208 



PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 



To express the results geometrically, 



Log. A = A + Bp 



Wliore A is the thermoraetric range at a depth p in French feet ; A and B are con- 

 stants, the second of which is always negative. Tliese constants are important, 

 and tlieir 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 j9=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 Fourier 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. Eanges in Centigrade Degrees. 



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 2^^ be this depth. Then, since Log. A=Log. 10=1, 

 the equation above becomes 



1 = A -f B/ijo 

 1- A 



and B 



PlO 



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



