408 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



for these two dates gives directly a measure of the difference between 

 the greatest and the smallest quantities of heat contained in the 

 ground during the annual period; of course it is assumed that the 

 volume capacity of the ground is known. 



But this difference is the quantity of heat that is exchanged 

 through the earth's surface within one year, omitting of course that 

 which is exchanged within the diurnal periods and of which the 

 remnant left over at the close of each day alone enters into this 

 present computation. 



"The consideration just expressed has led to the surprising result 

 that for the determination of the annual exchange of heat it 

 suffices to know the distribution of temperature in the ground at 

 those dates of the year when the increase of heat changes to a 

 decrease and vice versa. " 



In temperate latitudes these dates agree approximately with 

 the equinoxes. 



Of course the exchange of heat within the diurnal period can be 

 determined in a perfectly analogous way. 



We find the heat exchange within the diurnal period by select- 

 ing from the tautochrones for individual hours those two that are 

 perpendicular to the earth's surface and then determine the area 

 included between them or' from the corresponding integral. 



A determination of the moments of time at which this occurs, 

 i. e., of the hours of the day at which the energy in the ground 

 attains its maximum and minimum values is, of course, only possible 

 where hourly observations for the upper strata of the ground are 

 available or at least those for quite short intervals of time. 



In general we can at present only state that the changes from 

 increasing heat to diminishing heat occur some little time after 

 sunrise and a rather longer time before sunset. At Pavlovsk 13 this 

 occurs at the following hours: in December about n a.m. and 

 shortly before i p.m.; in January after n a.m. and before 2 p.m.; 

 in June after 5 a.m. and about 5:30 p.m.; in July about 5 a.m. and 

 before 6 p.m., as shown by the fact that at these hours the dif- 

 ference between the temperature at depths of 0.01 meter and 0.02 

 meter changes its sign. 



At Nukuss 14 these changes occur in January at about 8 a.m. and 

 4:30 p.m. but in July at 6 a.m. and 6 p.m. 



13 Leyst: " Bodentemperaturen, " in Wild Repertorium fur Meteorologie. 

 Band XIII, No. 7, 1890. 



14 H. Wild: Ueber die Bodentemperatur in St. Petersburg und Nukuss. 

 Wild Repertorium fur Meteorologie. Band VI, No. 4, 1878. 



