its heating surface, and the amount of heating surface in any
flue or tube is proportional to the product of the length of the tube and
the square root of its sectional area, multiplied by a certain quantity
that is constant for each particular form. But in similar tubes the length
is proportional to the square root of the sectional area; therefore, in
similar tubes, the amount of heating surface is proportional to the
sectional area. On this area also depends the quantity of hot air passing
through the flue, supposing the intensity of the draught to remain
unaffected, and the quantity of hot air or smoke passing through the flue
should vary in the same ratio as the quantity of surface.

265. _Q._--A boiler, therefore, to exert four times the power, should have
four times the extent of heating surface, and four times the sectional area
of flue for the transmission of the smoke?

_A._--Yes; and if the same form of flue is to be retained, it should be of
twice the diameter and twice the length; or twice the height and width if
rectangular, and twice the length. As then the diameter or square root of
the area increases in the same ratio as the length, the square root of the
area divided by the length ought to be a constant quantity in each type of
boiler, in order that the same proportions of flue may be retained; and in
wagon boilers without an internal flue, the height in inches of the flue
encircling the boiler divided by the length of the flue in feet will be 1
very nearly. Instead of the square root of the area, the effective
perimeter, or outline of that part of the cross section of the flue which
is effective in generating steam, may be taken; and the effective perimeter
divided by the length ought to be a constant quantity in similar forms of
flues and with the same velocity of draught, whatever the size of the flue
may be.

266. _Q._--Will this proportion alter if the form of the flue be changed?

_A._--It is clear, that with any given area of flue, to increase the
perimeter by adopting a different shape is tantamount to a diminution of
the length of the flue; and, if the perimeter be diminished, the length of
the flue must at the same time be increased, else it will be impossible to
obtain the necessary amount of heating surface. In Boulton and Watt's wagon
boilers, the sectional area of the flue in square inches per square foot of
heating surface is 5.4 in the two horse boiler; in the three horse it is
4.74;