employment of Oblique Riders,- 3 1 1 
strain takes place, in a 74 gun ship, at the distance of about 18 
feet from the midships, amounting to about 10,000 tons, at the 
this Is the most probable cause of the deficiency in the velocity of waves, when their 
breadth is very small in proportion to the depth of the fluid. In the present calcula- 
tion, however, the considerations are more simple, and we have only to determine the 
effect of the difference produced during the passage of a wave in the quantity of water 
displaced by the ship, with respect to the general surface. The total height of the 
waves being 20 feet, and the total breadth 70, the section being supposed to con- 
stitute a figure of sines, the elevation or depression, at the distance x from the middle, 
6.28 2 
will be 10 cos. px, p being — — — .08976, the fluxion of the area io;c- cos. px. 
70 
10 
and the fluent — sin. px; at the constant distance 2 from the middle, the fluxion of 
the p strain will be (a: — z) iox<^px, In order to find the fluent of which we must 
take the fluxions of x^px, and (^px, which are xipx -f xpx(^px, and — px^px ; hence 
fxx(}px — xfpx -f ~ ^px; and the fluent of the strain will ^ 
— cpx -f which must vanish when w rr z, so that c r: — ^ cpz : now, when xzza, 
PP PP 
the corrected fluent becomes ~ (a — 2) fpa epa — cpz ; and if we take the 
P PP PP 
fluxion of this, making z variable, we find, for the maximum, — • 
10 .. 
—z{pa + 
P 
10 
J 
z^pz 
— o, and (pz -zz ^pa, so that z must be a — 70 n 18, whence the greatest strain is 
found, X 70 X. .999 — 7791, expressed in square feet of the longitudinal section, 
which, for a ship 47-*- feet wide, may be reduced into tons, by multiplying it by 
and will become 10572. It is true, that if the waves allowed time for the ascent or 
descent of the ship, so that she might float in equilibrium, the greatest strain would 
be little more than of this weight ; but the elevating force in the case here calcu- 
lated being only^V the whole weight, it would require almost a second to raise the 
ship 1.265 feet, and to restore the equilibrium ; so that notwithstanding its gradual 
application, dependent on the progressive velocity of the waves, which varies with the 
depth of the fluid, there must be an interval during which it operates very nearly in 
its whole extent, especially as the occurrence of a partial obstruction tends to increase 
die total 'height of a wave at the point where it is situated. 
S S 2 
