear character of the dependence of resistance on pressure, we determine, by interpolation, the entire scale of readings of our secondary manometer, without resorting to the services of the primary manometer.

For the purposes of the method, Bridgman carried out another major piece of work, which also has independent interest. The aim was to determine the coefficients of compression of a number of solid bodies, chiefly various grades of steel and glass.

Figure 7 shows an apparatus constructed by Bridgman for this purpose. \(AA\) is a thick-walled steel cylinder with an internal

Fig. 7.

channel, with enlargements at the ends to receive connections to the manometer and to the source of pressure1. On the cylinder there are two marks \(H\) and \(I\), whose positions are determined with microscopes. The empty cylinder is filled with liquid and connected to the source of pressure. Under the influence of pressure from inside outward, the cylinder lengthens; the magnitude of this elongation is calculated from the displacements of the marks \(H\) and \(I\). At \(6000\ \mathrm{kg}/\mathrm{sq.\ cm}\) the elongation was \(0.02\ \mathrm{m}/\mathrm{m}\). It is very important and interesting that this elongation possesses a small but unmistakable hysteresis: the elongations are greater at decreasing

pressures. The existence of this hysteresis is all the more surprising because the elongation of the cylinder amounts to \(\frac{1}{30}\) of the (calculated) value of the elongation at the elastic limit.

After determining the elongation of the cylinder, its channel is very carefully washed out with a stream of water, and the rod to be investigated is inserted into it. By means of suitable devices, the end \(B\) of the rod is held in a fixed position, while the end \(F\) is movable. This latter end is shown on an enlarged scale in Fig. 8. A bronze ring \(G\) with a mark \(M\) is fitted sufficiently tightly onto the end of the rod. On the rod itself there is the mark \(L\). Grooves run along the rod, through which liquid is transmitted from one end of the cylinder to the other. Under the influence of pressure the rod contracts; owing to the shoulder of the cylinder, the ring \(G\) cannot move to the left together with the contracting rod, and remains in place. After the pressure is removed, the rod expands to its former length, and since the ring has been fitted sufficiently tightly, it is carried to the right by the expanding rod.

Fig. 8.

The increase in the distance between the marks \(L\) and \(M\) gives us the apparent contraction of the rod; by introducing a correction (among other things, for the elongation of the cylinder), the coefficient of compression of the rod is calculated. A metallic rod 30 centimeters long, when the pressure is increased by 1000 kg/sq. centimeter, is shortened by 0.05 mm.

It is interesting to note that steel rods do not give residual changes of length; an aluminum rod, after the first experiments, gives a residual shortening equal to \(\frac{1}{30000}\) of its length. Up to 6500 kg/sq. cm, compression varies almost linearly with pressure.\(^{1}\)

\(^{1}\) The coefficients of compression found were:

From the boiler steel, rods were prepared along the direction of rolling \((\parallel)\) and in a direction perpendicular to it \((\perp)\). Hard-melting glass is compressed more strongly than easily fusible glass and, incidentally, is very easily crushed at high pressures.

“(and does not decrease, as in liquids); in aluminum one even observes a tendency for the compression to increase with pressure.

By the same “ring” method, Bridgman determined the coefficient of compression of liquid mercury. But these were only preliminary experiments; subsequently he developed new methods for liquids, much more perfect. We shall now turn to a description of these methods and of the results obtained by them. ^1)

(Continued in the next issue ^2).)

^1) Reported at the Physical Colloquium of the Moscow Scientific Institute.
^2) The literature of the subject will be indicated at the end of the survey. (Ed.)

1. The length of the cylinder is \(18'' = 45.7\) centimeters; the outer diameter is \(2''\), the inner diameter is \(\frac{3}{8}''\); the length of the rod under investigation is about 30 centimeters. ↩↩↩↩↩