342 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



We may say "The cooling that a mass of air experiences when 

 rising in a steady current without increase or diminution of heat, 

 is precisely the same as that which it would experience if under con- 

 stant pressure a quantity of heat were abstracted equivalent to the 

 work that would be performed by raising an equal weight through an 

 equal altitude," 



This theorem is analogous to that which refers to the circulation 

 of a particle of air under the influence of a gradient and which can be 

 expressed as follows: 



"The acceleration which a particle of air experiences when the 

 atmospheric equilibrium is disturbed in a horizontal direction, is the 

 same as that which a heavy mass would experience if it could glide 

 without friction on the rigid surface of equal pressure." 



Both these theorems are simple developments or illustrations of 

 the formula deduced from purely physical considerations. 



In order to avoid any misunderstanding I repeat that the work 

 done in lifting can be neglected only during steady motion. 



So long as this condition is not yet attained, as, for example, 

 in the above-described cases, it cannot be neglected although in fact 

 in general it is only a small portion of the w^ork done by expansion. 

 Certainly, however, one can imagine processes in which the work of 

 lifting becomes quite important. 



If, for example, we assume that a partially vacuous tube extends 

 above the atmosphere while at its bottom there is air within an 

 enclosure and we now by opening a slot let this air enter into the 

 tube, then after equilibrium is attained the center of gravity of the 

 whole mass will lie much higher than before and then of course the 

 work done in lifting must be considered in addition to the work done 

 by expansion, as the former, like the latter, will be done at the expense 

 of the internal energy, that is to say by cooling. 6 



If we are to investigate such cases then we cannot apply the 

 ordinary formulae of the mechanical theory of heat, but must rather 

 add to these equations another term expressing the work of lifting. 



We must indeed never forget that all the ordinary formulas of this 

 theory are based on the assumption that the work needed to raise 



6 This example is not strictly appropriate, but rather in this special case 

 according to the well-known experiments of Joule, the work of expansion will 

 wholly disappear, or at best is to be considered as a small quantity of high 

 order wherever the work of lifting comes completely into consideration. 

 Hence cases may be imagined in nature in which the work of lifting cannot 

 be neglected; but these are always irreversible processes that must be espe- 

 cially investigated in each individual case. (Note added in 1905. W. v. B.) 



