+ 



1-541 N 



+ 



•792 N 



+ 



•430 N 



+ 



•276 N 



+ 



•117 N. 



as deduced from Experiments made "with the Pendulum. 9 



We shall only add the pendulum at Unst, which has been 

 determined both by Captain Kater and M. Biot, and which 

 the latter thinks is one of the most certain that has yet been 

 found experimentally. The two results, however, are different 

 •000007 of a metre, or -00027 of an inch*. 



Now if the lengths of the pendulums be uncertain in the 

 fourth and following places of figures, the same must be true 

 of the quotients of the lengths, and of all the small numbers 

 on the left-hand side of the equations for finding M and N. 

 It appears, therefore, that the values found by those equations 

 cannot be reckoned quite sure in the fourth place of figures, 

 and are uncertain in all the following figures. 



Divide all the terms of each of the equations 'mentioned by 

 the coefficient of M ; then 



M = -003322 

 M = -003432 

 M = -003369 

 M = -003362 

 M = -003280 



If we neglect quantities of the second order as in the usual 

 solution of the problem, then N = 0, and M will coincide 

 with the ellipticity, of which, therefore, we have five different 

 values derived from independent experiments. These values 

 agree very well with the remarks that have been made, and 

 they likewise prove the accuracy of the experiments. For great 

 care must have been taken to insure accuracy in such deli- 

 cate operations, when the extremes of five independent results 

 differ from one another less than ^ of the whole, and from 

 the mean quantity only ^ of the whole. It is plainly im- 

 possible to improve the solution by assigning any value what- 

 ever to N. The experimental quantities leave the numbers 

 uncertain in the fourth and fifth places of figures, and the 

 same numbers should be exact, at least to the sixth place of 

 figures inclusively, in order to determine with any consistency 

 quantities of the second order. We may therefore safely 

 conclude that Clairaut's theory, without being carried to any 

 greater approximation, is fully sufficient in all our researches 

 concerning the figure of the earth. 



In order to confirm the foregoing reasoning, I shall conclude 

 with adding two other instances, both of great accuracy, viz. 



Latitude. _ Pendulum. 



Paris . . . 48° 50' 14" 39-12930 



Unst . . . 60 45 28 39-17146 



* Supp. Encyc. Brit. vol. vi. p. 130. 

 Vol. 68. No. 339. July 1826. B By 



