100
THE NATURE AND
[sect. II.
Its differential must therefore be = 0, or
1127 x 6(i + 100)»rfi _ 25 {l + d)dt
30 x 177 6 Id
whence
30 x 177 6 x 25 (l+d
1127 x WTd
100.
Which reduces to
t = 321 (LLf)" - ioo.
k / d y
166. When l —2d, or the length of stroke is double-the diameter,
348-2
d i
100;
or in logarithms, log. (t + 100) = 2-54180 - } (log. d in feet).
167. Hence it appears, that when the length of the cylinder is double its
diameter, the temperature of condensation, which gives the minimum loss of heat,
varies inversely as the fifth root of the diameter of the cylinder. When the dia
meter d = 6 feet, the temperature of condensation t — 143-3 ; when d — 3 feet, the
temperature of condensation should be 179*5 ; and by using a table of logarithms,
the best temperature for condensation for any other diameter may be easily found
by the rule. 1
Of the Ascent of Smoke in Chimneys.
168. If a bent tube, of uniform diameter, A C B, were continued to the sur
face of the atmosphere, the lowest point of the curve being at C, the centre of the
aperture of a chimney, and the tube of the same size as a chimney, then the tem
peratures being equal at the same height in the two branches, the whole would be
in equilibrio; but if a part, C D, be of a more elevated temperature than the
corresponding part of the other branch of the tube, that air being of less density
than cold air, the balance will be destroyed, and motion will take place, the moving
force being the difference between the weights of the columns of air. Now a
chimney may be considered part of such a tube ; for though, in a chimney, the
column of air is confined only as far as the short canal or tube of the chimney
extends, the actual pressures which occur in the atmosphere are equivalent to the
pressures in the bent tube, and must be measured in the same manner.
1 The Rule suggested by the formula is as follows :—Take out from a table of logarithms the
logarithm of the diameter, expressed in feet, and divide it by 5 : subtract the quotient from
2-54180, and the remainder will be the logarithm of a number, which diminished by 100, the result
will express the required temperature of condensation, in degrees.