vercome by another means; and
the whole available engineering and ship-building talent of Great
Britain and the United States has been directed not entirely to the
engine department, but to the hulls and to the production of a large
class of ships, which are admissibly cheaper in proportion to size and
expense of running when compared with smaller vessels, if they are
always employed and have full freights and passage. It is well
established that large steamers run proportionally cheaper than small
ones. (_See Table III., page 76._) This arises from the important fact
that the length increases far more rapidly than the breadth and depth.
Consequently the tonnage of the vessel increases much faster than the
resistance. In passing through the water the vessel cuts out a canal
as large as the largest part of its body, which is at the middle of
the ship. If the vessel be here cut in two, the width and depth, or
the beam and hold being multiplied together will give the square
contents of the midship section. Now, when a vessel is doubled in all
of its dimensions, this midship section and consequently the size of
the canal which it cuts in the water, does not increase as rapidly as
the solid contents of the whole ship, and consequently, as the
tonnage. Hence, the resistance to the vessel in passing through the
water does not increase so rapidly as the tonnage which the vessel
will carry.

To make this clearer, let us suppose a vessel of good proportion,
whose length is seven times the beam, or 280 ft. long, 40 ft. wide,
and 30 feet deep. The midship section will be 40 x 30 = 1,200 square
feet: the solid contents will be 40 x 30 x 280 = 336,000 solid feet.
Again, let us double these dimensions, and the ship will be 80 ft.
wide, 60 ft. deep, and 560 feet long. The midship section will be 80 x
60 = 4,800 square feet: the solid contents will be 80 x 60 x 560 =
2,688,000 solid feet. Now, comparing the midship sections, and also
the said contents in each case we have,

Midship Section, 4,800
----- = 4 to 1. Increase as the squares:
Midship Section, 1,200

Solid Contents, 2,688,000
--------- = 8 to 1. Increase as the cubes.
Solid Contents, 336,000

Thus, the midship resistance has increased as four to one, or as the
square, while the solid contents, representing the tonnage, have
increased as eight to one, or as the cube. It is evident that the ship
has but four times