482 ME. E. J. EEED ON THE EELATION OF FOEM AND DIMENSIONS TO 
mical in her first cost, would cost much less than the other for use, for maintenance, 
and for repairs during the whole period of her existence, and would possess the inesti- 
mable advantage of greatly superior handiness in action. 
I will now pass from the consideration of existing ships, and take a more abstract case. 
Let us presume that we have a ship with prismatic sides vertically, as before, but 
with curves of sines for horizontal sections. 
The weight of hull is to be distributed equally over the sides and bottom. 
And let us in the first instance take the proportion of length to breadth to be 7 to 1. 
It will be found by construction that the length along the curve is to the breadth as 
7T to 1. 
Let 6 = half breadth extreme. 
w — weight per sq. ft. of surface for hull. 
2 w' = weight per sq. ft. of armour and backing. 
d' = depth of armoured side. 
d' 
- = depth of lower edge of armour below water. 
d = draught of water. 
3W = weight of equipment (exclusive of engines, boilers, and coal) 
s = required speed in knots. 
Surface for weight of hull . . =4 x 7T6(^ + f<6') + 146 2 
=28-46(d+f<) + 146 2 . 
Surface for armour and backing = 4x 7T6x^' 
=28-4 bd'. 
Let us assume in this case that Professor Rankine’s rule for the calculation of horse- 
power and speed holds, viz. that the indicated horse-power equals the “augmented 
surface” multiplied by the cube of the speed and divided by a certain “ coefficient of 
propulsion where the “ augmented surface ” is the immersed surface multiplied by a 
coefficient of augmentation, which is equal to 1 + 4 (sine of greatest obliquity of water- 
line) 2 -!- the 4th power of the same sine. The coefficient of propulsion for a clean iron 
ship of good form is 20000. 
In the present case, 
Angle of maximum obliquity of water-line curve=^-|^X y = 12y. 
Therefore coefficient of augmentation = 1 -j- 4 sin 12y 2 + sin 12^* J 
= l + 4x-2225l 2 + -2225Y 
=l + 4x-0495 + *0024 
And augmented surface . 
and I.H.P 
= 1 - 2 . 
=146(2<Z+6)xL2 
= 16-86(2^+6), 
16-8b{2d+b)s 3 
— 20000 ’ 
2-46(2^+ 6) s 3 
and nom. H.P 
20000 
