PENDULUM AT THE ROYAL OBSERVATORY, CAPE OF GOOD HOPE. 175 
Note by Captain Sabine. 
The observations which Mr. Fallows has communicated to the Society in 
this memoir, having been corrected for buoyancy and expansion, before the 
volume of the Phil. Trans, had reached the Cape, in which the true value of 
those corrections is assigned from experiments with a pendulum of the same 
materials and figure as that employed by Mr. Fallows, I have re-computed 
his results with the correct elements of reduction, and find the retardation of 
the vibrations at the Cape, compared with those in London, to be 67-15 per 
diem, instead of 67.12, the difference between Mr. Fallows’s calculation and 
mine amounting only to three hundredths of a vibration per diem. 
The small amount of the difference, on the employment of the more 
correct elements of reduction, is an illustration of the remark, with which 
I concluded the paper on the reduction to a vacuum of an invariable pendu- 
lum (Phil. Trans. 1829, page 236.) ; that in relative experiment^, computed be- 
fore the true reduction to a vacuum was known, and in which a correction for 
expansion was employed, derived directly from the vibration of the pendulum 
at the same spot in different temperatures, (as is the case in Mr. Fallows’s cal- 
culation,) a compensation takes place of the errors of the respective reductions 
for expansion and resistance, leaving the only uncompensated error in the final 
result, that arising from barometric differences, which in all cases of compa- 
rison between stations not far removed from the level of the sea, cannot be 
otherwise than extremely small. 
In Mr. Fallows’s calculation he has taken the rate in London of the invari- 
able pendulum which Captain Ronald took out to the Cape, solely from my 
observations with it : if, however, Captain Ronald’s observations with the same 
pendulum in London be added to mine, and a true mean be taken correspond- 
ing to the number of observations of each observer, the retardation is precisely 
that stated by Mr. Fallows ; namely, 67.12 vibrations per diem. 
