162 



Trans. Acad. Sci. of St. Louis. 



The ratio ^fr is computed for various gases which conform 



closely to eq. (1) at high temperatures. The results are given 

 in the annexed table. The fifth column gives the specific heat 

 of gravitational compression represented in eq. (33). 



Gas 



jsr 







Air 



O 



3.409 

 0.2438 

 0.2175 

 0.2375 



C 



4.13 X 107 



2.97 X 106 



2.60 X 106 



2.88 X 106 



Cp-f 4 



C 



7.352 

 0.5274 

 0.4655 

 0.5123 



1 

 W 



0.75 

 0.75 

 0.75 

 0.75 



It will be observed that this ratio is constant for all these 

 gases. Kepresenting this ratio by c we have by (43) 



0^ = ^ 



G 4 — 3c 



J 2c— 1 



(45) 



From the equations Cp — C^= -y and Cp = /cC^ we 

 have 





Hence by (45) and (46) 



_5/c— 4 

 ^=5/^ — 3 



Also from (43) and (47) 



W^Q 1 



= 0.753. 



W 



5 K 



= 0.247. 



(46) 



(47) 



(48) 



If we consider only that part of the heat energy which is 

 applied to the mass M^ of radius B, we may also write an 



