of the Barometer near Edinburgh. 181 



amount. The curve YM#, drawn through these points, AX be- 

 ing the axis of the abscissas, AY that of the ordinates, represents 

 the formula of greatest probability, just found. Since the oscil- 

 lation becomes negative, there must be some point M where the 

 curve crosses the axis, or where the oscillation is 0. This la- 

 titude, which may be denoted by L, is readily found by equating 

 the value of z to zero, which gives 



cos L = , and L = 64 8' 6". 



By putting 6 and 6 90, we obtain for the equatorial oscil- 

 lation, or AY, 2 mm .650; and for the polar, or X#, CT'.SSl ; or 

 .119 and .015 English inches. 



17. By means of the formula z = a, cos" 6-\- (putting for a 

 and the corrected numbers), we may further deduce the mean 

 amount of the atmospheric tide for the quadrantal arc of the 

 meridian, and likewise corresponding to the entire surface of a 

 hemisphere. In the first case, its mean value will correspond to 

 the integral of zd0, taken between the limits 6 and 6 = 90, 

 and divided by the length of the quadrant of latitude, or 



- /( cos" 6 + ) dt. 



In the second case, we must introduce the expression for the 

 length of the parallel of latitude, and divide the integral taken 

 within the same limits as before, by the surface of the hemi- 

 sphere , that is, 



/ 



cos" +1 



Since we have employed n |, the integration of both these ex^ 



pressions comes under that of elliptic transcendentals ; by a 

 simple alteration, however, we shall obtain a direct solution, 

 abundantly accurate for our present purpose. We have seen 



that n 2.6 ; if, therefore, we make it = 3, instead of |, and mo- 



VOL. XII. PART I. A a 



