230 SIXTH REPORT 1836. 



If this law, which requires confirmation by observations more 

 in number, and extended over a greater portion of the earth's 

 surface, should be finally established, the usual formula for the 

 barometric determination of heights will require some modifica- 

 tion. The mathematical reasoning in this problem ought also 

 in strictness to proceed on the supposition that the atmosphere 

 is in motion, and not, as is always supposed, at rest ; but this 

 improvement in the theory is not likely to be effected till at the 

 same time a mathematical theory of the periodic oscillations of 

 the barometer can be given. 



It remains to notice the attempts of a purely theoretical cha- 

 racter which liave been made to furnish the second equation 

 above spoken of, and by it to assign a relation between the tem- 

 perature, pressure, and density of the air at different elevations. 

 If we conceive the atmosphere to be at rest, and every point of 

 it to be in its mean state with respect to temperature, there will 

 be a certain temperature corresponding to a certain density ; in 

 other terms, the density will be a function of the temperature. 

 Now by experiment it is found that when a given mass of air is 

 suddenly rarefied by mechanical means, at the first instant, before 

 it receives any accession of heat from surrounding bodies, its 

 temperature is lowered, and it is supposed to absorb a quantity 

 of heat equal to the diminution of temperature. The heat that 

 has disappeared is conceived to become latent, while the total 

 quantity of heat, consisting of the latent heat, and that indicated 

 by the thermometer, remains the same in the given mass, till 

 the temperature is raised by the position of the mass in the midst 

 of bodies of a higher temperature. Dr. Dalton conceived the 

 condition of the air in this experiment at the first moment of ra- 

 refaction to be analogous to that of air of the same state of ra- 

 refaction in the atmosphere, and consequently infers that to the 

 same quantity of atmospheric air the same quantity of heat is 

 always attached, a loss of temperature being compensated for by 

 an increase of latent heat, or, as it is also called, heat of combi- 

 nation, and an increase of temperature being due to a develop- 

 ment of latent heat. Admitting, therefore, that the density of 

 the atmosphere is a function of the temperature, it will follow 

 from this hypothesis that it is also a function of the latent heat . 

 The truth of this theory can be judged of only by its forming a 

 basis for mathematical calculation, and so allowing us to compare 

 the consequences that flow from it with experience. Mr. Ivory 

 has enabled us to judge of it in this manner by a series of valu- 

 able papers on this subject contained in the fiGth volume of the 

 Philosophical Magazine*. Mr. Ivory admits with Dr. Dalton 

 * pp. 12, 81, 241. 



