Dr, Young^s Remarks on the 
508 
escaped notice ; that is, the partial pressure of the water in a 
longitudinal direction, affecting the lower parts of the ship 
only, and tending to compress and shorten the keel, while it has 
no immediate action on the upper decks. The pressure, thus 
applied, must obviously occasion a curvature, if the angles 
made with the decks by the timbers are supposed to remain 
c —f, and c (^bd^—^d*) ~ ef, and from the former we have c {\bd^—^\d*) 
= ^df; and, by subtraction, -^\cd* = consequently the force / may be 
considered as acting on a lever of the length e — ^d : and if we take any other value 
for a, the fractional multiplier of d, instead of will be thus if a ~ we 
have r— for the length of the lever. In order to find the mean distance e at 
which the pressure of the water acts, we may suppose the form of the mean trans- 
verse section of the ship to be parabolic, and the area such as to correspond to the 
bulk of 3000 tons of water, each containing 35 cubic feet, the length being 176 feet, 
and the breadth 47^, whence the depth must be 18.84 feet: then the centre of gra- 
vity of a parabola being at the distance of -f- of the depth from the vertex, (Vince’s 
Fluxions, p. ioi,) and the centre of oscillation at |, when the point of suspension is 
at the vertex (p. 1 ii,) the distance of these points /j- will be increased to when 
the point of suspension is removed to the termination of the absciss, and the distance 
of the centre of pressure from the vertex will be | — -/j-rz f, and | x 18.84 = 8.074, 
which, subtracted from x 40 n; 17.777, leaves 9.703 for the length of the lever. 
Now the magnitude of the pressure on this section must be to 3000 tons, as the depth 
of the centre of gravity, 7,536 feet, to 176, that is, 128.45 tons, which, acting at the 
distance 9.703, will produce a strain of 1247 tons, or, in the terms of the preceding 
calculation, .1247, which is the multiple of ^x' indicating the fall. These different 
causes of arching being independent of each other in their operation, their effects will 
be simply united into a common result : and the whole curvature of the ship, sup- 
jxising its strength equable throughout its length, may be thus represented. 
Dist. from the stern o 22 44 66 88 110 132 154 176 
Strain 1247-fo 605 1993 2815 2224 2655 4610 1875 o 
Fall - .04828 .02716 .01207 .00302 .00000 .00302 .01207 .02716 .04828 
.08697 .05325 .02514 .00552 .00000 .00507 .02531 .06705 .12325 
.13525 .08041 .03721 .00854 .00000 .00809 ’03738 .09421 .17153 
For 12 inches 
of arching 10.58 6.29 2.91 .67 .00 .63 2.93 7.37 13.42 
