518 Prof. A. W. Porter and Mr. E. R. Martin on the 

 the solution of which is 



where K a = j a kdO. 



Differentiating with regard to b we have 



o% L _ ae b h 



Hence the critical radius is given by 



d0> H 



db ~ 27rbk b ; 



or since H = <? . 2irb6b^ 



hb db \ebr 



where d B dOb ~b 



db = zi + 55" a*' 



the values being those for 6 equal to the critical radius, and 

 therefore 



<20* = H 



db 2irbkb ' 



If we can neglect the variation of e with the radius at 

 constant temperature as we can do when the radius ceases to 

 be very small, the critical radius becomes 



h _h(, H_ ^L\ 



° e ~ e h \ 2ire b k h ^ej 



Thus the critical radius is seen to depend upon the rate of 

 heat supply. The value in the simple theory is the value for 

 a very slow supply of heat. 



The above is worked out on the assumption that the value 

 of H is constant. 



Addendum (in conjunction with Mr. E. R. Martin). 



The lagging of steam-pipes. 



A similar theorem to that proved above is, of course, valid 

 also for the case of the condensation of steam in pipes. The 

 amount of condensation is proportional to the escape of heat 

 from the surface. We have as before 



e '=£(m + l l0 * b a)- 



