CO! Dr. A. Russell on the Convection of Heat 



where m 2 = 7rs<rVjak, we deduce that* 



_ 4#o f her mR ber mr + bei mR bei mr . ttI ttx 



it ^ ber 2 mR + bei 2 ??iR 2a a ' 



1 ber m J 3R ber m^/Sr -f bei m^/3R bei m \/?>r . Zirl Zirx 

 3 ber 2 m^/'&R + bei 2 m^/'SR 2a a 



+ 



ber mR bei mr — bei mR ber mr . irl . ttx 



sin — sin 



ber 2 mR + bei 2 mR 2a a ' 



1 ber m v'SR bei ms/?>r — bei m sj 3R ber m V 3r . 37rZ . 37j\r 

 3 ~ ber 2 m v/ 3R + bei 2 m \/3R Sm ~2a SU1 ~a~ ' 



} 



where R is the radius of the tube. 



This value of satisfies (18), and when r = R, = 6 from 

 — 112 to +112, &c, and thus the boundary conditions are 

 satisfied. 



Hence the loss of heat H per second from the portion of 

 the tube from — 1\2 to +1/2 is given by 



2ttR/c ~dx, whenr = R, 



C+ij 

 H = 



J -1/2 



= 16R^/^^ 6 (f(mR) sii 



1/2 V' 



ttI 



2a 



+ w| /( W \/^ R ) sin2 ^' 



where /(f) = j^, 



.} . . . . (19) 



ber f ber'f 4- bei £ bei'f 

 ~ ber 2 f + bei 2 f ' 



It will be seen that H is proportional to O , but except in 

 the case when mR is great it is not proportional to 



I have to thank Mr. H. Savidge for permission to publish 

 the table of the values of Z/X given below. This, in addition 



* Russell, Phil. Mag. April 1909, p. 535. 



