208 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 
To express the results geometrically, 
Log. A= A+ Bp 
Where a is the thermometric range at a depth p in French feet; A and B are con- 
stants, the second of which is always negative. These constants are important, 
and their determination may be considered as the primary object of this investi- 
gation. A is manifestly equal to the logarithm of the thermometric range at the 
surface, or when p=0; B is a constant which determines the rate of diminution 
of the range in the interior of the earth, being smaller in proportion as the heat 
penetrates more readily, or as the conductivity of the soil is greater. It was 
shewn by Fourtrr to be directly proportional to the square root of the specific 
heat of the soil, and inversely as the square root of the conductivity.* 
These quantities A and B have reference to the thermometric scale employed, 
and therefore it is convenient, in order to obtain comparable results, to use the 
same unit as MM. Poisson and QuETELET have done in their comparison of theory 
with observation, that is, the centigrade scale. For this purpose, the ranges are 
expressed in the following table in centigrade degrees. 
TABLE IX. RANGES IN CENTIGRADE DEGREES. 

3 Feet. 6 Feet. 12 Feet. 24 Feet. 


Experi- 
mental 
Garden. 
Experi- 
mental 
Garden. 
Experi- 
mental 
Garden. 
Experi- 
mental 
Garden. 
Craig- || Observa- 
Craig- || Observa- 
leith. tory. 
Craig- || Observa- 
leith. tory. 
leith. tory. 
Craig- 
leith. 
Observa- 
tory. 









1837 ||10°53 |11-22 | 9:58 | 661 | 8:30| 7-72 3:05 | 419 | 5-22 || 0-80 | 1°16 | 2:28 
1838 || 9:83 |11-30 |10-29 | 622 | 810 | 7-91 | 2:80] 3-94 | 5-16 || 0-70 | 1-05 | 2:13 
1839 || 9:64 |10-55 | 9-14 | 5°73 | 7-76 | 7-40 | 2-69 | 3-95 | 4-64 || 0-76 | 0-79 | 2:20 
1840 || 8-29 |10-14 | 8:98 || 5-70] 7-35 | 7-28 || 2:50] 3:72 | 4-63 || 0-89 | 1-06 | 2-07 
1841 | 7-79 | 9:80] 8:28 || 571 | 7-45] 7-20] 2:66 | 3°83 | 4:83 | 0-76! 1-11 | 2-16 




















Means,| 9°02 |10°60 | 9°25 || 5°99 | 7°79 | 7:50 || 2°74 | 3:93 | 4:89 || 0-78 | 1:03 | 2-17 





Two results are sufficient for eliminating the constants A and B at each sta- 
tion, and the most probable combination may be had by the method of least 
squares. I have preferred, however, the graphical method already referred to for 
finding, by means of a diagram and a pair of proportional compasses, the loga- 
rithmic curve which best represents the observations. This being done as shewn 
in Plates IX. and X., the values of A and B may be deduced thus. A, as al- 
ready observed, is the logarithmic range at the surface. Taking a space equal to 
10° Cent. (or 18° Fahr.) in the compasses, find the depth at which the curve has 
this quantity for an ordinate, let p,, be this depth. Then, since Log. a=Log. 10=1, 
the equation above becomes 
1=A+ Boy 
dL. Aik 
Pio 
and B= 

* For farther particulars, see the Appendix at the end of this memoir, and also Sub-Section F. 

