306 
Proceedings of Royal Society of Edinburgh. [sess. 
tion, obtained from tlie general expressions by putting x equal to 
zero, may then be taken as representing fairly well the variation 
of temperature at the surface. The combined expression is 
V = 10-48 £ - oom * cos (y t - 0-00371* + 0-963) 
+ 1-656 c - 0 ' 00583 * cos (ft - 0-00515* + 1-925). 
Calculating the numerical values at the surface ( x = 0) for the 
successive months, we get a set of temperatures which may con- 
veniently be tabulated along with the means of the observed 
temperatures at the different depths. We are now furnished with 
five columns of numbers, each row containing the simultaneous 
temperatures at the surface and the positions occupied by the 
thermometers. The calculated values of the surface temperatures 
are given in the last column of the table on p. 302 above. We 
may now get fairly accurate determinations of the accumulated 
heat within the crust at any time by multiplying the mean of the 
temperatures at each pair of consecutive positions as we descend 
by the distance between the corresponding positions measured in 
centimetres. The four quantities so obtained are then added 
together, and the result multiplied by the thermal capacity per 
unit volume. Reducing to the Centigrade as unit, and subtracting 
the smallest of the numbers from all the others, we finally obtain 
a series of numbers representing the annual gain and loss of heat 
under each square centimetre of the earth’s surface. In this cal- 
culation we neglect the heat which penetrates below the deepest 
thermometer. This, however, is comparatively small, and besides 
the determination of the surface temperatures will almost certainly 
involve as large errors. The final results are shown graphically in 
the Plate, fig. 3, and are given in the following table, which con- 
tains, in addition to the monthly values deduced from the tempera- 
tures as originally tabulated, intermediate values obtained by cal- 
culation from the interpolated values taken from the curves. 
