SECT. II.] 
PROPERTIES OF STEAM. 
101 
169. When C A is the height of a uniform 
atmosphere, C D the height of the chimney, and 
D E the quantity the air expands by the heat it 
receives in passing through the fire, the height E D, 
or F G its equal, represents the height of the co 
lumn of air which produces the motion, and the 
velocity will be that a heavy body would acquire 
by falling through the height F G. If the whole 
of C A were empty, then B H, the height of the 
atmosphere, would be the height through which the 
body must fall to acquire the velocity with which 
the air would move into the tube, provided it suf 
fered no contraction at the entrance; but such a 
contraction is well known to take place in air as 
well as in water. 
170. When this is applied to a chimney, the smoke being sometimes of a 
density different from common air at the same pressure and temperature, the same 
excess of temperature will produce a greater or less effect in proportion as it is of 
less or greater density than common air. This will be found by subtracting from 
the expansion the specific gravity of the smoke or vapour, that of air of the same 
temperature and pressure being unity. Or it may be done by an allowance of a 
portion of the temperature for the difference of density : either method gives the 
same result when properly calculated. In this case I intend to adopt the former 
method. The latter is followed in my book £ On Warming and Ventilating 
Buildings.’ 1 
171. Let h be the height in feet from the place where the flue enters to the 
top of the chimney; e = the bulk to which one foot of air increases by the change 
Fig. 14. 
A. -B 
1 The principles of calculation followed, both in this and in the work referred to, are perfectly 
identical with those employed by Mr. Gilbert, in an excellent paper on the subject in the 
‘Quarterly Journal of Science,’ vol. xiii. p. 113 : but the notation and methods of managing the 
processes are different; and Mr. Gilbert’s mode of calculating the expansion does not afford quite 
satisfactory results : besides, he makes no allowances for the contractions and loss of force in 
curvilinear motion. I mention the circumstance, because some people compare and criticise, and 
imagine those things to be different which are in reality identical, as may easily be shown by 
putting both in the same notation, and reducing by the rules of algebra. The great object of a 
practical analyst is to render the final equation as easy of application as possible. As to those who 
question principles, it is rather unfortunate for them to question those established principles of 
pneumatics which are confirmed by experiment. It is only when theory and experiment do not 
agree, that the principles can be called in question.