, we shall have 



6v A' dt |^llIL^ = 



Let 



L.et \/A' D =a? 

 from which we have 



d A' = 2 x d a?, 



and hence 



dA' 2xdx 



Cai. 120. Now the integral of = is equal to multiplied by an 



x 2 + yV V 



arc whose tangent is ^, radius being 1 . 

 Whence 

 i H ^_? x - X an arc whose tang, is ^- ^-^ + Ct 



When 



t = 0, A' is equal to A, 

 and 



c = X an arc whose tang, is \ A D 

 6v \ D 



Let the former arc be represented by a and the latter by a' ; we 

 shall have 



When the time is required in which the density of the air 

 contained in the vessel shall be reduced to that of the external 

 atmosphere ; as A x = D, in this case, it follows that a = 0, 

 and 





