Purser — Applicdtion^i of BesaeVs Functions to Physics. 27 



whence difereutiatiug-, we have 



. 1 cM^ 3z 5 9 ., ) 



kir^^" ( 32 5 9 ) 



(-1) 



whence 1 / Sz- \ 



/i,(:r)r,W= -(^l - .j. (0) 



It is to be noted that it is easily seen from the definitions that 

 R\{x)Y,{x)-K,{x)Y„{x)=^^. (6) 



I should add that I have, in the present paper, employed the 

 symbols cr(w), 8 (?^) to denote cosh (w), sinh (w). 



ArPLICATIONS. 



A. — Heat Conduction. 



The terminal faces of a solid conducting-cylinder are maintained 

 at zero temperature, the curved surface at temperature V, to find the 

 temperature at any point of interior. 



Let a be radius of cylinder, 2h its height; let the middle point 

 ' of the axis of cylinder be taken as axis of z, and take 



» = (•-'» + 1)^. 



s having all integer values, including ; then the expression for v 

 will be 



V = X^L\{nr)IJi,{na){- ly—L- cos nz. (7) 



Let the cylinder be fiat ; then, for values of /• corresponding to 

 points near curved surface, we may employ approximately the formula 



for A'y(^), where x = nr. 



We may then write 



/" 2. (- 1 )'-^ cos «= = i^ han-'J7, (8) 



where _ ttz (,-n(»-r) 



a = cos tan 2tan~^ — — , 



a formula which gives the diminution of temperature as we proceed 

 into interior. 



C2 



