INTERCHANGE OF HEAT VON BEZOLD 409 



Unfortunately these moments in the diurnal period can scarcely 

 ever be determined very accurately since it is precisely in the 

 upper strata of ground that most disturbances occur. 



But circumstances are still more unfavorable to the determina- 

 tion of the quantity of heat that is exchanged during the diurnal 

 period, since the volume capacity of the ground is subjected to 

 continual variations and especially in these upper strata on 

 account of their varying content of water. 



Therefore in determining the annual exchange we do well to first 

 leave the uppermost strata quite out of consideration and confine 

 ourself to the determination of the quantity of heat that is exchanged 

 through a plane lying somewhat below the surface, e. g., at a depth 

 of 0.5 meter, and then correct the error thus incurred by an addi- 

 tion that will, however, intrinsically be less trustworthy than the 

 other numbers. 



All the views hitherto set forth rest on the assumption that we 

 have to do either with a perfectly dry soil or else that the tem- 

 peratures d t and 6 2 on the Centigrade scale have the same sign. 



This latter condition is always fulfilled in evaluating the annual 

 exchange so long as we confine the investigation to regions where 

 the ground is free from frost or ice at the time of the equinoxes. 



If we wish to free ourselves from the above-mentioned restric- 

 tions and include also those cases in which ^<o and d 2 >o and 

 where also the soil contains water, then we obtain the corresponding 

 formulas from the following considerations : 



Let c be the volume capacity of the perfectly dry porous earth, 

 x the water contained in a unit volume expressed as a fraction of 

 the unit of mass, then for the volume capacity C of the saturated 

 ground we have 



C = c -f x for d > Centigrade 

 but for that of the frozen ground 



C = c + 0.5 x for < Cent grade 



Moreover, the thawing out of a unit volume of frozen ground at 

 o° C. requires heat to the extent of 8ox calories. 



Now assume that in its initial condition at the time t x the ground 

 is frozen to the depth H t and that corresponding to this we have 

 d x <o for h>H and d x >o for h>H x — but that at the time t 2 the 

 ground is completely free from ice and therefore 6 2 >o, then instead 

 of equation (23) we have the following more complicated one: 



