77 



from the top of the chimney, 6 the temperature there : if we con- 

 sider the differentials, d 6 is as 6 x dh, for dh is as the coohng sur- 

 face, and the decrement of 6 depends on 6 and the magnitude 



d i 



of that surface, then — = m. d h, in being a coefficient depend- 

 ing on the conducting power of the walls of the chimney, 

 and I. (f) = h m + C now make h — o and C — I. t, t be- 

 ing the temperature at the top of the tube, to be determined by 



experiment, the complete integral is I (^—\ = m/i.(/) In respect of 



the S. G. of heated air, it appears from the experiments of Dalton and 

 Lussac that all gaseous bodies expand equally and uniformly by equal 

 additions of heat ; therefore if 1 of air became 1 + e by one degree 

 of Fahrenheit, it would by ^'^ become 1 + 60, and its S. G. being in- 

 plying thermometers to different parts of its length, found that by erecting perpendi. 

 culars at those points proportional to the temperatures there, the line connecting tlieir 

 extremities was a logarithmic curve, it was the reverse of the case which we are at present 

 considering, the heated body was a solid, cooled by air, here it is air cooled by a solid. He 

 ascribes the phenomenon to the conducting power of bodies which he supposes to vary 

 according to this law. 



(/) The tube after some time becomes hot, and abstracts caloric from the air less rapidly 

 than at first, but as its temperature is proportional to that of the included air, the decrements 

 of heat must be also proportional, and the equation continues true but with a different value 

 of m. 



We may easily find what the temperature would be if it were uniform throughout the tube, 



r e 

 for calling it x we have j- X '* = t 9 y. d h =z [• C, but when 6 z= t, h = o, therefore 



C = — -— ! and a: A = or x == . It has been asserted that knowing 



"T 

 this we could find the S. G. of a uniform column of equal dimiensions with that contained 



in the chimney, but the sum of all the is very different from 



1 -l-e 8_ ■" •-•' " I + <r^ 



