Dr, Young’s Remarks on the 
306 
duced from data which have been obligingly furnished by an 
acute and experienced member of the Navy Board. 
feet, and the excess of weight at the extremity must become 19.7 per foot, the neutral 
point being at 156.5. The equilibrium of the forces will then be expressed by the 
equation 72 x 16.3 — 108 X 59 + * 18 x 94 — 119 X 134 5 — 155 X 144-8 + 192 
X 169.5 — o, which is sufficiently accurate for every purpose. 
From this distribution of the forces, we obtain a determination of the strain for each 
point of the respective portions, which is in the joint ratio of the magnitudes and 
distances of all the forces concerned, on either side of the point, reduced into a common 
1 ^ ... 144 , T 144 -V 
result. For the first portion it is — -x x — - . — 
49 49 49 
~ , X- being the distance from the stern : for the 2d, 72 (a: — 164) — t* 
— : 3d, 72 (j: - 164) _ 54 (a: _ 55I) - ^ (x - 59)^ + ^ ~ • 
x-^x = 
Zi * 
6 
49 
(a: — 59)* : 4th, 72 {x — 164) — 108 — 59) -f 4 . — . : 5th, 
25 
118 
'j 
72(.r-i64)-io8(a:_ 59) + 59 (a:-94) +— (ar_94) - 
6th, from 1 19 to 125.6, 72 {x — 164) — 108 {x — 59) 1 18 (ar — 94) : for the 
, j j , iiQ (a: — I2 c.6)3 
7th, we must add to this expression — 4 ^ • 
13-4 
13-4 
and, in the last 37 
f 1 76 — ar)* 
feet, the strain will be expressed by ( 176 — x) 19.7 x f (176 — x ) — -5- ^9-7 * ' ig ^ — * 
Hence we find the strain, at seven points, 22 feet distant from each other and from the 
ends, 605, 1993, 2815, 2244, 2655, 4610, and 1875 ; and by taking the fluxion of x 
in the seventh portion, we determine tne maximum at 141! feet, amounting to 5261 
tons, supposed to act at the distance of one foot. 
In order to form an idea of the curve which would be produced by such a strain, 
acting on a uniformly flexible substance, we may consider the curvature as represented 
by the second fluxion of the ordinate y, and by finding and correcting the fluent 
separately for each portion, we may obtain the ordinate or fall at any given point 
corresponding to a given extent of arching of the whole fabric. It will however be 
sufficiently accurate for this purpose, to consider the forces as concentrated in a limited 
number of points, dividing those which act in the extreme portions into two parts, in 
order that the curvature may be continued to the ends ; so that -the whole of the forces 
may be thus distributed: at o, 36; at 324, 36 j at 59, — 108, at 94, 118; at 134.5, 
