102
THE NATURE AND
[sect. it.
of temperature ; v the velocity; s the specific gravity of the smoke, air being 1 ;
and a = the area of the chimney in inches.
Then h — C D, and the expansion being as the height in feet, h (e — 1)
= D E = F G. But the velocity is that which a heavy body would acquire by
falling through the height F G ; hence, v = 8 V F G = 8 v h (e — .s-). 1 * * * When F G
is equal to B H, the line A B representing the upper line of a uniform atmosphere,
it becomes v = 8 V B H ; and in all other cases it is as the difference, D C — C E
= ED, when E C is reduced to the same density as G H.
If B be the volume of air before it be heated, then in its heated state it is B e;
therefore,
va 8a
144 ~ 144
h (e — s) = Be;
8 a
144 e
\/ h (e — s) = B ;
also,
a
Î44
B e
v/
8 v h (e — s)
The expansion e may be found from the table, ‘ Treatise on Warming, 5 &c. (art. 220.)
But the bulk of a gaseous body at the temperature t' is
_ 459 + t'
6 459 + t ’
when the bulk at the temperature t is unity ; hence,
459 +1'
e — s —
459 + t
Substituting these expressions in the preceding equation, we have
B <? B (459 + O J (459 + t)
8 (459 + 0 ^ h(t' — ts — 459 (s — 1) ) ‘
a
Î44
8 V h (e — s)
172. The divisor, 8, should be changed according to the species of aperture,
(see art. 133.) but that which generally applies is 5; and t will be the mean
temperature of 52°; in this case B being the quantity per hour,
B (459 + 0 . 1
“ 5 x 22-6 x 25 x V h {t 1 - 52s — 459 (s - 1) ) '
1 [This, in strictness, should be 8 ^ h e ~ since h — = the column of vapour equivalent to
the column h of atmosphere, and h ~ — h = h is the excess through which a heavy body
must fall to acquire the requisite velocity : but the omission in the text cannot affect the final
results, as s is so nearly equal to unity, and the coefficient 8 of the expression itself offers only a
rude approximation, though sufficient for common practical purposes. See art. 172.—Ed.]