of a Spherical Mass of Gas. 



165 



Also if the density at the centre is 1 lb. per cubic foot the 

 radios of the containing sphere is about 25100 miles. 



I will now investigate what effect the contraction of the 

 gas has on the temperature. 



Let us first transform the equation of equilibrium so as to 

 .make 6, the temperature, the dependent variable, instead of p. 



AVe have assumed 



But 



Hence 

 Thus, since 



the equation o£ equilibrium becomes 

 d& K '" 





P ^ 

 P 



w. 



C P 7 



-l _ 



-Ed. 



d( P y- 



- 1 ) 



•E^ 



dr 





dr 



R 



7 dd k r , 



— -- -r-.= g 1 4:77 or- c 



K f /R0\A o , 



(8) 



Xow if the gas loses heat c will diminish. Let us find 

 the changes in r and 6 for the same element of gas — or 

 rather, for the gas occupying the same relative position in 

 the mass, corresponding to a diminution in c. 



Suppose the new value of c is c x such that 



c l = nc, 



n being less than unity: and let n 1} 6 1 be the new values of 

 r, 6 for the corresponding element of gas. Then it can 

 easily be shown that 



/•j = n a r 



X - n*d 



satisfy all the conditions of the problem provided a and ft 

 be properly chosen. For, the new equation of equilibrium is 



7-1 dr x J \ncJ 



Phil. Man. S. 6. Vol. 13. No. 76. April 1907. 



(9) 



2K 



