TRANSACTIONS OF SECTION A. 257 



These expressions cannot be integrated, since we are ignorant of the laws 

 according to which V 3 , V 2 , and I are distributed round the origin. But the form 

 of the series which will express them can be obtained on the hypotheses that the 

 gas is perfect, and that CI and K are capable of being expanded in integer powers 



of — . The expressions which result are 



- p ^-=AU + BU 3 + &c (1) 



p = A'U 2 + B'U 4 + &c (2) 



p = A"W 2 + B"W 4 + &c . . . . (3) 



. TT , , . P e„ldT, ^, ^ r , . VaM.Q, , 



where U stands for -^- p -^ and W stands for p ,~ the coefficients A, B, 



&c, being numerical quantities, the same in all ' perfect ' gases, which remain to be 

 determined by experiment. In these equations G is the flow of heat, K the polari- 



sation stress, P the tension of the residual gas, T its temperature, -j- the rate at 



which the temperature decreases across the layer, T and P standard temperature 

 and pressure, e„ the mean free path of the molecules at standard temperature and 

 pressure, cr the specific gravity of the gas compared with a standard gas (say 

 hydrogen), and M a standard mass (say one gramme). 



The method by which the foregoing expansions were obtained is believed to be 

 new. The expressions for G and K must be compatible with any change in the 

 gas which is consistent with its continuing a ' perfect ' gas. Accordingly a succes- 

 sion of such changes was conceived as happening, and the forms under which 

 P, o-, T, e, must enter were thereby successively determined, the final determina- 

 tion being made by the condition of homogeneity. 



The first term of expansion (1) is the approximate expression which Clausius 

 found for the flow of heat ; and the first term of expansion (3) is the approximate 

 expression which the author of the present communication found for the polarisa- 

 tion stress. Acccordingly the approximate expressions which had before been 

 known prove to be the first terms of the complete expansions. 



9. On the Action of Magnets on Liquid Jets. 

 By Professor Silvanus P. Thompson, B.A., D.Sc. 



In studying the phenomena of the voltaic arc, the author has been led to inquire 

 into the actions produced by magnets upon movable conductors, such as jointed 

 wires, flexible metallic leaves, liquid conductors, gases in high rarefaction, flames, 

 and liquid jets, traversed by currents. 



Nearly all the phenomena of rotations and translations due to electrodynamic 

 and electromagnetic attraction or repulsion have been demonstrated to hold good 

 for liquid conductors, both those which possess metallic conductivity and those 

 which possess only electrolytic conductivity. Davy, Oasselmann, and Walker have 

 shown the electric arc to behave as a mobile conductor. Pliicker and De la Pave, 

 and more recently Grookes, have observed the existence of these electro-dynamic 

 actions on the luminous discharges in highly rarefied media, and which appear to 

 be electric convection currents rather than electric currents proper. 



The author has examined the case of liquid veins, both of dilute acid and of 

 mercury traversed by currents, and finds that these, when subjected to the action of 

 powerful magnets, exhibit analogous motions of translation, rotation, &c. Thus a 

 liquid vein carrying a current between the poles of a horizontal horseshoe electro- 

 magnet no lunger falls straight but is thrust aside and falls down an inverted curve. 

 A vein falling in front of the pole of a vertical magnet is likewise drawn aside, 

 1879. s 



