284 Mr. Atwood's Disquisition on 
M l, h\J , Ik, c R, perpendicular to CH; and, in the line /U* 
take a line l L, which is to /U as the curvilinear area AH/6 is 
to the area ASH£. Through the points S, in all the sections, 
let a line Yf be drawn perpendicular to SH ; the same plane 
will pass through all these lines. LS will be the distance of the 
centre of gravity of the area ASH/j from the plane Yf. The 
products arising from multiplying each area ASH/6 into the 
distance SL, of its centre of gravity, from the plane Yf are to be 
calculated in all the sections ; from which products, by means 
of the Rules* 1. 11. and hi. the sum of the products arising from 
multiplying each evanescent solid, of which the base is the 
area ASH b, and the thickness a small increment of the axis,, 
into the distance SL of its centre of gravity from the plane 
Yf will be obtained. The sum of these products, divided by 
the solid contents of the volume immersed A, will be the 
distance of the centre of gravity of that volume from the ver- 
tical plane Yf Suppose this distance to be equal to the line 
SQ : let the d istance PS, of the centre of gravity of the vo- 
lume emerged, or BSCc, from the plane Yf be found from 
similar computations ; the line PQ will be the distance of the 
centres of gravity of the volumes ASH/j, BSCc, estimated 
In the direction of the line CH, perpendicular to the plane 
F /• 
The solid contents of the entire volume displaced by the ship,, 
are to be obtained; from the, areas, either of the vertical or hori- 
zontal sections.. 
* Whenever the Rules x. 11. and in. are referred to, it is meant that the compu- 
tation is to be made from one or more of these rules, according to the number of or- 
dinates, given, or as other circumstances may direct, . 
f See Appendix, 
