322 Planetary Atmospheres [CH. xvii 



This integral cannot be evaluated in finite terms. Since, however, 

 we are ultimately going to take R nearly equal to a, we can obtain a 

 sufficiently accurate value of the integral as follows. 



The integral may be replaced by 



rB j^4 ^ ft2 _ 2 

 J a wv * ~a? e JP 



and this again is equal to 



a' 4 r R ' 



Arm > a2hmga \ /, 



TP/I Vn t/ t/ 



a 2 J a JV 



where a' is some quantity intermediate between a and R. The value of the 

 integral in this expression is 



V 



so that the whole expression is equal to 



hmg a 2 

 389. The loss per second, from formula (763), is 



2& Vo <Tw ^^ (l + Zkmg |) ............... (765), 



so that the fraction of the whole which is lost per second the ratio of 

 expression (765) to expression (764) is 



- 



......... < 766 > 



1 e 



As regards order of magnitude, we may replace 7 - by unity, and 



Cb 



a? 

 1 + 2hmg by 1 + 2hmga. If for brevity we replace 2hmga by x, expression 



(766) becomes 



e 



For the earth and all the other planets g is of the order of magnitude 



of 10 3 . The value of \/ is \/ ^ ^ , and may therefore be supposed to 

 V TT V ZTT U 



be of the order of 10~ 5 . Hence, roughly, expression (767) may be replaced by 



10-* (1+ ape-* 



