Wp 



314 Mr. S. R. Burbury on some Problems 



may express it, the above function is, as a function of h, of 

 zero dimensions. Therefore, since X=X%(A)^(AMo> 2 ) &c, 

 the expression 



x I cZa27rsinaX+ af 



must have, as a function of h, dimensions . - ? the factor 



\/A 



v/^ appearing in the denominator on account of the intro- 



M 4- m 

 duction of 7rs 2 /) ; or tts 1 R, its' 2 being in the cases now 



considered independent of p. 

 In like manner the expression 



( v)' (~))yy^-^ V* r rflfc^ 5 ^* *^= EL 



x i dflt,2wsba jf(X + .«) 2 KS 



will, as a function of h, have dimensions v __ y . 



Vh 



And therefore -j- (see (13)) will, as a function of /*, have 

 dimensions ¥z — _£ • 



s/h 



20. We have next to treat — in the same way. The re- 

 sult will be different for diffusion and for conduction of heat. 

 In diffusion 



d* V it J das 9 



Also 



og F = log | N (^) f ] - AMq) 9 + X % (/z)(#)(AM W 2 ), 

 og/=log {n (^f j -hmiri + X'xiWihmyjr*). 



