the mean Denjity of the Earth . 753 
another, or by taking the radii in arithmetical progref- 
fion. And d will be conftant, by drawing the radii fo as 
to form with an angles whofe fines flrall be in arithme- 
tical progrefiion; for then d is the common difference of 
the fines of thofe angles. Hence then we are eafily led 
to the belt manner of dividing the plan into the fmall 
fpaces, viz. from the center a defcribe a fufficient num- 
ber of concentric and equi-dift ant circles ; divide the ra- 
dius a 1 of any one of them into a fufficient number of 
equal parts, and from the points of divifion ereCt perpen- 
diculars to meet the circle; then through the points of 
interfeCtion draw radii, and they will divide the circles 
in the manner required. 
In a computation of this kind, we need only calculate 
the attraction of the matter above the plane or horizon 
of each obfervatory, and the attraction of fo much matter 
as is wanting to fill up the vacuity below that plane lying 
between it and the furface of the lower part of the hill. 
For the South obfervatory, the attraction of the Southern 
parts that are above it muft be fubtraCted from that of 
the Northern parts, to obtain the attraction of the whole 
towards the North ; that is, the Southern elevations are 
negative, and the Northern ones affirmative. The con- 
trary names take place with refpeCt to the depreffions, or 
the vacuities below the plane of the obfervatory ; for if 
Vol. LXVIII. 5 A the 
