7S 



versely as its bulk would be = ^ !_ ^ ^ , s being its S. G. at the tem- 



peratuie of the atmosphere. The differential of the column of heated 

 air is therefore rr^g^dh or -^jx^, the integral of which is 



~ X / (7^) + C. Now when the weight of the columnrro that 

 is when h=o, C= — '— x / (^-^ ^herefore the weight=-|;- x(/-(7) 

 - I (-7-5-)) ^""^^ ^^^^ draught is the difference between this and the 

 weight of an external column of the height h, therefore = h- - 

 -i-x(/.(i-).— /.(^). j or (substituting for -^ its value ^-TT\') 



^x( ^ ""^'^ AfJ + ^ \e i+i)y jjj ^jjjg equation m is not found, and 



• '(I) 



we must ascertain t and 6 by experimeijt, the number obtained by in- 

 troducing their values will give the space through which a bo- 

 dy must fall to acquire the velocity with which air rushes into 

 the furnace. This increases with h, but not as any manageable 



function of it, it also augments with the fraction — , but at a 



much slower rate, we can however deduce some important practical 

 conclusions. In the first place, is there any maximum of draughty 

 or in other words can a chimney be made too long? to answer 



this let the differential of it, or dh — —x^r^.=o and by subslitu- 



lion and transposition, -^ = — x ^r:^ and 1 -\-ee=s, or, — = e.now as 

 { cannot be negative this is possible only when the contents of the tube 



