the mean Denfity of the Earth. 757 
of the fame relative altitude : by fo doing, I obtained a 
great number of irregular polygons lying within, and 
at fome diftance from, one another, and bearing a confi- 
derable degree of refemblance to each other : thefe poly- 
gons were the figures of fo many level or horizontal fec- 
tions of the hills, the relative altitudes of all the parts of 
them being known ; and as every bafe or little fpace had 
feveral of them pafiing through it, I was thereby able to 
determine the altitude belonging to each fpace with 
much eafe and accuracv. In this eftimation I could qe- 
nerally be pretty fure of the altitude to within ten feet, 
and often within five, which on an average might be 
about the 100th part of the whole altitude; and when 
we confider that the number of fuch eftimated altitudes 
is very great, and that it is probable the fmall errors 
among them would nearly balance one another, the de- 
fe<ft of thofe that might be reckoned too little being com- 
penfated by the excefs in thofe which might be taken too 
great, we need not hefitate to pronounce, that the error 
arifing from the eftimation of the altitudes is probably 
ftift much lefs than that part. 
It was neceffary to determine thefe altitudes of the 
pillars, in order to compute the fines of the angles of 
elevation fubtended by them, as the theorem requires 
the ufe of thefe fines; and the very eafy method ufed in 
6 deducing 
