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.]