340 NEWTON S PRINCIPIA. 



station, between it and the level of the sea, the more dis 

 tant parts cause an increase in gravity, since the attraction 

 they exert is not wholly horizontal, on account of the 

 curvature of the earth. Again the horizontal attractions 

 due to the neighbourhood of a continent would cause a 

 plumb line to point slightly towards it, and since a level 

 surface is everywhere perpendicular to the vertical, the 

 level of the sea must be higher than it would be if the 

 continent did not exist. The correction therefore reduces 

 the observation to a point more distant from the centre of 

 the earth than if the continent were away ; and therefore 

 on this account gravity is less on a continent than on an 

 island. The investigation shows this latter effect more 

 than counterbalances the former ; so that, on the whole, 

 gravity is greater on an island than on a continent.&quot; 



It is also probable that the ellipticity deduced by Airy 

 is a little too great, owing to the decided preponderance 

 of oceanic stations in low latitudes among the group 

 where the observations were taken. On looking at the 

 expression for g, we see that, in consequence, the calcu 

 lated values of gravity would be a little too small, par 

 ticularly for places near the pole. This will enable us to 

 show that Airy s second conclusion is a mere repetition 

 of the first ; for that in high north latitudes, the formula 

 should give too small a result is no more than what we 

 should expect ; while about 45, the places of observation 

 being all continental, the formula naturally gives too large 

 a result. Thus we are now enabled to account, at least 

 in great measure, for the anomalies that Airy has noticed. 



In considering the earth as an irregular figure, we must 

 define what we mean by the ellipticity. Let a be the 

 mean radius of the earth, r the radius of any point whose 

 colatitude is 0. Then since the earth is nearly a spheroid, 



r a 



\ - cos. 2 

 is very nearly constant. Its variations, as we go from 



