pr opoftd trigonometrical Operation. 202 
lations for this purpofe were firfi; made foon after * Lord Mul- 
grave’s return from his Voyage towards the North Pole in 
1 773 - 
* The moft northern experiments hitherto made with the pendulum, arcr 
thofe at Spitzbergen, in latitude 79 0 50', whereof an account has been given in 
the Voyage towards the North Pole in 1773. The mac hine made ufe of on that 
occafion belonged originally to the celebrated watch-maker, Mr. Graham, and 
was lent for the purpofe by its prefen t proprietor, Mr. Cum mi kg, who has fince 
obligingly permitted it to remain for feveral years, at two different times, in my 
pofleffion, where it now is. Soon after the return from Spitzbergen, I afeertained 
its rate cf going by my obfervatory clock, for a great while together, in very 
different temperatures ; and thereby found, that the variation from heat and 
cold, namely, -^-ths of a fecond for each degree of Fahrenheit, was confi- 
derably more than had been allowed for it, in determining the acceleration from 
London to Spitzbergen. About this time likewife, Dr Horsley difeovered that 
an error had been committed by the aftronomer (the late Mr. Israel Lyons) 
employed by the Board of Longitude on that Voyage, in calculating the fpherical 
triangle for the correction of the time between the 16th and 17th of July, on 
account of the obliquity of the tranfit-inffrument. From Dr. Horsley’s printed 
letter on this fubjeCt in 1774, it appears, that the difference from that caufe 
amounted to 37 feconds in time, as given by the obfervation with the inffrument 
and by the watch. And ftnee there was reafon to fufpeCt, that the telefcope had 
by accident been moved (one could not tell how much), it was judged fafeft to 
adhere to the acceleration 71". 08 as given by the w r atch. The correction for the 
greater contraction of the fteel rod, I found to be to be fubtraCted, where* 
fore the acceleration from London to Spitzbergen became 68 ;/ .5, and that from 
the equator to London being 156'', the total acceleration from the equator to 
Spitzbergen consequently was 224". 5. Now, fuppofing the length of the pen- 
dulum at the equator to be, as M. Bouguer made it, juft 38.9949 inches, we 
fhall have its length at Spitzbergen 39. 1 978 inches ; and thence the ratio of the 
femi-diameters of the earth, conlidered as an homogeneous ellipfoid, will be that 
of 193.1 to 192. 1, inftead of 183.7 to 182.7, which the acceleration 72". 7 
uncorreCted would have given. And here it feem3 neceffaiy to mention feme 
other miftakes of computation, inadvertently fallen into by the aftronomer, in 
deducing the ratios of the femi-diameters of the earth, as ftated in the 179th 
page of the Voyage to the North Pole, not hitherto noticed that I know of. 
D d 2 With 
