292 



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



For n = h 



4i (V / r 3 V 



TTOb 



T = — » 

 ft) 



from which, it appears that 3*142a//>' is a superior limit for a uniform 

 disk. 



For » = 1, 



/ - ^-'SH'-S)' <'»•' 



- - $■ <"•> 



This case is remarkable as giving a resistance nearly uniform over 

 the disk, except close to the edge, where it rapidly increases. The 

 second column in the following table gives the resistance at various 

 distances from the centre ; the third column, the corresponding thick- 

 nesses in terms of the thickness at the centre, the material of the 

 disk being supposed uniform. 



rja. 



p'/p'o- 



Thickness. 







1-000 



1-000 



o-i 



0-998 



1-002 



0-2 



0-990 



1-010 



0-3 



0-978 



1-023 



0-4 



0-960 



1-041 



0-5 



0-938 



1 -066 



0-6 



0-913 



1-096 



07 



0-886 



1-129 



0-8 



0-867 



1-154 



0-9 



0-900 



1 111 



0-95 



1-035 



0-966 



0-99 



1-878 



0-532 



1-00 



00 







The minimum value of p is 0'8660/V; corresponding to rja = 0*8165. 

 Denoting this minimum by p^ t we find from (11) — 



t = 2437 



Pi 



This is an inferior limit to the value of t for a disk of uniform 

 resistance /?/. 



