1874.] 117 [Marsh, 



changed during the process. In other words, the latent heat is inde- 

 pendent of temperature, and is therefore the same per volume for air of 

 any given density, whatever may be its temperature or previous history. 



Hence, as this heat reijresents the force which is employed in main- 

 taining the volume of the air, and as its amount depends upon the volume 

 alone, it may perhaps more properly be termed the "latent heat of 

 volume" — or briefly, the "volume lieaV of air. 



It is evident that we may readily determine, in terms of x, the amount 

 of latent heat (in excess of that rendered latent between the liquid condi- 

 tion and the standard pressure) contained in a given volume, or in a given 

 weight, of the atmosphere at any height. The known law of variation of 

 density is such that at the height of 3.43 miles the density is half that 

 at the level of the sea. — at twice that height, \ — at three times, §-, and so 

 on — the density diminishing in a geometric, as the height increases in an 

 arithmetic ratio. Whence we see that one volume at sea-level, at the 

 height of 



3.43 miles becomes 2 vols. — containing x deg. of latent heat the No. 



in each vol, being Jx 



6.86 " 4 " " 3x " " " fx 



10.29 " 8 " " 7x " " " |x 



34.30 " 1024 " " 1023x " " " \%\\yi 

 68.60 " 1,048,576 " l,048,575x " J'SJwe^ 

 and so on. 



The volume, and consequently the latent heat, of a given weight of air 

 being doubled by each addition of 3.43 miles to the height, it is evident 

 that each molecule of air, near the upper limits of the atmosphere, has, 

 associated with it, an enormous amount of latent heat. But this need 

 not excite great surprise : for when we consider that ^ of a grain of air at 

 the surface of the earth occupies only one cubic inch, whilst at the height 

 of one hundred miles the same occupies one thousand millions of cubic 

 inches, every part filled completely and equably, each molecule being held 

 in its place; at a certain definite distance from its fellows, we cannot 

 doubt that it has abundant use for all its stores of energy, in constructing 

 and maintaining the framework of this vast edifice ; unless, indeed, we 

 conclude that space-filling is a kind of work which — unlike every other — 

 does itself. 



We may form some idea of the value of x, by comparing the heat ex- 

 pended with the work done, in the experiment already quoted from Tyn- 

 dall. He shows that the expediture of heat, in excess of that required 

 to raise the temperature under constant volume, is competent to raise 1° 

 the temperature of 2.8 lbs. of water. If we take 772 foot-pounds as the 

 mechanical equivalent, the same would be competent to raise 2.8 X 772 

 = 2161.6 lbs. one foot high, showing an excess of 1.6 lbs. over the weight 

 actually lifted. The amount of heat applicable to the work of expan- 

 sion or space-filling, for this value of the equivalent, is therefore very 



