1 826.] of the Length of the Pendulum at the Equator, 349 



Also, 



f First 39-0200869218 



1 Second. .. 39-0208425551 



Sets (R)^ 



Mean. 39*020464738 



Third 39-0221758674 



Fourth .... 39-02215983605 



Mean 39-0221678517 



Mean of thefour sets (R)39-0213162951 

 Mean of thefoursets (L)39-0212036577 



Length of the pendulum at Pulo Gaunsah Lout by the mean 

 of all the experiments, 39*0212599764 inches. 



The latitude of Pulo Gaunsah Lout, according to the mean of 

 the meridian observations, as hereafter deduced, is 0° V 48*78''' 

 north. 



Then by combining the London observations and those at 

 Gaunsah Lout, we have the length of the pendulum at the 

 Equator 39*02125994 inches. 



We now proceed to deduce the length of the pendulum at 

 Madras by the specific gravity found at the Mint. 



During the time of taking the first series of experiments at 

 Madras, the mean height of the thermometer was 83*48°, of the 

 barometer 30*121, the number of vibrations in 24 hours 

 86166*108. Hence we find that the correction for the buoyancy 

 of the atmosphere is + 6*376. The mean height of the ther- 

 mometer during the time of taking the second series was 

 85*49% of the barometer 30*258, the number of vibrations in 24 

 hours 86166*048 ; and the correction now deduced for the 

 buoyancy of the atmosphere, + 6*378. The correction for the 

 height above the level of the sea, as formerly found, is + 0*095. 

 These corrections being appHed, we shall find the true number 

 of vibrations in 24 hours by the first series 86172*579 ; and by 

 the second series 86172*521 ; the mean being 86172*550. 



Hence the length of the pendulum at the Madras Observa- 

 tory, in latitude 13° 4' 9*1^' north, by the first series, will be 

 39*0268350769 ; and by the second series 39-0267825415 ; the 

 mean of both bein^ 39*0268088092 inches. 



Then by combining the London with the Madras experiments, 

 and taking the length of the pendulum at the Equator, deduced 

 from the Gaunsah Lout experiments,* we find the diminution of 

 gravity from the Pole to the Equator to be -0052756159 ; and 



the ellipticity of the earth ^g^. . 



* The length of the pendulum at the Equator by computation, with the data here 

 given, will be 39*01628254 inches ; differing from the measurement 0-00497740 of an 

 inch ; the diminution of gravity from the Pole to the Equator, using the computed 



length of the pendulum will be '00527629, and the ellipticity of the earth . 



