Lithological Survey of Schehallien. 367 
The whole cylinder of which OR is the axis being divided 
into 960 columns, the quarter of it must consist of 24,0, all of 
which, as far as their bases are concerned, are of equal force 
in attracting the plummet at O, so that the difference of their 
effects depends entirely on their altitude. Let O, (Fig. 1.) 
represent the south observatory, ON the meridian, and the 
quadrant ONW a horizontal section through O of one-fourth 
of the cylinder, on which the bases of the columns are marked 
as in the figure. Let a b c be the bounding line of the 
quartz projected on the plane of this section, the columns 
whose bases are within that line being supposed wholly of 
quartz, and those without it of micaceous schistus. If we sup- 
pose the columns that have their tops in this section to be ex- 
tended downwards to the depth of 1440 feet, we shall have 
the quarter cylinder divided into 240 columns, that would be 
of equal disturbing forces, were they of equal density, and 
equal apparent depression below the point O. The inspection 
of the figure serves to distinguish the columns of quartz from 
those of micaceous schistus. In those columns which consist 
of both rocks, the proportion of the quartzy to the micaceous 
part could be judged of with sufficient accuracy by the eye. 
To assist the eye, however, the figure being first constructed 
to a large scale, I used to stretch a fine thread either in the 
direction of a radius passing through O, or in a line at right 
angles to that direction (according as the case seemed to re- 
quire), so as to divide the quadrilateral into two quadrilaterals 
equal, as nearly as the eye could judge, to the irregular di- 
visions made by the boundary of the quartz and schistus. 
The proportion of the parts was then easily ascertained. Now, 
by the first of the theorems laid down above, the attraction of 
