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IX. On Radiation from a Cylindrical Wall. 

 By A. C. Bartlett, B.A* 



ON page 359 and succeeding pages of the Phil. Mao-, 

 of Starch 1920, in a paper under the ahove heading, 

 an expression is obtained for the amount of heat radiated 

 from the inner walls of a vertical cylinder on to a horizontal 

 coaxial disk. 



The result is obtained from first principles by quadruple 

 integration over the surfaces of the disk and cylinder, and 

 the process is long - and laborious. It is, however, possible to 

 deduce the result, by a method which is not only much simpler 

 but much more powerful. 



It has been shown by Sumpner (Phys. Soc. 1892) that if 

 an element ciS of the surface of a sphere is radiating according 

 to a cosine law, and ds is any other element of surface of the 

 sphere, then the radiated energy received by ds from 6?S is 

 independent of the position of ds on the sphere. 



It can be shown that the amount of energy received by 

 ds is 



A ' 



where N is the normal radiation from dS ; 1\ is the tempe- 

 rature of d$ and T 2 of ds ; A is the area of the sphere. 



This result will obviously hold for finite portions of the 

 spherical surface; therefore, if S and s are two non-intersecting 

 curves lying on a sphere enclosing spherical areas S' and s' 

 respectively, and maintained at constant temperatures T\ 

 and T 2 respectively, the energy received by s' from S' is 



^'OY-T/). 



This result will still be true if the surfaces s' and S' are 

 replaced by any two surfaces s" and S" provided that s" and 

 8" satisfy the following three conditions : — 



(1) Their boundary curves s and S lie on a sphere. 



(2) If V is any point in S", then no portion of the surface 

 s" visible from V lies outside the cone vertex V passing 

 through the curve s. 



(3) If condition (2) is true when S and s and S" and s" 

 are interchanged. 



* Communicated by the Author. 



