employment oj Oblique Riders, 
307 
Longitudinal Pressure, 
To this strain another is added, from a cause, which, 
although not very inconsiderable, appears hitherto to have 
— 119; at 144.. 8, — 155; at 163, 96; and at 176, 96. The strain for each portion 
may then be represented by a — bx, whence 7 axx — hxxx,y — axx — -^bx^x -f- 
cx, and y — ^ax* — ^bx'^ cx -{- d. It will be most convenient, in calculation, to 
make x begin anew with each portion, setting out from the middle, and to divide the 
numbers by too, in order to shorten the operations : thus, for the middle portion, 
from 88 to 59, the strain will be .2028 -p .^6x, a being .2028, and — — .36 ; and 
y 
when X becomes .22, y is .00552, and when x — .29, — .0740, and y ~ .cot i ; 
X 
which values being substituted in the equations for the next portion, we have c — 
.074, and d zz .0011 : and by going through the whole length in this manner, we 
find the fall at the extremes and at seven equidistant intermediate points, .08697, 
.05325, .02514, .00552, o, .00507, .02531, .06705, and .12325. If we wish to find 
the point at which the curve is parallel to the chord of the whole, we must inquire 
where c zz (.12325 — .08697) : 1.76, which will be at 98 feet, or 10 feet before the 
midships. 
We must next determine the magnitude of the strain arising from the longitudinal 
pressure acting on the lower part of the ship only. The resistance being supposed 
to be proportional in tlie first instance to the degree of compression or extension, ac- 
cording to the cemmon and almost necessary law of the constitution of elastic bodies, 
and varying also in the direct ratio of the strength of the fabric, which may be as- 
sumed to be either equable, or, in the case of a ship, proportional to the distance 
from a point more or less^ remote, we must form an equation of equilibrium for the 
absolute equality of the forces in opposite directions, and another for their powers of 
acting with resj ect to any given point as the fulcrum of a lever. Thus the fluxion 
of the absolute resistance at the distance x from the upper surface, supposing the 
strength to be as a-f x, and the neutral point, at which the compression and extension 
cease, to be at the distance b, will be (b — x) c + x zz c (ab — ax-^hx — xx) x, 
which, when x is equal to the depth rf, must become equal to the force f producing 
the strain, or/ — c (abx — 4 f 6a:* — and for the second equation, referring 
the forces to the upp-er suriace as a fulcrum, the fluent of c (b — .r) must 
be equal to ef, e being the distance at which the force e is applied; whence ef — c 
{l^abd^— \ad'-\--^bd^ — \d^)> Now if we make a — d zz x, the equations become 
