Variation of Temperature ^ Sfc. in the Atmosphere, 173 



a height of 4^ miles. The depression of temp., as we have 

 seen in the table, differs likewise only about 1-^°, 



It should here be observed, that if Laplace's formula coin- 

 cided perfectly with observations at moderate heights, yet it 

 could not be true at greater elevations ; and the greater the 

 height the more it must diverge from nature ; for by that 

 formula, the atmosphere must be infinite in extent, a palpable 

 absurdity, which Laplace himself acknowledges. However, 

 the differences which we have shewn to exist between the two 

 formulae, are much within the limits of error to which pro- 

 bably the best observations could pretend in such heights. 



There is a source of error in barometric admeasurements, 

 which it will be difficult for any theory to estimate or avoid ; 

 namely, the unequal distribution of vapour in the atmosphere. 

 This will in general tend to depress the lower barometer too 

 much, and consequently to give the altitudes too little. It is 

 probable this may never occasion an error of serious moment, 

 but it will undoubtedly always have some influence. 



If we suppose D, d to denote the densities of the air cor- 

 responding to P, Pi the combination of our two theorems gives 



or in Lussac's ^ = (.432)^ = 9"nT9«' ^^^^^"^S ^^^"^ ^^s J 



by only a -j^th part. 



From these instances some idea may be formed of the per- 

 fect fidelity with which the theorems I have given represent 

 phenomena. Probably it will not be hazarding too much to 

 affirm, that the success of them is greater than could have 

 been anticipated ; and that there is scarcely a parallel instance 

 in science in which investigations, begun and conducted so 

 absolutely independent of experimental aid, have been so tho- 

 roughly confirmed by phenomena. Their mathematical ana- 

 lysis will appear in the work already alluded to. 



Several important consequences flow from these theorems, 

 besides those we have mentioned ; some of which we shall 

 here notice. 



1st. The velocities of sound and the transmission of heat by 

 the air are the same. 



