184 Dr. E. H. Kennard on 



more than two simultaneous equations at a time. The result 

 for the outer space was 



V=T { --259 + 1-067 log r 



-cosh (•327ar)[-0205J (-327r) + -0352 Ko(-327r)] 



-cosh (-292j?) [-0027 J (-292r)--0111Ko(-292r)]}, 



where a? = distance along axis from centre, Y = potential at 

 centre of outer cylinder, and 



v or 



K = J log^+^(l)-^p(l + i)....; 



with a similar result for the inner space (between shaft and 

 cylinder and guard-rings). 



The charge on the insulated inner cylinder is the difference 

 between the electric fluxes just outside and just inside the 

 cylinder; this turns out to be ( — 7*62 + 1*40) V = -6-22V . 

 From the degree of accuracy of the work and the following 

 analysis of possible sources of error, it appears that the solution 

 result should be accurate to one-half per cent. 



The residual error in the boundary values of the potential 

 exceeded 0*003 V only over the end plates and near the end 

 ■of the outer cylinder, where it rose quickly to 0'04V . The 

 effect of the rather large error over the end plates may be 

 estimated by assimilating the space to a rectangular slab 

 and employing as an approximate harmonic the expression 



TTZ 



r 



A<? r 2-n s i n 77- L. It is easily shown that even if A were 



^qual to V the effect of such a term upon the insulated 

 cylinder would be negligible. Evidently the same must be 

 true of the small error near the end of the outer cylinder. The 

 connecting wire will also be charged, but the charge on the 

 part of it inside the shaft is easily shown to be negligible by 

 treating it as one coating of a small condenser. The longi- 

 tudinal part attached to the cylinder will be at a lower 

 potential than would exist at that point in the absence of the 

 wire, because the potential due to induction is proportional 

 to r 2 , while that due to the charges will contain chiefly logr; 

 hence the wire will be negatively charged. Calculation 

 shows that the difference in potentials would be about 

 0*03V ; estimating the capacity of the wire at 2/3 elst. unit, 

 we have a charge on it of — 002V . 



Turning now to the amber insulators, — if the entire space 

 were filled with amber there would be no effect upon the dis- 

 tribution of electrification*; but here we have to do with 



* E. H. Kennard, Phys. Zeits. Dec. 1, 1912, p. 1155 ; March 15, 1913, 

 p. 256. 



