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.