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The following points may be noted:

1. The transversal effect is smaller when the current of heat is parallel to the crystallographic axis than when it is at right angles.

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Fig. 6.

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2. In the first case negative values are obtained at a mean temperature of 73° C., similar to those found by v. Everdingen and Yamaguchi for electrolytic bismuth.

3. Whereas Yamaguchi found the transversal effect for electrolytic bismuth to increase continuously as the temperature sank, I find for crystalline bismuth for low temperatures and large field-strengths a diminution of the effect.

§ 7. The Thermoelectric Force.-The potential-difference between the two coppers D and E (fig. 3) gives the thermoelectric force for copper-bismuth for a temperature-difference shown by the iron-constantan thermo-elements d and d'. These temperatures were determined before and after the measurement of the electromotive force, the difference of temperature being produced in exactly the same way as described in § 4.

Tables VII. and VIII. contain the results for the range 0° to -70°, parallel and perpendicular to the chief crystallographic axis respectively. The thermoelectric force is reckoned positive when the current flows from the bismuth to the copper through the junction at the higher temperature.

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The results can be represented by the formula

e=a(t1—t2)+B(t12 — t22),

where t t are the temperatures of the two junctions in degrees centigrade, e the corresponding thermoelectric force in microvolts. a and B were calculated by the method of least squares. From the calculated values of a and B neutral temperatures should occur at -185°-8 and -80°.9 respectively.

From determinations, however, at temperatures produced

by the application of liquid air the curve appears to be discontinuous, as will be seen from the following data :

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:

e calculated from
a=1302, p=0·3504.

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Data for temperature-intervals between -80° and -160° were sought by stopping the current of water in G and observing the thermoelectric force as the temperature of d' fell. The fall of temperature was, however, too rapid for one to commute accurately the curve between these limits (the temperature changing in some cases by as much as 3° during the time of observation of the thermoforce). The results are given below; they serve at least to show that the neutral temperature in the first case is higher than -185°8.

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The discontinuity in the curve at low temperatures was found by Fleming and Dewar* for both pure and commercial bismuth. Their sample of pure bismuth was not obtained, however, by electrolytic deposition; and I am not aware of any determination of the thermoelectric force for an electrolytically prepared specimen of bismuth. It would be of importance to know this, as the discontinuity may be due to impurities.

Perrot has already determined the thermoelectric force in the same directions with relation to the axis, as in this work, the range of temperature being from 10° to 100°. For purpose of comparison the thermoelectric force for the present crystal was determined over a similar temperature

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1. Parallel to the crystallographic axis:

t1=1207; t=91°; e=9267 microvolts,
or 118.35 mv. per 1°.

2. Perpendicular to the crystallographic axis :
t1=15°3; t2=85°•9; e=4377 microvolts,
or 61.94 mv. per 1o.

Ratio = 1.91.

Perrot found the ratio to several prisms used by him. the best gave the ratio 2.00.

vary from 1.85 to 2:10 for the The specimens he considered

My best thanks are due to and encouragement during the progress of this work. Physical Institute, Berlin University.

Prof. Warburg for suggestions

* J. A. Fleming and J. Dewar, Phil. Mag. xl. p. 95 (1895).
† Perrot, Arch. des Scien, phys. et nat. Aug. 1898.

Phil. Mag. S. 6. Vol. 2. No. 10. Oct. 1901.

2 A

XXXIV. On the Laws of Viscosity. By LADISLAS NATANSON, Professor of Natural Philosophy at the University of Cracow*.

THE

HE fundamental conception on which the present investigation is based is due to Poisson †. Consider a fluid, originally in equilibrium, which is subjected to a deformation. According to Poisson, the fluid, in order to adapt itself to the deformation impressed upon it and arrive, even approximately, at a new state of equilibrium, requires a certain time which, for different substances, is of very different duration. The period of transition is characterized by inequalities of pressure which, called into play by the deformation, tend to disappear of their own accord, but a complete disappearance of which does not take place until the new state of equilibrium has become fully established. Thus Poisson succeeded in bringing into prominence an intricate phenomenon, termed relaxation, which is only one example of that fundamental property possessed by matter but not by the luminiferous æther, of the "constraint" of perturbations produced in its interior ‡.

The reality of the phenomenon of relaxation has, after Poisson, been admitted by Sir G. G. Stokes §, as well as by Clerk-Maxwell, who, in his memoir || on the kinetic theory of gases, has made a detailed study of it. Maxwell, however, in the course of some general considerations which serve as an introduction to the memoir to which we have just alluded, has shown how the conception of Poisson may be reduced to its essential features. In our studies on this subject, we have tried to develop this method of Maxwell's, which is purely descriptive and independent of any hypothesis. On account of this method, Poisson's ideas regarding the nature of the fluid state appear to us to be destined to play an important part in the dynamics of viscous bodies. It will be seen, in fact, from what follows that they lead to a generalized Translated from the Bulletin de l'Académie des Sciences de Cracovie, February 1901. Communicated by the Author.

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† Mémoire sur les Equations Générales de l'Equilibre et du Mouvement des Corps solides élastiques et des Fluides, lu à l'Académie des Sciences le 12 Octobre, 1829. Journal de l'Ecole Polytechnique, xx. Cahier, tome xiii., Février 1831.

Bulletin international de l'Académie des Sciences de Cracovie, Année 1893, p. 348; Année 1894, p. 295; Année 1896, p. 117; Année 1897, p. 155.

§ Transactions of the Cambridge Philosophical Society, vol. viii. p. 287 (1845); Mathematical and Physical Papers,' vol. i. p. 75 (1880).; || Philosophical Transactions, vol. clvii. p. 49 (1867). Scientific Papers, vol. ii. p. 26 (1890).

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