SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 381 



For an average temperature diminution of O^.S 0. for each 100 meters, 

 the meau annual temperature will be — 5^ C. at an altitude of 3,000 

 meters above Vienna (— G<^.6 is observed at the Theodul Pass, altitude 

 3,330 meters). If we substitute these values for h and 4, we find 

 \o^m = or < 0.48342 and po = or < 3.9 millimeters. 



Therefore, even were the air, at 3,200 meters altitude, saturated with 

 vai)or, the vapor-tension in Vienna would, at the highest, be only 

 3.9°^™; in fact, however, it is observed to be 6.9™". In order to make 

 this tension possible, the temperature at 3,000 meters altitude must be 

 + 2^.4 C, and therefore the rate of decrease of temperature would 

 amount to only 0°.25 C. for each 100 meters. 



If now we seek to represent the observed diminution of vapor-tension 

 by means of an empirical formala, we can either choose a simple expres- 

 sion of the form 



p=Xh (1 + «/i + &/r), 



or examine whether the observed values proceed in a geometrical pro- 

 gression, in which case the value of C is to be determined, which must 

 be much smaller than the above given theoretical value. 



I first deduced, according to the method of least squares, from the 

 mean of the series Himalaya («) and [h) and Balloon Voyages {a) and (Z>), 

 the formula 



Ij =2h (I - 0.078/i -f 0.001G4/t2), 



where h is given in units of 1,000 English feet each. If we use also the 

 observation of Glaisher that for h = 28,000 feet j; is nearly equal to 

 zero, we find 



p =j)o (1 - 0.075 /t + 0.0014G/t2), h in units of 1,000 English feet; 

 or 



p =po (1 - 0.24G Jl + 0.01569 /i2), h in units of 1,000 meters. 



These formulae of interpolation represent, with almost perfect accu- 

 racy, the observations on which they are based, but are inapplicable to 

 altitudes above 7,800 meters, since for higher altitudes they give increas- 

 ing values of p (for h = 26,000 feet, the second formula gives j? = 0.04). 

 But this does not prevent their application to all cases that actually 

 occur. 



In order to express the definitive mean values of our table, the quan- 

 tities -^\ by a geometrical progression, I have pursued the following 

 method: The general formula is, for our case, converted into 



\og(p:po}' 

 I now computed the values of G for 14 of the intervals of the table 



(excluding the last [22], because for this the E. depends upon too few 



Po 



log ~ I = — >, ; whence C = 



LPoJ 6" 



