1887.] Electric Time-constant of a Circular Disk. 291 



in the usual notation of hypergeometric series. 



In the electrical problem, then, to a current-function of the form 

 (3) corresponds the current-strength — 



_d0 _ vV r(w+ l) r /, r 2 y-* 

 dr a ' Y(n + 



and the electric momentum — 



dF 7t 2 r ^ / rt r 2 \ ^ v 



7* = 2 • S F (-**•* s} (6 -> 



The assumption (3) will correspond accurately to a normal type for 

 a non-uniform disk, provided the law of resistance be properly 

 adjusted. For (2) is satisfied if — 



that is, , ' = - pj j ^ (I--, sin**) sin2 X <J X + (l-- a j . (7.) 



= ^(-».f.2,5)^(l-5f 1 (8-> 



where p ' is the resistance at the centre ; and the time-constant is — 



7 - X " r(n + l) 2 Po " (y -> 



For w = 0, we have — 



ft = Po '(l-r^)i 



Since />' diminishes from the centre outwards, we see that 4"935a-/// is 

 a superior limit for a disk of uniform resistance p. 



