Temperatures of a Thin- Rod. 



These give 



A=- 



\o 2 V 



X^-X, 



-2r 



B = 





235 



(22) 



and the complete solution on this second approximation is 

 therefore 



"= x^v t v exp (_M) ( 1_ ¥) 



-X 2 *exp(-V)(l--r.)] 

 For au axial point at distance x 



V 





v-**» 



[X, 2 exp( — X^r) — X 2 2 exp ( — Ai«) ] • 



(23) 



(24) 



Numerical calculation will show that in most cases 

 Xo 2 exp ( —\ x x) is negligible in comparison with Xj 2 exp 

 ( — X 2 <r) unless a? be small. The following table of values is 

 cited in illustration for the case of bismuth bars of two 

 different radii. L is taken as 60 cms. For substances for 

 which L is greater or a is smaller, the relative magnitude of 

 the two expressions is still smaller. 





X. 



X x 2 exp (— X 2 #). 



X 2 2 exp (— \ x x). 



L = 60 ^ 



1 <z— 4 ! 



1 



0-4645 



00040 



• \ 2 = 0-5085 . 1 

 ; A o 2 =00082 . f 

 |\;=0-7131... | 



o 



0-3233 



000023 



10 



0-2056 



0-000007 



X 2 = 0-09055 . ; 



20 



00832 



0*000000005 



L=60 1 



«=1 ! 



1 



6-695 



0-0019 



X 1 2 = 8-0335 . ! 

 X, 2 =0-0332 . f 

 Xi= 2-8344... | 



5 



3-231 



000000002 



10 



1-299 



0-0 13 2 



X o =0-1822...; 



20 



0-210 



0-0 2G 8 



The 



The 



All lengths are expressed in centimetres. 



result (23) may therefore be taken 



•-3?=s?'[xi'«b(-V')(i^^)} • (25) 



family of isothermal surfaces will therefore be given 



■\ 2,- > 2 v 



— A ^ -flog | 1 — -j = a parameter, 



