of Electrical Conductivities* 85 



recommended in which, of the four angles of a long side-face, 

 two adjacent to a long edge are connected with the battery, 

 and the two others with the galvanometer-wire : the electrode 

 surfaces 1, 2, 3, 4 are then the octants of four infmitesimal- 

 sphere surfaces whose centres are in the four angles mentioned. 

 This method is very convenient in execution, and is also inter- 

 esting inasmuch as it is an application of the beautiful theory 

 of the propagation of a current in a rectangular parallelepi- 

 pedon. 



Mr. Greenhill* has already, for the potential in a point of a 

 rectangular parallelepipedon, to which electricity flows through 

 one point and is withdrawn through a second, constructed an 

 expression which can here be taken for a starting-point. Let 

 the point of an angle of the parallelepipedon be the origin of 

 coordinates, let the edges proceeding from it be the axes of 

 coordinates, a, b, c the lengths of the edges, w 1} y 1} z 1 the coor- 

 dinates of the positive, # 4 , y 4 , z 4 the coordinates of the nega- 

 tive electrode; further, let the intensity of the current be = 1, 

 and k be the conductivity of the parallelepiped ; then the po- 

 tential <£ in reference to the point («£, y, z) is 



where 



Fi - vK^r' wr^Ksr &)) 



F 4 results from F x when the index 4 is substituted for the 

 index 1, and 



6 z (w,r)=l l e v ^ w+v ^ 7ri , 



the sum being taken so that all the whole numbers from — oo 

 to + oo are put for v. 



By employing the partial differential equation which is 

 satisfied by the 6 functions it can be demonstrated, in the way 

 marked out by Mr. Greenhill, that the hereby defined function 

 (f> satisfies the partial differential equation which it ought to 

 satisfy; it can further be shown that the boundary-conditions 

 and the conditions of constancy are fulfilled which hold for </>, 



* Proc. Camb. Phil. Soc, Oct. to Dec. 1879, p. 293. 



