91 



Also making m and Q vary in equation (3) 

 We get by help of Taylor's Theorem 

 Q = Qn — 1) tan. 6 &c. 



Hence substituting in equal. (5) 



li == Q (_ w— ) tan. ^^ ^^^ found before in art. 3. 



^' a COS. ^ 9 



Hypothesis of density decreasing uniformly. 



Q. 13y the density decreasing uniformly is understood, that 

 the density is as the distance from the highest part of the 

 atmosphere. It is obvious that in this hypothesis, not taking 

 into consideration the variation of gravity, the height of the 

 atmosphere will be double of that of an uniform atmosphere 

 of an uniform gravity. And it is also obvious that the effect 

 of the variation of gravity can be but small. Lest however 

 there should be any doubt on this head, it will be safer to 

 investigate the height of the atmosphere on this hypothesis, 

 gravity being supposed to vary. 



Let this height = t 



the pressure at any height z =p 



the pressure at the surface = (p) 

 a, /, g &c. as before. 



Then p == 7^-7x1-} the gravity at the surface being re- 

 presented by unity. 



o 2 



