the mean Denfity of the Earth. 749 
from the altitudes of the points in the plan which fall 
within and near the bafe of the pillar: then, having- 
given the altitude of this axis,, with the pofition of its 
bafe, and the matter fuppofed to be collected into it, a 
theorem can eafily be given by which the effect of its 
attraction may be computed. But to retain the proper 
degree of accuracy in this computation, it is evident that 
the plan mull be divided into a great number of parts,, 
perhaps not lefs than a thoufand for each obfervatory, 
in order that they may be fufficiently fmall, and by 
this means forming about two thoufand of fucli pillars- 
of matter, whofe attractions mull be feparately com- 
puted, as mentioned above. The labour and time ne- 
ceffary for fitch computation, it is evident, would be very 
great, perhaps not lefs than thofe employed in all the. 
preceding computations of the fections, and all the other 
points and lines concerned in this bullnefs . For this rea- 
fon I was defirous of obtaining a theorem or method by 
which the attractions of the fmall and numerous pillars 
might be computed with the fame degree of accuracy, 
but with lefs expence of labour and time than when 
computed feparately as above mentioned. And in this 
inquiry the fuccefs has been equal to my wifhes, having 
at length met with a method by which the bufinefs has 
been, effected, in perhaps one-fourth or one-fifth, of the 
time; 
