for determining the Length of the Pendulum. 351 



p. 28. But of these latter numbers no explanation is any 

 where to be found, neither are they ever referred to, nor used 

 in any calculation. Two of these equations of condition are 

 indeed set down at the bottom of p. 28, but this must be an 

 inadvertence; for the calculation which is repeated at p. 229, 

 is performed with the lengths in p. 26. It would however be 

 very satisfactory to know upon what grounds the relative 

 lengths in p. 28 were computed, and why they were rejected, 

 because in general they agree better with the experiments of 

 others than the lengths definitely adopted by the author. 



If now, by means of the data in the foregoing table, we 

 compute the lengths of the pendulums at the several stations 

 by my formula in the last number of this Journal, we shall 

 obtain as follows : 





Computed 



Excess of 





Pendulum. 



Calculation 



Falkland Islands . . 



39-13960 



+ '00248 



Cape of Good Hope 



39-07648 



— •00169 



Port Jackson .... 



39-07637 



— •00409 





39-04336 



— •00035 



Isle of France .... 



39-03646 



— •01121 





39-01170 



— •00309 





39-02301 



— •00722 



Mowi 



39-03816 



— •00921 



The inspection of this table shows that the pendulum at 

 Rio Janeiro is the same by the experiments of M. de Freyci- 

 net as by those of Captain Hall and Foster. At the Falkland 

 Islands M. de Freycinet makes the pendulum shorter than 

 M. Duperrey ; the error is greater, but it still falls within the 

 limits of my table. The Cape of Good Hope is a new station 

 to be added to my table; and the same may be said of the 

 Island Rawak, the error in this latter case falling upon the 

 extreme limit. We have therefore now 28 independent expe- 

 riments which concur, with very small discrepancies, to give 

 the same figure to the earth. 



At Port Jackson there is evidently a considerable irregula- 

 rity ; for, according to the latitude, the pendulum should be 

 shorter than at the Cape of Good Hope, whereas it is longer 

 •00229 in. This station is on the same main land with Para- 

 matta, and indeed in the vicinity of it, the difference of longi- 

 tude being about 14', and the difference of latitude no more 

 than 3'. We have two determinations of the pendulum at 

 Paramatta; one by Sir T. Brisbane, which makes it 39-07696; 

 and the other by Mr. Dunlop, of which the result is 39*07751* ; 

 and, as the addition for the small difference of latitude is in- 



* Phil Trans. 18.24. 



significant, 



