Marsh.] ^^^ [March 6, 



process of heating and expanding might be continued indefinitely, with 

 like results. That is to say, P^ P^, P^ &c., being at intervals of one 

 foot, the upper surface of the air will stand at P^ when the temperature 

 has risen twice 490° ; at P^ when it has risen three times 490° F., and so 

 on ; one volume being added for each rise of 490° in temperature, and 

 the expenditure of heat being the same for each. 



If we take for our unit, the heat required to raise the temperature of 

 one volume of air 1° under constant volume, the total expenditure of 

 heat whilst one volume is added to the bulk, will be 490OXl-4=686O; and 

 the heat expended, in excess of that required to produce the elevation of 

 temperature alone, will be 686°— 490O=196o. 



This expenditure has enabled the air to accomplish two results ; to lift 

 2160 lbs. one foot high, and to fill an additi>nal volume. Pro^ Tyndall 

 assumes that the space-filling was accomplished without the expenditure 

 of any force whatever, and that the whole 196° were employed in lifting 

 the weight. But, inasmuch as this may be considered an open question, 

 we will take x to represent the heat, if any, employed in producing and 

 maintaining the change of bulk ; that is to say, the "latent heat of ex- 

 pansion ;" and proceed to consider what must be the relation of latent 

 heat to volume, independently of any particular value of x. 



Since both the expenditure of heat, and the weight lifted, are precisely 

 the same, during the addition of each volume, the remainder,— repre- 

 sented by x — must also be the same. Hence, when one volume has ex- 

 panded so as to fill 



2 vols. — these contain x degrees of latent heat, the No. in each being |x 



3 " " 2x " " " " fx 



4 " " 3x " " " ** |x 

 100 " " 99x " " " " xViyX 

 and so on. 



Whence it appears that the less the density of the air, the greater will 

 be the amount of latent heat, in a given volume ; although, for air of 

 considerable rarity, the change is so slight that the latent heat per 

 volume may be considered as sensibly constant. We have treated only 

 of the heat rendered latent during the expansion of air of standard 

 density, which must already contain latent heat. If, however, we start 

 from the liquid condition of air, a similar train of reasoning leads to the 

 conclusion, that the total amount of latent heat per volume is absolutely 

 the same for air of all densities. It must also be the same for all tempera- 

 tures. For if, when the surface of the air is at P^ we suppose the top of 

 the vessel to be prevented from moving, and the whole to be cooled down 

 until the temperature of the air returns to 32° — the specific heat under 

 constant volume being the same for all temperatures — the heat given out 

 during each degree of cooling will be the same ; bf ing exactly equal to 

 that which, under constant volume, would be required to raise the tem- 

 perature one degree. Consequently, the latent heat must remain un- 



