SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 405 



The preceding tables give iu a convenient manner answers to all ques- 

 tions that relate to the temperature of an ascending saturated current 

 of air. If the ascending air is not saturated with moisture, its cooling 

 follows at first the laws for dry air, and the figures of the above table 

 first come into application when the cooling has reached the dew-point. 



But before we draw any further conclusions, we must first refer to the 

 equation for the expansion of saturated moist air which Eeje has de- 

 duced (see "Die Wirbelstiirme, p. 215, or Schlomilch, Zeitschrift Math, 

 und Physik, 1864). It is the analogue of Poisson's equation for the 

 elasticity of dry air. If we designate by x and x' the specific quantity 

 of vapor for the absolute temperatures T and T' (that is to say, the 

 maximum weight in kilograms of the vapor contained in one cubic 

 meter), by n the initial pressure in the atmosphere, by r and r' the 

 latent heat of aqueous vapor at the temperatures T and T', and, instead 

 of the numerical coefficients, write their logarithms within brackets, we 

 obtain the following equation:**' 



This formula enables us, for a given initial and final temperature and 

 a given initial pressure (in atmospheres), to compute the pressure cor- 

 responding to the final temperature. For instance, the initial tempera- 

 ture of a moist current of air which rises from the earth's surface, where 

 % = 1, is 20° C, or T' = 293° j and if we desire the pressure, or the alti- 

 tude at the moment when the temperature has sunk to 10° C.,or T' = 283, 

 then we have x' = 0.01715, x = 0.00936 kilograms, ro = 592.6, r = 599.5, 

 and there results 



log^, = 0.23660 + 0.100235 -^; 

 by means of many trials, we find from this, 



^ = 0.780, 



or a barometric pressure of 



0.780 X 760 = 593 millimeters. 



This for a mean temperature of 15° 0. corresponds to an altitude above 

 sea-level of 2,105 meters. The average diminution of temperature of 

 the ascending current is therefore 0°.47 0. per 100 meters. Using our 

 table, page 29, we should, starting first with 20°, have found 0^.45 C. 

 per 100 meters, or approximately 10° in 2,200 meters, therefore at a 

 pressure of somewhat less than 600 millimeters. Since now for 10° 

 sind 600 millimeters, according to the table, the diminution of tempera- 

 ture is 0.49 per 100 meters, therefore the mean diminution is 0.47, and 

 the exact elevation for a cooling of 10° is given, as above, almost with- 

 out computation. 



If, however, we inquire with what temperature a saturated moist cur- 



