t 60 miles an hour, 29 lbs. per ton. If we suppose the
same law of progression to continue up to 120 miles an hour, the resistance
at that speed will be 92.2 lbs. per ton, and at 240 miles an hour the
resistance will be 344.8 lbs. per ton. Thus, in doubling the speed from 60
to 120 miles per hour, the resistance does not fall much short of being
increased fourfold, and the same remark applies to the increase of the
speed from 120 to 240 miles an hour. These deductions and other deductions
from Mr. Gooch's experiments on the resistance of railway trains, are fully
discussed by Mr. Clark, in his Treatise on railway machinery, who gives the
following rule for ascertaining the resistance of a train, supposing the
line to be in good order, and free from curves:--To find the total
resistance of the engine, tender, and train in pounds per ton, at any given
speed. Square the speed in miles per hour; divide it by 171, and add 8 to
the quotient. The result is the total resistance at the rails in lbs. per
ton.

500._Q._--How comes it, that the resistance of fluids increases as the
square of the velocity, instead of the velocity simply?

_A._--Because the height necessary to generate the velocity with which the
moving object strikes the fluid, or the fluid strikes the object, increases
as the _square_ of the velocity, and the resistance or the weight of a
column of any fluid varies as the height. A falling body, as has been
already explained, to have acquired twice the velocity, must have fallen
through four times the height; the velocity generated by a column of any
fluid is equal to that acquired by a body falling through the height of the
column; and it is therefore clear, that the pressure due to any given
velocity must be as the square of that velocity, the pressure being in
every case as twice the altitude of the column. The work done, however, by
a stream of air or other fluid in a given time, will vary as the cube of
the velocity; for if the velocity of a stream of air be doubled, there will
not only be four times the pressure exerted per square foot, but twice the
quantity of air will be employed; and in windmills, accordingly, it is
found, that the work done varies nearly as the cube of the velocity of the
wind. If, however, the work done by _a given quantity_ of air moving at
different speeds be considered, it will vary as the squares of the speeds.

501. _Q._--But in a case where there is no work done, and the resistanc