314 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



pressures are /?, and /? 2 must receive the quantity of heat 



Q = 13.6 c p ftdp 

 A 



in order to warm it from o c 



FIG. 46 



C. up to the temperature corresponding 

 to its temporary condition — where 

 /?! is the lower pressure at its upper 

 boundary and /? 2 the higher pressure 

 at its lower boundary surface. 



Assume that the straight line B t 

 B 2 in fig. 46 corresponds to the zero 

 of the temperature scale and that 

 /?! and /? 2 are the ordinates belong- 

 ing to B l and B 2 , and furthermore let 

 the curves through the points T l T 2 

 and T x ' T 2 be two curves of condi- 

 tion representing the course of the 

 temperatures t' and t then will 



rA 



A 



be the surface bounded by the straight lines B t B 2 , B t T, , B 2 T 2 

 and the portion 7\ T 2 of the curve of condition where the points 

 T x and T 2 correspond to the temperatures t x and t 2 . 



We can thus convert the above given equation into the form 



Q 



13-6 c p F 



where the surface B x T x T 2 B 2 is represented by F. 



Now imagine another condition for .which we have the tempera- 

 tures ty and t 2 corresponding to the same pressures /? x and /? 2 as 

 before, then the quantity of heat Q' that is now to be added in order 

 to bring that portion of the column of air which at first had the 

 temperature o° C. up to the temperature condition represented by 

 the second curve will be given by the equation Q' = 13.6 c p F' 

 where F' is the area of the figure B x 7\' T 2 B 2 . 



Finally the quantity of heat that is neele 1 to convert t^e portion 

 of the air column between the pressures /? t and /? 2 from the condition 



