14^ 



Bowditch on the Oblateness of the Earili. 



differs from unity by quantities of the order y, the difference of the 



h 



I 



two expressions 0,00865 — 7j and 0,00865 — —, is of the same or- 



der, as the neglected terras, so that it would he difficult to deter- 

 mine which would be the most correct, without a new investigation 



we should conform to the degree of accuracy 

 lion by taking for unity the length of the pen- 



formula, and 



used in the 



dulum in any latitude from the equator to the pole ; but in such cas- 



I 



es it is generally found to be mostaccurate to take a mean value, 

 and the length at Paris is much nearer to the mean value than 

 that at the equator, so that there does not appear to be any suf- 

 ficient reason for altering the calculation of La Place in this part. 



i 



SECTION SECOND. 



1^ 



In Book III, § Si, of La Place's Mecanique Celeste is given 



the following equation to determine the quantity xused in finding 



the limit of the centrifugal force with which the equilibrium is pos- 

 sible in a proposed hypothesis relative to the form of the earth : 







7AJ -(- 30 A3 4- 9.7x 



(l+A^) C3+a2).(9+a2) 



ang. tan. a. 



The author has not however noticed that this expression may be 

 considerably simplified. For, by rejecting the factor 3 + x^ com- 

 mon to" the numerator and denominator of the first terra, it be- 



comes 



7^. fl-f-A^) 



(i+A2).(^9 + A^) 



ang. tan. k 







«r by reduction 



o 



1 



2.A 



8 1+A2 "^ 



9 

 8 



A 



3 



< 



ang. tan. a 







and since 



2A 



l+A' 



sin. 3 (ang. tan. k) this expression may be put 



under this simple fona ; 



I 



k 



