410 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



u 2 _ Uj = _ I / c + - ) t dh + 80 x H t + \ (c + x) d 2 dh 



H Hi 



+ f (c + x) (Q 2 - d,) dh = c f (0 2 - d t ) dh 



H, ° 



Hi H 



+ x f ( 2 ~ ° l )dh + (c + x) f (0 2 - X ) dh + 80 x H v 



■ (27) 



where, however, we have still always to remember that d 2 is always 

 positive, whereas in the first two integrals d l occurs with the nega- 

 tive sign. 



We can of course also represent this formula geometrically, but as 

 the presentation thus obtained is by far not so simple and clear as 

 above, where the temperatures are either wholly above or wholly 

 below the freezing point, therefore we refrain from reproducing 

 them here. 



From these two expositions we see how very easy it is to deter- 

 mine the quantity of heat exchanged through the earth's surface 

 if only one knows the course of the temperature at different depths 

 as well as the volume capacity of the ground and for temperatures 

 below freezing, as also the water content. 



By so much the more it is to be regretted that there is such a 

 remarkably small number 15 of series of observations of earth tem- 

 peratures for which the volume -capacity of the ground is known 

 from direct experimental determinations. 



In a subsequent communication I will attempt to show how far 

 the available observations can be utilized in order to determine 

 numerically from them the annual and perhaps also in some cases 

 the diurnal heat exchange in the ground for different places and 

 under climatic conditions as various as possible. 



15 Such values for the actual soil in which the temperature observations 

 were made, I have only been able to find in the memoir by Lord Kelvin 

 (William Thomson "On the Reduction of Underground Temperature." 

 Edinburgh. Trans. Vol. XXII; Part II, pp. 405-427. i860) in which the 

 determinations made by Forbes are discussed. The values there given are: 

 trap rock of Calton Hill, 0.5283; sand from the observation station in the 

 garden, 0.3006; sandstone of Craigleith, 0.4623. 



