294 Prof. H. Lamb. On the Principal [Apr. 21, 



to the true value. The following table gives the values of Tpja for 

 different values -of n: — 



n. 



rp'ja. 

 • 



0-5 



2-133 



0-6 



2-201 



0-7 



2-239 



0-8 



2-257 



0*9 



2 261 



10 



2-256 



11 



2-245 



1-2 



2-229 



1-3 



2-210 



1-4 



2-189 



1-5 



2-167 



2-0 



2-051 



It appears that the value (14) of t is a maximum for n = 09 about, 

 and, hence, that the principal time-constant of a circular disk is not 

 less than 2-26a///. We have seen that the value of obtained by 

 putting n = 1 in (3) must be a pretty fair representation of the most 

 persistent type of free currents in a uniform disk, and the case of 

 n = 0'9 will not be materially different. The " stationary " property 

 already alluded to therefore warrants us in asserting that the value 

 just given must be a close approximation to the truth. If S be the 

 thickness, p the specific resistance of the material, we may write our 

 result thus — 



, = 2-26^. 



P 



For a disk of copper \_p = 1600 C.Gr.S.], a decimetre in radius, and 

 2'5 mm. in thickness, this gives t = 0*0035 sec. . 



Addendum.— April 11, 1887. 



In the above calculations it is assumed that the current-intensity 

 is sensibly uniform throughout the thickness of the disk. This will 

 be the case, at all events for a non-magnetisable substance, if the 

 radius be a moderately large multiple of the thickness. To examine 

 this point more closely, it will be sufficient to consider a simpler 

 problem in which all the circumstances can be calculated with exact- 

 ness. Let us suppose then that we have a system of free currents 

 everywhere parallel to the axis of z in a stratum of conducting matter 

 bounded by the planes y = +8/2. With the usual notation we shall 

 have — 



