80 Prof. G . Kirchhoff on the Measuring 



and thus proved that the potential in question must, to within 

 an additive constant, bo equal to the expression adduced. 



In order to obtain the value of </> which corresponds to the 

 arrangement described above, let us put 



#i=0, ?A =0, *-0. 



#4 = 0, 3/4 = 0, z±=c. 



Taking advantage of the circumstance that 



O s (io±i, t) = S(-1)V( 2w +^-=6> ^, t), 

 we get 



*.-*-*& SHfe 5) Hb £)-*& SD> 



or, since 



6 3 (w, t)-0 q (w, t) = 26 2 (2w, 4r), 



*=wf".&S)».(S' 8K-5D* 



To find the resistance denoted by p, we have to form the dif- 

 ference of the values taken by this expression for 



«r=a, y=0, z — 0, 

 and for 



#=«, y=0, s=c, 



provided that b is the length of that edge which is perpendi- 

 cular to the surface of the four angles used as electrodes. 

 Taking into consideration that 



6 2 (w + 1, t) = — 2 (w, t), 



and writing, for the sake of shortness, 



0{t) for 0(0, r), 

 we get 



'-if*HS)*(S)M?> 



The numerical calculation of this integral becomes proportion- 

 ally easy if we, by inserting an intermediate boundary, divide 

 it into two, and at suitable places introduce, instead of the 6 

 functions with the modulus r, the 6 functions with the mo- 

 dulus . Since 



T 



