248 Mr. Ivory's Disquisition concerning the Length of the 



The same method of calculation applied to these 14 experi- 

 ments will bring out these results, viz. 



= 3-14372/— 0-65828 



A + 0-36760/ — 0-0888 = <r 

 /= -20939 

 A = 39-01192 + er. 

 From various combinations of the experiments made by 

 different observers we have now obtained four results, which 

 are extremely near one another. So very inconsiderable in- 

 deed are the differences, that one cannot help drawing the 

 inference, That the experiments with the pendulum agree bet- 

 ter with the figure of an elliptical spheroid than has hitherto 

 been supposed. I have further applied the same method of 

 calculation to 25 stations; namely, all in the following table, 

 except the first, which is not different from London, the one 

 place being as much south of the equator as the other is north 

 of it : the results are these, viz. 



= 8-09462/— 1-68657 

 A + 0-49585/— 0-11508 = <r 

 f= 0-20835, 

 L = 39-01178 + <r. 

 From the great number of experiments combined in the cal- 

 culation, the results now obtained are probably not far from 

 the truth, and in reality we have no means of approaching near 

 to it. Leaving out the last figure in the value of L, which 

 nearly equalizes the sums of the positive and negative errors, 

 we may finally adopt this formula for the length of the pen- 

 dulum in all latitudes, viz. 



1 = 39-0117 -1- -20835 sin 2 A. 



The ellipticity deduced from this formula is -00331 ; and it 

 deserves to be remarked that, in all the five calculations the 

 ellipticity is between the quantity now set down and -00329 : 

 it may, therefore, be estimated at -00330, or gl ? . 



Having now deduced by analysis the general expression of 

 the length of the pendulum, we must next proceed in a retro- 

 grade order, and inquire with what degree of accuracy the 

 formula represents the phaenomena. This is done in the fol- 

 lowing table, which contains 26 independent experiments, 

 made by different observers, and extending from 51° south of 

 the equator to 80° north of it. Every experiment fs excluded 

 from the table, the error of which is greater than + -003 in., 

 limits answering to +0 mra, 06 with respect to the decimal pen- 

 dulum in millimetres. 



Falk- 



