suppose. The effect moreover is particularly marked if the telephone is open, i.e. with no connection between the clamps. The stray vibrating field produced by a small electromagnet (say inch iron, 2 inches long) is thus quite audible even beyond 50 cm. from the electromagnet. The degree of response depends moreover on the orientation (fig. 6) of the telephone relative to the electromagnet E. If we take the three cardinal positions of the plane of the coil or the diaphragm, the vertical positions e, d, f, and the fore and aft horizontal positions h, g, i, have their maximum response in the plane of symmetry g d E. The right and left horizontal positions d", b, a, c, d', give minimum response (telephone silent) in this plane (E, a), with maxima at symmetrical positions, b and c. A convenient reversal of magnetic field is thus obtained.

Although all telephones show the phenomenon pretty well, since it is more distinct on open circuit (which implies a current oscillating from damp to clamp) it would be well worth while to wind a telephonic bobbin provided with a capacity for the particular purpose of catching the stray magnetic field, such as is here encountered. Without proceeding to this extent, I used the telephone as a secondary as shown in figure 7, where E is the electromagnet of the interruptor I, s being the vibrating break circuit spring. The telephone depending adjustably from the sleeve a may be slid right and left or rotated into any horizontal position relative to E, and the current obtained measured by the vibrator.

In the endeavor to minimize the mechanical coupling, the telescope (separately mounted) was placed at about a meter from the vibrator. In this case the phase difference of the vibrations of fringes and objective was annulled, but the bands in the absence of current were nevertheless somewhat oblique to the direction of the vibration of the objective, showing that the fringes still vibrated.

With this exception the behavior of the telephone inductor was admirable. In passing from the positions b to c by sliding the telephone, the ellipses regularly passed through the oblique bands, indicating that these successive ellipses, even if of nearly equal size, were opposite in their phase rotation. This was the case when the secondary was closed with 5000 ohms and the inevitable inductance; also when a capacity was placed in the secondary and finally on passing from an inductance to a capacity in the secondary. The effect produced by changes of capacity of 0.5 microfarad was marked. The alternate-current effect, moreover, was still apparent when the circuit was closed with 25,000 ohms and the telephone practically silent.

The most direct criterion as to changes of phase is the rotation of ellipses as indicated in figure 8. I shall give a few examples of what is observed in the telephone displacement in question.

In the absence of current the fringe bands were nearly horizontal parallel lines. The secondary was closed with 5000 ohms and the inductance of the three telephones. From the position b (ellipse 1, figure 8 quiescent) the inductor telephone was quickly displaced to position c. The enormously eccentric, finally linear ellipse, 2, follows, which then rotates and contracts counterclockwise through the figures 3 and 4 into the sharp bands (usually but not always) no. 5. These duplications then separate on further rotation into the final quiescent form, 7. The arrows indicate the drift of one of the four points of tangency. On returning from c, by quickly sliding the telephone inductor into the position b, the figures roll clockwise from 7' to 1'. Number 7' passes at once through the highly eccentric ellipse 6', though in other slower adjustments intermediate sharp duplicates like 5 may be detected between 6' and 7'. The stretched ellipses, which follow immediately after the change of aspect of the telephone bobbin to the magnetic lines, are noteworthy. They result from the sudden reversal of the magnetic field in spite of the vibration. Ellipses cross over or change sign of rotation at 2 and 6', but not near 3'or between 5, the latter being oscillations. The corresponding cases for capacity, were similar on the whole, though less pronounced. Moreover the first and final forms were not quite in opposed phases.

10. Narrow bifilar.-After obtaining the favorable results just described, it seemed obvious that the sensitiveness could be further increased by diminishing the distance between the bifilar wires. Accordingly, with the same inductor, figure 4, the above wires (diameter 0.023 cm.) were adjusted at but 1.5 cm. apart by decreasing the diameter of the lower pulley. A few other modifications were added. The results however were disappointing throughout.

