Intelligence and Miscellaneous Articles. 87 



the atmosphere when t , H , and H x are. given. Now it conducts 

 to temperatures too low. Thus, taking H o = 750 millims. and 

 * =+15°, ForH= 650 550 450 millims. 



We find t L = + 3°-3 -9°*8 -24°*8, 

 while Mr. Glaisher's observations (Eeports of the British Associa- 

 tion, 1862-1864) have given, for the same initial temperature and 

 the same pressures : — 



During the ascent of September 5, 1862 +8-2 -fl-4 —5*4 



Means of several balloon f with a clear sky .... +5*6 —1-3 —7*6 



observations { „ cloudy sky . . +7*0 +0*2 —6-2 



Observations on mountains have led to similar results. M. 

 Plantamour gives for Greneva the annual means 2 =9 o, 21, H =726*6 

 milhms. ; for St. Bernard, where 1^=563*9, the annual tempera- 

 ture t x , calculated by aid of the relation (1), would be — 10 c *8, while 

 the observed temperature is — 1°*76. Formula (1), combined with 

 the hypsometric formula, leads to the conclusion that, whatever H 

 and t may be, a fall of 1 degree in the temperature will correspond 



to an elevation z of 101*2 metres*; that is to say, ^ =— 101*2 



metres ; and yet, in the Alps, the temperature only falls 1 degree 

 for an elevation of 150 metres in summer, and of 300 metres in 

 winter. Humboldt, Boussingault, and others have found that, in 

 the tropics, an elevation of 180-250 metres corresponds to a fall of 

 1° temperature. 



Nevertheless it is beyond question that ~~ is a function of the 



initial temperature and pressure, but not a constant as indicated by 

 formula (1). 



The results to which this formula leads being very different 

 from those given by observation, recourse is had in practice, and 

 especially for the calculation of atmospheric refractions, to various 

 interpolation formulae with one or more constants, calculated from 

 observations made in the higher strata (Laplace, Ivory, Kamtz, 

 Bauerfeind, Kowalsky, &c). On the other hand, the cause of the 

 difference between the temperatures calculated by the relation (1) 

 and the observed temperatures has been supposed to be found in 

 the more perfect transparency of the upper strata, in the absorp- 

 tion of a portion of the heat of the sun by the atmosphere, &c. These 

 hypotheses are gratuitous ; their results cannot be submitted to cal- 

 culation ; and, besides, they are not required. 



On comparing the data of the observations with those of formula 

 (1), it is seen that there exists a source of heat in the upper strata of 

 the atmosphere ; for the observed are constantly higher than the 

 calculated temperatures. This source is doubtless to be found in 

 the aqueous vapour of the atmosphere. Two arguments in favour 



* Formula (1) gives "5H= — ^ — ~V ^t; the differential equation 

 l-\-oct # 291 jj -q 2 



which conducts to the hypsometric formula is ^H = — for 



lat. 45°, whence ^l=a— 7 ®®* = -101*2, the quantity z being the height 



expressed in metres. 



