Bowditch on the Oblatevess of the Earth, 



43 



values of A is F = 4,0906(5. The sum of the six first terms of h 

 is equal to 1,6636 1 <y i^i the sum of the spven first terms is 

 2,07t83> 4- Fj whence we obtaia from the formulas (Q), r 

 therefore the error of the seventh of the 



put equal to nothing or a:^"^ 



ith of the equations [¥ 

 0, whence we get y 



riM 



0.00'225 

 0,41119 



0,005 173, and ;5 = 0,999^3 — 2^, 0,43710 =0,99684, consequent 



ly the ellipticity 0,00865 



^ 



0,003178 



1 



S14. 



^ : so that the ra- 



f the polar to the equatorial diameter of the earth is as 314 to 



nearly, instead of 3:5 to 336 found by La Place. Putting 



^^ for the latitude of any place we shall have p = sin ^f^ and 



the general expression of the length of a pendulum z +p y 



^ 



This for 



f 



99994, and as the actual lensth, according to La Placf 



,741887, the general expression of the le 



metres will 



- . , 0m.741887 , 



be found by multiplying the preceding expression by - ,. nan... ?Py 



0, 999^4 



which means it b 



,739587 + 0"',004060 sin ^|. 



instead of La PI 



.m 



739502 + 0"',001S0vS, sin ^ 



The writer of the same article in the Cyclopedia objects to La 



Place's method of finding the ellipticity from the forraul 

 ^, in which y is expressed in parts of the length of i 

 pendulum, whereas it ought according tothat writer to b 

 ed in parts of the pendulum at the equator, or in other w 



Paris 



H-" 



the ellipticity ought to be 0,00865 



^, which if we use La 



instead of 



Place's values of;;;, y, would make it -^g^ 



it may be observed, that in the investigation of the form 



835.78 



But 



y^ 



terms of the order y 



are generally neglected 



and as 



