NEWTON S PRINCIPIA. 339 



form.&quot; If g be the force of gravity in latitude A, then by 

 Clairaut s theorem 



g = G{l+n sin 2 *}. 



The values of n and Gr that are found to suit best with the 

 forty-nine &amp;lt;f first-rate observations &quot; are 



n = 005133 

 G = 7r 2 x 39-01677 



Now if m be the ratio of the centrifugal force at the 

 equator to equatorial gravity, 



5 



n = - m e, 



whence since m 0034672, the ellipticity is easily seen to 

 bee = -003535. 



The above expression for g enables us to find the force 

 of gravity in any latitude. From a comparison of the 

 results of the forty- nine observations with those given by 

 this formula Airy has deduced. 



1. That, cceteris paribus, gravity is greater on islands 

 than continents. 



2. That in high north latitudes the formula gives too 

 small, and about latitude 45 too large a value of g ; near 

 the equator the errors are about equally balanced. 



3. There is no reason to think gravity to be different 

 in different longitudes, as the irregularities on different 

 meridians do not appear greater than those at places near 

 one another. Nor does it appear that there is any differ 

 ence between the northern and southern hemispheres. 



The observations were all reduced to the level of the 

 sea by Dr. Young s rule, which makes an allowance for 

 the attraction of the earth above the level of the sea. 

 But it has been pointed out by Professor Stokes, in the 

 &quot; Transactions of the Cambridge Society&quot; for 1849, that this 

 rule does not take into account all the effects of the irre 

 gular distribution of land and sea. &quot; Besides the attrac 

 tion of the land lying immediately under a continental 



z 2 



