320 Planetary Atmospheres [CH. xvn 



where 7 1} 7 2 are formally the same as 7, but in I I the variables are subject 

 only to the condition that w is positive, while in 7 2 they are subject to this 

 condition and also to the condition that 



c 2 ................................. (762). 



We begin by performing the integration with respect to w in 7,. The 

 upper limit for w z is c fl 2 w 2 w 2 , the lower limit is zero. Hence 



= _ /T 



- hm ^+^ - e - h *) dudv, 



Zhm 



in which u and v are now subject to 



9 i *> ^. > 



rt 2 4- v- < c 2 . 



Writing t< = p cos 0, v = p sin 0, the first integral in the above expression 

 for 7 9 becomes 



f [ 



6=0 p=0 



while the value of the second integral is 



- 7rc 2 e- 

 Hence the value of / 2 is 





Putting c = oo , we obtain the value of 7 1} which is therefore 



rrr 



7i = 



and hence by subtraction, 



7 = 7,-7 2 



*7T 



385. The value of expression (761), the number of molecules which cross 

 the sphere r = R outwards in time dt, is accordingly 



r Idt = 2 R * V J T- e ~ hmc(? ( l + hmc fi dt - 

 7T 3 V hm 



Replacing c 2 by its value -- and replacing v from equation (760) this 

 expression becomes 



(763). 



