266 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



stituted where I is the latent heat of melting ice. But so long- as the 

 melting point of ice is not exceeded, we can safely consider fas con- 

 stant, as the following consideration shows. The following equation,* 

 the extremely simple deduction of which may here be omitted, gives the 



value of c: 



c = 0.2375 + 0.00024 y. 



Now a glance at the table given in the appendix shows that c will 

 not exceed the value 0.2447, such as corresponds to a temperature 32° 

 C. under 760 milimetres pressure. Since however on the other hand, 

 for temperatures between 0° and 32° according to Regnault's figures,t r 

 is confined between the limits 606.5 and 584.2, therefore the extreme 



values that 10(J( . can have for a pressure of 700 milimetres are 2.55 



for t = 0° and 2.39 for t = 32°. 



For lower pressures (that is to say at greater altitudes), c is larger 

 for a given temperature; but at the same time it is precisely under 

 these conditions that only lower temperatures occur, and therefore only 

 the higher values of r are to be considered, so that JTstill remains nearly 

 within the same limits. 



On account of the remarkably slight influence that the change of one 

 unit in the first decimal place in the value of K has on the final result 

 we can for brevity put K = 2.5, so long as t > 0°. 



If t <0°, then we have to add the quantity 80 [calories] U the value of 

 r. If we consider this and then compute K for 0° and for — 30°, first 

 for /3 = 760 milimetres, and next for fi = 400 milimetres we obtain as 

 extreme values 2.87 and 2.98. so that here with even more right we can 

 assume K to be constant and as we in fact will do equal to 2.9. 



According to this, without important error, we may consider the lines 

 F 3 F, in general, as parallel straight lines which experience only a slight 

 bend at the point corresponding to 0°. 



In the actual application of the above-explained graphic method we 

 do best to place upon the system of coordinates, on which we have en- 

 tered the saturation curve, a group of straight lines representing the 

 series F s F, of which those on the left of the zero coordinate are inclined 



to the axis of abscissas so that tan «=on, but those to the right of the 



zero coordinate have tan a= ?r ^ 



2.5. 



* Hann, Zeit. Oeat. Gesell. Met., 1874, vol. ix, p. 324. [Sinithson. Rep., 1877, p, 399.] 

 t According to the investigations of Dieterici (Wiedemann's Annalen, 1889, xxxvn, 

 pp. 494-508), as well as according to those of Ekholm (Bihaiig K. Svenska Vet. Akad. 

 HavdL, 1889, xv, Part I, No. 6.) ; these numbers are indeed not quite free from criti- 

 cism. Since however on the one hand, the correction of these numbers scarcely 

 comes into consideration in the final result here desired, and since on the other hand 

 the value of the capacity for heat of dry air here adopted is based on the caloric used 

 by Regnault, it appeared to me proper, if not even necessary, also to make use of the 

 older value for r. 



