of Heights by the Barometer. 403 



the value of the distance r corresponding to every value of p, 

 and of jo, t, vr. We can thus have all the physical elements of 

 the atmosphere, without having recourse to any hypothesis what- 

 ever on the decrease of heat or of density. 



Before applying this process of calculation to Mr. Glaisher's 

 results, let us put equation (1) under another form. We shall 

 characterize by an index the quantities which belong to the 

 inferior stratum of air ; and we shall introduce an auxiliary con- 

 stant h, such that 



Po=ffoP<fi, 



whereby h will be the height of a homogeneous atmosphere of 

 the same state as the air at the lower station. 



Taking into account the variation of gravity according to the 

 vertical height, we have 



Wherefore equation (1) becomes 



VV h Po W 

 Integrating from p to p, and from r to r, we get 



r X P W 



and putting 



we obtain the following equation instead of (1), 



x = h C P «fL d (P\ (3) 



J P Po W 



We must observe that, since in the extent of the atmosphere 



the value of — is always very near unity, it follows that x repre- 



r 

 sents very nearly the difference of level between the two stations. 

 The following Table exhibits the mean results obtained by 

 Mr. Glaisher in his eight balloon-ascents, made in 1862*. 



* An Account of Meteorological and Physical Observations in eight Bal- 

 loon-Ascents, made at the request of the Committee. By James Glaisher, 

 F.R.S. London, 1863. 



2D 2 



