358 Hydrostatics. 



dp^ .. ' dh 



p " 



Nothing can be inferred from this equation until the value of n 

 is given in terms of h. Now we know that the temperature de- 

 creases as we ascend from the surface of the earth, but the law 

 of this decrease has not been determined in a manner altogether 

 satisfactory. Fortunately, this law has little influence upon our 

 results in the calculation of heights by the barometer, on ac- 

 count of the smallness of the coefficient e; and we may, in ques- 

 tions of this kind, consider the temperature as constant, provided 

 we take for n, in each particular case, the mean of the tempera- 

 tures observed at the two extreme points of the height h to be 

 determined. Moreover, R being the radius of the earth, and g 

 the gravity at the surface, we have, at the distance R + h from 

 the centre, 



/ - 



(a + hy ' 



since this force varies in the inverse ratio of the square of the 

 distance. The preceding equation becomes, by this substitu- 

 tion, 



dp g R 2 d h 



Whence, by integrating on the supposition that n is constant, we 

 have 



m being equal to 0,434295, log. denotes the common logarithm 

 'of/?. To determine the constant C, let -or be the value of p an- 

 swering to h = ; arid we shall have 



Consequently, .by subtracting the preceding equation from this, 

 we obtain 



h f . 



This equation, taken in connection with equation (i.), gives the 

 values of p and A in terms of h. Thus we have equations con- 