A final observation may be added. The auxiliary audible telephone responded with about equal loudness when the telephone circuit was closed with 400 ohms and when a condenser of 1 microfarad capacity was inserted. But the vibrator reacted in the former case (resistance and selfinduction) with a deflection of 23 scale-parts, whereas in the latter (capacity) the response was at most 2 scale-parts; and this required a slightly different tension of wire. The metallically closed circuit therefore affected the vibrator at least 12 times more strongly than the oscillation due to the capacity of 1 microfarad. Small capaci

ties like 0.1 microfarad fail to influence the vibrator though to the ear the sound is quite loud. The capacity should have to be increased to 10 or 20 microfarads for equal effects on telephone and vibrator. In another experiment the closed circuit gave 20 scale-parts. The insertion of 4 microfarads decreased this to 4 scale-parts, which is again a demand of about 20 microfarads for an equality of behavior. On the other hand, while the telephone responds for a phenomenally small capacity, it soon ceases to increase in loudness (for 1, 2, 3, 4, mf., or resistances), whereas the deflections of the vibrator increase regularly.

1 Advance note from a Report to the Carnegie Institution of Washington, D. C. 2 These PROCEEDINGS, 5, 211-217, (1919).

These PROCEEDINGS, 4, 328–333, (1918). Carneg. Publ. No. 249, 3, 1919, chap. v.

ON THE PRESSURE VARIATION OF SPECIFIC HEAT OF

LIQUIDS

BY C. BARUS

DEPARTMENT OF PHYSICS, BROWN UNIVERSITY

Communicated June 13, 1919

1. Introductory.—The measurement of the specific heat of a liquid in its relation to pressure is surrounded by so many difficulties, that any method which gives a fair promise of success deserves to be carefully scrutinized. During the course of my recent work on interferometry, I have had this in view, and the plan which the present paper proposes is particularly interesting as it seems to be quite selfcontained. 2. Equations. If 0, p, p, c, denote the absolute temperature, the pressure, the density, and the specific heat at constant pressure, respectively, of the liquid, and if a' (dv/v)/de is its coefficient of volume expansion, the relation of these quantities may be expressed by the well known thermodynamic equation

=

where J is the mechanical equivalent of heat, and the transformation is along an adiabatic. The main difficulty involved would therefore be the measurement of the temperature increment; for dp could be read off on a Bourdon gauge after a partial stroke of the lever of my screw compressor, with facility. It is my purpose to find de by the displacement interferometer. To fix the ideas; suppose the liquid in

question is introduced into a long steel tube TT, figure 1, and that the tubulure p conveys the increments of pressure dp. The end p is rigidly fixed. The other end q of the tube is free to move. By aid of the stylus, e, the elongation is registered on the plate n of a contact lever read by interferometry, the lever being identical in construction with the apparatus described in my paper on magnetic elongation. Thus the interferometer will indicate the elongations due both to the pressure increment and to the corresponding temperature increment of the suddenly compressed liquid, and it becomes a question to what degree the two may be adequately separated. If Al, AP, Ao are corresponding increments of the length, 1, of the tube and the

pressure and temperature of its liquid content, we may write successively,

where a is the coefficient of expansion, k the bulk modulus, r1 and r2 the internal and external radius of the steel tube of length 7. Hence

Hence c may be found from observations of Al and Ap, provided a' and p, a and ẞ are sufficiently known.

3. Measurement of the Pressure Coefficient B. For this purpose the tube TT, figure 1, is placed in a water jacket of constant temperature, and ẞ found by internal pressure, directly. Experiments of this kind were contributed with some detail in an earlier paper. The method then used consisted in finding ẞ from the displacement of the spectrum ellipses under known conditions; but the present method of the contact lever and achromatic fringes may be considered preferable, particularly if the tube contains water, for which the thermal discrepancy is small. Moreover, since A0 is primarily aimed at, ẞ should be made as small as possible. This may be done by selecting relatively thick walled tubes of small external diameter. A few data are here desirable. Using an ocular micrometer plate 1 cm. long with scale parts of 0.01 cm. each and fringes of moderate size (one or two scale parts in width) we may write as in the preceding paper (1. c.)

where Ae is the displacement of the achromatic fringe on the ocular scale corresponding to the elongation Al/l.

Hence for steel tubes (k = 1.8 X 1012) the following data apply

4. Measurement of a. For this purpose the tube TT is to be clean and empty, the nozzle p removed and a long-stemmed thermometer passed from end to end of the tube, through the end p. Externally the tube is surrounded by a coil of wire for electric heating and appropriately jacketed. Measurements made in this way with a brass tube are given in figures 2 and 3 and they would have been quite satisfactory if the tube had been properly protected from loss by radiation. (AN is read off on the displacement micrometer at an interferometer mirror; Ae in the ocular scale).

If for the steel tube, a = 10-5 × 12, equations (3) and (6) then give us