propofed trigonometrical Operation. 2C 5 
nature feems to require, and which at fome future period 
ihould, and probably will, be undertaken on a more extended 
plan, with the very bed: machines that can be condructed for 
the purpofe. Many ages may elapfe before meafurements of 
any confiderable portion of the furface of the earth can be 
made in very high fouthern latitudes, fo as to determine, with 
any tolerable degree of exadlnefs, whether the fouthern femi- 
fpheroid be dmilar to the northern, fuppofing both to be figures 
of revolution. But by good experiments with the pendulum 
alone, eafily repeated in all latitudes, the ratio of the femi- 
diimeter of the equator to the femi-axis on both fides may be 
readily obtained. In the mean time I thought it might be ufe~ 
ful to fhew the refult of a companion of the mod confident ex- 
periments of that fort, that have hitherto been made in different 
latitudes, after having applied to thofe at Spitzbergen certain 
corrections, which feemed neceflary, as further explained in 
the note. Thus it appears, that the arithmetical mean of 75 
comparifons between Spitzbergen and the equator gives the 
the 8th of April and 6th of June, 1776; and the beam made ufe of, with- 
15 lbs. weight in each fcale, was true to three grains. 
The machine, in its prefent ftate, although better fitted for experiments than^ 
it was originally, fince it has a wheel added, whereby it regifters its own time, 
and now goes for 12 hours without winding up, is no longer the fame that per- 
formed at Spitzbergen : for in the interim of the two times it has been in my 
poffeffion, the fleel rod having by accident been broken, Mr. Cumming fubfti- 
tuted another, as like to the former as poffible with regard to fize, but which 
will, in all probability, be fufceptible of a different expansion and contraction 
from the effe&s of heat and cold. In the application of the machine, I have 
xifually loaded the top of it with about 24 lbs. weight of lead, in order to render 
the center of fufpenfxon as little liable to motion as poffible : yet, notwithflanding 
this precaution, a pointed plummet, fufpended to the top of the frame, has a 
{mail degree of counter-vibration to that of the ball, which no doubt muft pro- 
duce fome effect. 
ratio 
