362 Hydrostatics. 



riation of gravity in different latitudes, if g represent the value 

 of this force in the latitude of 45, and g' that of any other lati- 

 tude L, we shall have 



g 7 = g (I 0,002837 cos 2 L). t 



At 45, therefore, where cos 2 L = 0, g / =. g, or the correction 

 is ; and for higher latitudes the correction is , or subtractive, 

 and for lower latitudes it is -f- or additive. Whence, generally, 



= 10000 fath - (1 + 0,002837 cos. 2 L.) 

 mg 



By means of this value of , substituted in equation (iv.) 



tThe value of g' in different latitudes depends upon the particu- 

 lar figure of the terrestrial spheroid, the determination of which 

 belongs to astronomy. We will merely observe in this place, that a 

 comparison of articles 346, 347, conducts us directly to the equation 



o, a', being the lengths of the pendulum corresponding to the parts 

 of the earth in which the intensities of gravity are g, g', respective- 

 ly. Now it is found that the general expression for the length of 

 the seconds pendulum, the day being divided into 100000 seconds, is 



metre. metre. 



a' = 0,739502 + 0,004208 (sin L) 2 . 

 Hence, since 



(sin L) 2 i (1 cos 2 JL), and (sin 45) 2 i. 

 Trig. 20- we shall have 

 Trig. 27. JL = JL =- 0,739502 -f 0,002104 



a' ~ ' g 1 0,739502 -f 0,004208 (sin Lp ? 



_ 1 



1 _ 0,002837 cos 2 L 5 

 therefore, 



g' g (1 0,002837 cos 2 L). 



In the original memoir of M. Ramond, the coefficient stood 

 0,002845, and it was thus copied by Laplace and others. It was 

 afterward corrected by M. Oltmanus, and the error acknowledged by 

 the author in a separate edition of the memoir. 



