Thermal Conductivity of Vulcanite. 17 



where J and J 1 represent Bessel's Functions of the zeroth 

 and first order respectively, and x p is the pth root in order of 

 magnitude of the equation J (#)==0. 

 Jf 



_, Jo(f)-sinh(y) 



it follows that 



V= V(1-2T,,, -2T,. ,_,) + 2V,T M +2V„T r ,,_ 2 ; 



and if, moreover, 



V =Y,= 0, then V = 2V T r , ,_,. 



By using ten-place logarithms and, in some instances, more 

 than sixty terms, we computed the numerical values of the 

 series T rz for about thirty different values of r, z, and a /I. 

 We found, for instance, that if a is as great as 51 and if r is not 

 greater than /, T, v does not, for any value of z, differ from the 

 corresponding value for the same r and z when a is infinite, 

 earlier than in the fifth decimal place; and that, keeping four 

 decimal places, we may write in this case 



* T r ,z. 



o-oooo 



il 0-1250 



\l 0-2500 



\l 0-3750 



I 0-5000 



The following table gives values of T V}Z at points on the 

 axis of the cylinder (where r = 0) for various values of a/L 





z=0. 



*=i* 



*=**■ 



z — § I. 



z=l. 



a=\l 







0-0006 



00065 



0-0703 



0-5 



a=\l 







00196 



0-0697 



0-2116 



0-5 



a=%l 







0-0558 



0-1427 



02908 



0-5 



a=l 







0-0857 



0-1920 



03320 



0-5 



a=\l 







0-1144 



0-2349 



0-3642 



0-5 



a=2l 







01224 



0-2464 



0-3724 



05 



a=3l 







0-1249 



0-2498 



0-3748 



0-5 



a=5l 







0-1250 



0-2500 



0-3750 



0-5 



Phil. Mag. S. 5. Vol, 49. No. 296. Jan. 1900. 



O 



