Mr. Galbraith on the Figure of the Earth. 325 



such as an error in the experimental results, a protuberance 

 of the earth at that latitude, a diminution of density, &c. This 

 has occurred to me from some of my own computations, as 

 well as from those of others which I have seen, but which 

 seem to disappear when the proper (the reduced) latitude is 

 employed. In order to obtain correct results, the formulae 

 should possess all the accuracy which can be given them. For 

 this purpose I have elsewhere reconsidered the usual method 

 of obtaining the compression, and made some slight cor- 

 rection. 



If <p denote the centrifugal force at the equator, r the radius 

 of the equator, t the time of rotation of the earth about its axis, 



and I the length of the pendulum, then <p = ( (1) 



V~2/ l 

 and consequently the ratio of the centrifugal force to gravity 



will be expressed by r~- = \ yi = q (2) 



If the most accurate values of these quantities be introduced, 

 q will be found to be 0*003455 = g 6 , somewhat less 



than -Tj-, that usually employed. Now if t denote the ellip- 



ticity, p a certain coefficient to be found from an investigation 

 of the conditions of equilibrium of a spheroid, y the excess of 

 the polar above the equatorial pendulum, and % the length of 

 the equatorial pendulum, then 



e = —tL -fc (3) 



Since by considerations derived from the case of a homo- 

 geneous spheroid, which may be supposed very nearly appli- 

 cable to the case of the earth, the value of j?is 2*4?91516, in- 

 stead of 2*5, that commonly adopted ; whence it follows that 



6 = 0-0086082-^- (4) 



This formula will, I believe, give the ellipticity as nearly cor- 

 rect as the necessary data required in the substitutions can 

 be depended on. 



As we have not as yet a sufficient variety of experiments in 

 different longitudes under the same parallel, affected by the 

 various irregularities tending to destroy each other, neither 

 have we sufficient data to reduce them to a substratum of a 

 given density, as formerly proposed; it remains to employ the 

 only method left, which may perhaps effect nearly the same 

 thing. This consists in reducing as many lengths of the pen- 

 dulum as possible to the same point which are very near it, by 



the 



