3^4 Mr . Playfair’s Account of a 
which the contiguous radius makes with the meridian by ~ 
of the radius ; that is, if sine GON — sine HON. =— , &c. 
then shall every one of the twenty concentric rings be divided into 
twelve spaces, upon each of which if columns of homogeneous 
matter be supposed to stand, and to be of such altitudes as to 
subtend equal angles from O, the attraction of each column 
on the plummet at O, in the direction of the meridian ON, 
will be the same. 
The attraction of any of these columns, as of that which 
stands on the base GHKL, is measured thus. Let b = GL, 
the breadth of the column in the direction of the radius, 
= ■ 4 °°°° = 666.666 feet ; d — difference between the sines of 
3.12 
the angles of azimuth, or sin. GON — sin. HON = d; E = 
angle of elevation of the column above O: then the attraction 
= bd x sin. E.* * 
I have also used a theorem in these computations, which 
gives an accurate value of the attraction of a half cylinder 
of any altitude a , and any radius r, on a point in the 
centre of its base, and in the direction of a line bisecting the 
base. Let A be equal to that attraction ; then A = 2 a Log. 
Fig. 2 . represents a vertical section of Schehallien in the 
direction of the meridian of the south observatory Q.-f The 
line OR represents the level of the lowest part of the base of 
• Phil. Trans. Vol. LXVIII. p. 751. 
f The observatories O and P are nor in the same meridian ; they are however nearly 
so ; and the section through P in the direction of the meridian would not differ sen- 
sibly from that which is here given 
r + Va 1 + 
a 
Y 
, or A = 2 a Log. — 
