and when so compensated, it is evident that on the assumptions
as given, the chimney height would have to be increased at a ratio
inversely proportional to the square of the normal barometric pressure.

In designing a boiler for high altitudes, as already stated, the
assumption is usually made that a given grade of fuel will require the
same draft measured in inches of water at the boiler damper as at sea
level, and this leads to making the stack height inversely as the
barometric pressures, instead of inversely as the square of the
barometric pressures. The correct height, no doubt, falls somewhere
between the two values as larger flues are usually used at the higher
altitudes, whereas to obtain the ratio of the squares, the flues must be
the same size in each case, and again the effect of an increased
velocity of a given weight of air through the fire at a high altitude,
on the combustion, must be neglected. In making capacity tests with coal
fuel, no difference has been noted in the rates of combustion for a
given draft suction measured by a water column at high and low
altitudes, and this would make it appear that the correct height to use
is more nearly that obtained by the inverse ratio of the barometric
readings than by the inverse ratio of the squares of the barometric
readings. If the assumption is made that the value falls midway between
the two formulae, the error in using a stack figured in the ordinary way
by making the height inversely proportional to the barometric readings
would differ about 10 per cent in capacity at an altitude of 10,000
feet, which difference is well within the probable variation of the size
determined by different methods. It would, therefore, appear that ample
accuracy is obtained in all cases by simply making the height inversely
proportional to the barometric readings and increasing the diameter so
that the stacks used at high altitudes have the same frictional
resistance as those used at low altitudes, although, if desired, the
stack may be made somewhat higher at high altitudes than this rule calls
for in order to be on the safe side.

The increase of stack diameter necessary to maintain the same friction
loss is inversely as the two-fifths power of the barometric pressure.

Table 54 gives the ratio of barometric readings of various altitudes to
sea level, values for the square of this ratio and values of the
two-fifths power of this ratio.