398 SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 



dt, the slight change of temperature which is produced by dQ; 



J, the mechauical equivalent of a unit of heat = 424 kilogram- meters j 



K, the constant quantity ^^^, which for the atmosphere equals 29.3, 



and where jJo is the pressure of one atmosphere upon a square meter = 

 10,333 kilograms; 



ro is the volume of a unit of weight of air at the pressure jpo and tern- 

 perture 0° C; 



273 is the zero-point of the Celsius scale according to scale of abso- 

 lute temperatures; 



T, the temperature measured from the absolute zero-point = 273<^ + t; 



t, the temperature according to the Celsius scale. 



We now have the equation^ 



,^ J, RT dp 



dQ = c dt — — ; i- . 



J p 



If the mass of vapor rises, and if, as is the case in nature, heat is 

 neither added nor taken away, its temperature will change, since under 

 diminishing pressure p its volume increases. In this case, dQ = 0, and 

 the connection between the temperature and the change of pressure is 

 given by the equation 



= cdt-^.^. 

 J p 



For the slight elevation dh, the diminution of pressure dp is given by 



the equation 



— dp = p dh, 



where p is the density of the air under the pressure j). 

 From pv = R T it follows, since 



1 

 v = -, 



P 



that 



whence 



P=^ and -dp = ^dh', 

 = cdt+^ dh, 



or, when the values of J and c are introduced, 



^l = -~= - 0.009907 ; 

 dh Jc 



the quotient -^ represents the relation between the variation of tem- 

 perature and of altitude, and therefore gives the change in temperature 

 or the cooling of the rising mass of air for an ascent of one unit of length ; 

 that is to say, for one meter. Consequently, the cooling of the ascend- 

 ing air amounts to almost exactly 1° O. for every 100 meters, and 

 remains the same no matter at what level the ascent begins^ or what the 



