a general Formula for the Le?igth of the Seconds Pendulum. 245 



tain Sabine, which is that of the least squares, the resulting 

 ellipticity being '00346. It may be observed of that gentle- 

 man's experiments, that the pendulums are too long near the 

 equator, and in some instances the excesses are very great ; 

 on the other hand the pendulums are too short at Drontheim, 

 Hammerfest, and Greenland. Hence it is probable that <r_ is 

 negative, and § positive. For the sake of illustration, let us 

 suppose, o- = — "001 



g = -f -001 ; 



then A = -01225, L = 39-01225 



/ = -20864, 

 and the ellipticity — -00330. 



It is evident that a calculation, founded upon data not rigo- 

 rously exact, is entirely unworthy of trust, when such minute 

 errors produce variations of so great magnitude. 



In this Journal for August last, I used a mode of calcula^- 

 tion which, although founded on a particular arrangement of 

 the pendulums, is not liable to the same fault as the method 

 of the least squares. In the equations (A) suppose the least 

 pendulum is placed first, and the rest in the order of their 

 lengths ; then subtract the first equation from every one of the 

 rest, and there will be obtained a number of equations of con- 

 dition involving f only without A ; applying now to these 

 equations the method of the least squares, the coefficient of 

 f in the final equation will not be a small fraction, but, sup- 

 posing the experiments combined to be well chosen, it will 

 generally amount to several units; so that the error of the 

 equation will not be increased but diminished in the value of 

 f. Thus at p. 100 of the Journal cited, the coefficient ofjTis 

 more than 3 in the instance of Captain Kater's experiments, 

 and the error of the equation is diminished in the value of J 

 in the proportion of 1 to 3. When f is known, A will be 

 found by means of any one of the original equations ; but it 

 will be a great improvement of this method to deduce A, not 

 from any one of the equations ( A), but from the sum of them 

 all ; or, which is the same thing, to employ the equation, 



A +.B./- .A=V, 



already obtained above. This method is sufficiently commo- 

 dious in practice, and it will probably be found as exact as 

 any other that can be devised. 



J. Ivory. 



XXXVII. Bis- 



