, and 20,000 horse
power, for a speed of 20 knots, with a coal capacity of 2,000 tons,
sufficient, with contingencies, for a voyage of six to eight days. Or
we may take a later 20 knot vessel, the Furst Bismarck, 500 ft. by
50ft., 8,000 tons, and 16,000 horse power, speed 20 knots, and coal
capacity 2,700 tons, to allow for the entire length of voyage to
Germany.

In Froude's method of comparison the laws of mechanical similitude are
preserved if we make the displacements of the model and of its copy in
the ratio of the sixth power of the speeds designed, or the length as
the square of the speed. Our new 24 knot vessel, taking the City of
Paris as a model, would therefore have 10,000 (24 / 20)^{6} = 29,860,
say 30,000 tons displacement, and would be 800 ft. x 90 ft. in
dimensions. The horse power would have to be as the _seventh_ power of
the speed, and our vessel would therefore have 20,000 (24 / 20)^{7},
or say 72,000 horse power. Further applications of Froude's laws of
similitude will show that the steam pressure and piston speed would
have to be raised 20 per cent., while the revolutions were discounted
20 per cent., supposing the engines and propellers to be increased in
size to scale. To provide the requisite enormous boiler power, all
geometrical scale would disappear; but it would carry us too far at
present to follow up this interesting comparison.

Our naval architect is not likely at present to proceed further with
this monstrous design, exceeding even the Great Eastern in size, if
only because no dock is in existence capable of receiving such a ship.
He has however learned something of value, namely, that this vessel,
if the proper similitude is carried out, is capable of keeping up a
speed of 24 knots for five days with ample coal supply, provided the
boilers are not found to occupy all the available space. For it is an
immediate consequence of Froude's laws that in similar vessels run at
corresponding speeds over the same voyage, the coal capacity is
proportionately the same, or that a ton of coal will carry the same
number of tons of displacement over the same distance. Thus our
enlarged City of Paris would require to carry about 4,000 tons of
coal, burning 800 tons a day.

With the Britannic and Germanic as models of 5,000 tons and 5,000
horse power at 16 knot speed, the 24 knot vessel would require to be
of 57,000 tons and 85,000 horse power, to carry sufficient coal for
the voyage of 3,000 miles.