287 
made with an invariable pendulum. 
Thus we have obtained 86x25,61 vibrations made by the pendulum by the tran- 
sits ofthe sun, and by the stars 86125,48. 
But the sum of the factors for the sun being 304, and that for the stars only 148, 
we have 0,04 to subtract from the vibrations given by the sun to arrive at 86125,57, 
the mean number of vibrations made by the pendulum in 24 hours. 
The ball of the pendulum was elevated above the level of the sea 72 feet, the 
correction for which is ,293 ; but from the nature of the ground on which the pen- 
dulum stood, this requires to be multiplied by T 6 5 to obtain the true correction due 
to this elevation, or +0,18. 
The correction for the buoyancy of the atmosphere is +5,80, to which must be 
added 0,18, and we obtain 5,98 for the final correction to be added to 86125,57, 
the mean number of vibrations made in 24 hours ; and thus we arrive at 86131,55, 
for the number of vibrations that would be made by the pendulum in vacuo at the 
level of the sea and temperature 68° at Rio de Janeiro in latilude 22 0 55' 22" south, 
and longitude 43 west from Greenwich. 
From the above data, with the number of this pendulum’s vibrations determined 
in London on the return,* and the length of the seconds’ pendulum there, the 
length ofthe pendulum vibrating seconds at Rio de Janeiro appears to be 39,04368 
inches ; and comparing this with the lengths ascertained at different places by 
Captain Kater, we obtain the following ellipticities. 
Stations compared with Rio de 
Janeiro in Lat. 22 0 55' 22" S. 
Diminution of 
Gravity from 
Pole to Equator 
Ellipticity. 
Length of 
Equatorial 
Pendulum. 
Unst . in Lat. 60 45 28 N. 
,00^726 
I 
39,01188 
305,07 
Portsoy . . 57 40 59 
,0053732 
I 
,OIl88 
3 ° 5> l 3 
Leith Fort . 55 58 41 
,0053570 
I 
3 ° 3> 6 3 
CO 
ON 
O 
Clifton . . 53 27 43 
,0053109 
I 
299,44 
,01225 
Arbury Hill . 52 12 55 
,0053565 
I 
3 ° 3 >S 9 
,01198 
London . . 5131 8 
,0053151 
I 
299,81 
,01223 
Shanklin Farm 50 37 24 
,0053163 
I 
,01222 
299,92 
= ,0053431 
1 
302,37 
39,01206 
* See Remarks after the Experiment, in the Appendix. 
