50 IVIr. Galbraith on Determining the Figure of the Earth 



the compression derived from a comparison of the English 

 and French arcs is less affected b}' any small error that may 

 be supposed to exist in either or both of the measures of 

 these arcs, than equal or even smaller errors in those of In- 

 dia and Peru, though the distance between the parallels of 

 the latter is greater than that between those of the former ; 

 and the same thing is true of those in similar circumstances 

 with respect to the pole. Arguing on similar principles, it 

 will appear that the ellipticity derived from arcs bisected by 

 the tropics and polar circles will be entitled to the greatest 

 confidence, as the length of a degree varies considerably at 

 those parallels, and they are sufficiently distant to counteract 

 any small error arising from a similar error in the measures of 

 the degrees. A great deal of discussion has taken place upon 

 this subject lately, and from which it may be supposed an im- 

 proved solution of the figure of the earth, whether from the 

 measurement of arcs or from experiments with the pendulum, 

 will be obtained. Mr. Ivory has given in the Philosophicai 

 Transactions for 1824, a new and, so far as I am able to judge, 

 an improved solution of equilibrium of a homogeneous body 

 revolving about an axis. Mr. Airy has endeavoured to extend 

 the celebrated proposition called Clairaut's theorem, by in- 

 cluding the terms of the second order. In this investigation, 

 however, Mr. Airy has not included the second condition of 

 equilibrium, which Mr. Ivory has thought requisite, and assigns 

 as a reason the insufficiency of that gentleman's arguments. 



Several of the French mathematicans have also contro- 

 verted some of Mr. Ivory's views on that subject, in which 

 perhaps prejudice and the authority of the late Laplace have 

 not been without their influence. Indeed, a very few only of 

 the first mathematicians are competent to enter with effect 

 upon such a difficult subject ; and as Mr. Ivory has apparently 

 succeeded in solving the question in its most general form, 

 without the rejection of the terms involving quantities of the 

 higher orders, which was required in former solutions, this 

 seems to be a strong argument in his favour. 



Mr. Airy, after having given his new solution of the problem, 

 proceeds to compare theory with observation, and selects Cap- 

 tain Sabine's series of experiments with the pendulum as the 

 best for his purpose. The compression comes out 0'0034'74' 

 = ^nV-iT> nearly the same as what Captain Sabine himself 

 had deduced from Clairaut's solution : so that according to 

 Mr. Airy's conclusion, not much more accuracy is obtained 

 when quantities of the second order are I'etained, than when, 

 according to Clauraut's raetliod, they are rejected : and it is 

 not probable that even by adopting Mr. Ivory's second con- 

 dition 



