ion, which is, 56.95 tons. Here the
speed has increased 12-1/2 per cent., while the quantity of fuel
consumed increased 42-1/2 per cent.

Suppose, again, that we wish to increase the speed from 8 to 10, and
from 8 to 16 miles per hour. The formula stands the same, thus:

Miles. Miles. Tons Coal. Tons Coal.
8^3 : 10^3 :: 40 : _x_, = 78.1
8^3 : 16^3 :: 40 : _x_, = 320.

II. TO FIND THE SPEED CORRESPONDING TO A DIMINISHED CONSUMPTION OF
FUEL.

Murray has given some convenient formulae, which I will here adopt.
Suppose a vessel of 500 horse power run 12 knots per hour on 40 tons
coal per day: what will be the speed if she burn only 30 tons per day?
Thus:

40 : 30 :: 12^3 : V^3 (or cube of the required velocity,)
Or, reduced, 4 : 3 :: 1728 : V^3,
Equation, 3 x 1728 = 5184 = 4V^3,
Or, 5184/4 =
Cube root of 1296 = 10.902 knots = V, required velocity.

Thus, we reduce the quantity of coal one fourth, but the speed is
reduced but little above one twelfth.

III. RELATION BETWEEN THE CONSUMPTION OF FUEL, AND THE LENGTH AND
VELOCITY OF VOYAGE.

The consumption of fuel on two or more given voyages will vary as the
square of the velocity multiplied into the distance travelled. Thus,
during a voyage of 1200 miles, average speed 10 knots, the consumption
of coal is 150 tons: we wish to know the consumption for 1800 miles at
8 knots. Thus:

150 tons : C required Consumption :: 10^2 knots x 1200 miles : 8^2,
Knots x 1800 miles.
Then, C x 100 x 1200 = 150 x 64 x 1800,*
Or, C x 120,000 = 17,280,000
Reduced to C = 1728/12 = 144 tons consumption.

Suppose, again, that we wish to know the rate of speed for 1800 miles,
if the coals used be the same as on another voyage of 1200 miles, with
150 tons coal, and ten knots speed:

We substitute former consumption, 150 tons for C, as in the equation
above, marked *, and V^2 (square of the required velocity) for 64, and
have,

150 x 100 x 1200 = 150 x V^2 x 1800,
Or, 120,000 = 1800V^2,
Reduced, 1200/18 = V^2,
And V = square root of 66.66 = 8.15 knots.

From the foregoing easily intelligible formulae we can ascertain with
approximate certainty the large quantity of coal necessary to increase
speed, the large saving of coal in reducing speed, as well as the
means of accommodating the f