102 THE NATURE AND [ SEC T. n. 



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, k (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 

 = E D, 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 80 , 8a 



144 ~~ 144 ^ h ( e ~ s ) =Be; or-j^ */h(es) = B; 



also, 



a B e , 



IT V 



144 8 h(e-s) 



The expansion e may be found from the table, ' Treatise on Warming,' &c. (art. 220.) 

 But the bulk of a gaseous body at the temperature t' is 



^ 459 + t' 

 45^+7' 



when the bulk at the temperature t is unity ; hence, 



459 + 1' 



e s = - s. 



459 + t 



Substituting these expressions in the preceding equation, we have 



a Be B (459 + Q (459 + Q 



144 " = 8 V h (e - ) = ; 8 (459 + t) V h (t' -ts- 459 (s - 1) ) ' 



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 + f ) 1 



5 x 22-6 x 25 x V * (f - 52s- 459 (s - 1) ) ' 



1 [This, in strictness, should be 8 v h e - 1 ; since h = the column of vapour equivalent to 



S S 



the column h of atmosphere, and A h = h e -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 * 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.] 



