beneath continents and oceans compared. 



The integral now becomes 



/ jz. — \ ,,. du, du 



, « -'cose (l-2/ztt + w 8 )* 



Taa 



= raa I 



u 2 du 



fJb — u 



= Taa 



i-i |_Vl — 2/juu+u 2 ], 



a 

 f 1 8,7 ft COS0-U 



I vsdu 1 



L t V Vi- 



2u cos + u 2 



Put w = 1 — x. .'. du = — doc. 

 The integral becomes 



Taa I ( 1 — x) 2 dx ( 1 



cos # — 1 + a? 

 Vl-2cos0 + (l-a/) ! 



a? — 2 sin 2 - 



= rota I (1 — xfdx I 1 — 



a/ 4 sin 2 x (1 -a;) + a; 2 



a; — 2 sin 2 



But 



4sin 2 ^(l — x) + x 2 



x — 2 sin 2 



2sin-J 1 _ 2sirj |_^ + ^ 



109 



2 sin - 4 sin 2 = 

 2 2 



And this can be expanded in a series of ascending powers of 



x 



2 sin ^ 

 2 



which when taken between the limits will give ascending powers of 



t 



2a. sin 



2 



and the series will be convergent when t is less than 2a sin - . 



