TRANSACTIONS OF SECTION A. 571 



'p-v-^-'--\[j-^^^y-^^y^ (17) 



and, eliminating u, v, w, "^ by tliis from (10), we find, on the assumption of k 

 constant, 



''|vV=£-'«'VV (18) 



The settlement of boundary conditions, when a finite piece of solid conductor 

 is the subject, involves consideration of u, v, w, and for it, therefore, equations 

 (17) and (12) must be taken into account; but when the subject is an infinite 

 homogeneous solid, whicli, for simplicity, we now suppose it to be, (18) suffices. 

 It is interesting and helpful to remark that this agrees with the equation for the 

 density of a viscous elastic fluid, found from Stokes's equations for sound in air 

 with viscosity taken into account; and that the values of u, v, w, given by (17) 

 and (10), when p has been determined, agree with the velocity components of the 

 elastic fluid if the simple and natural enough supposition be made that viscous 

 resistance acts only against change of shape, and not against change of volume 

 without change of shape. 



For a type-solution assume — 



p=AE-'"co3^-Hcos?!;^cos?!!^ (19) 



a b e 



and we find, by substitution in (18) — 



r-~<i+'^=o (20) 



where — 



L- = l/47r=C-L + JL+ l^ (21) 



Hence, by solution of the quadratic (20) for q — 



,=,^{>,^(:-£^)} (.., 



[In the communication to the Section numerical illustrations of non-oscillatory 

 and of oscillatory discharge were given.] 



7. Five Applications of Fourier's Law of Diffusion, illustrated by a Diagram 

 of Curves with Absolute Numerical Values, By Professor Sir William 

 Thomson, LL.D., F.E.S. 



1. Motion of a viscous fluid. 



2. Closed electric currents within a homogeneous conductor.' 



3. Heat. 



4. Substances In solution. 



'This subject is essentially the 'electro-magnetic induction' of Henry and 

 Faraday. It is essentially different from the ' diffusion of electricity ' through a 

 solid Investigated by Ohm in his celebrated paper ' Die Galvanische Kette mathe- 

 matisch bearbeitet,' Berlin, 1827 ; translated in Taylor's ' Scientific Memoirs,' vol. ii. 

 part viii., ' The Galvanic Circuit investigated Mathematically,' by Dr. G. S. Ohm. In 

 Ohm's work electro-magnetic induction is not taken into account, nor does any idea of 

 an electric analogue to inertia appear. The electro-motive force considered is simply 

 that due to the difference of electrostatic potential in different parts of the circuit, 

 unsatisfactorily, and even not accurately, explained by what, speaking in his pre- 

 Greenian time, he called ' the eletroscopic force of the body,' and defined or explained 

 as ' the force with which the electroscope is repelled or attracted by the body ; ' the 

 electroscope being ' a second movable body of invariable electric condition.' 



