Mr Wilson, On Convection of Heat. 413 



Let z = 2 wax, when this equation becomes 

 dry 1 dy 



The complete solution of this may be written in the form* 



y = AI (z).+ BK (z), 

 where A and B are constants, I (z) = J (iz) and 



K (z)=-I (z) (log| + 7) + !+ (l + |) 



X* 



2/ 2 2 . 4 2 



/ 1 1\ a* 

 + V + 2 + 37 2 2 .4 2 .6 2+ ""' 

 where 7 = 0-57721566.... 



Since when r = go the temperature must be zero, we have .4 = 0, 

 so that the solution of the problem takes the form 



It remains therefore to determine B. 



00 



When x is very small K (x) = — log - — 7, 

 so that S P d = ~£H l ° 8 W + ry )> 



. de -bq 



hence sp — - = _ — — £ . 



Thus when r is very small the flow of heat from the line 

 source is radial so that we must have 



-2 7 rrk C ^ = Q, 

 dr 



from which we see that B = 2, so that finally 



* See Whittaker's Modern Analysis, p. 307. 



