OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



185 



From these values of 



lire 



V "P 



k 

 the value of -, the conductivity of the rock expressed 



" in terms of the thermal capacity of a cubic foot of its own substance " can now be 

 deduced, and finally the value of k, the conductivity expressed in terms of the thermal 

 capacity of a cubic foot of water. In the following table these are compared with the 

 values deduced by Prof. Forbes, Lord Kelvin, and Prof. Everett. As the earlier com- 

 putations have been all referred to the French foot as the unit of measure, it has been 

 necessary to reduce them to the English foot.* The value of c, the specific heat of the 

 rock per unit of volume used, is 0'5283, the number determined by M. Regnault at 

 Prof. Forbes' request. 





firC 



V F 



k 

 c 



k 



Per 



French Foot. 



Per 



English Foot. 



Per 

 French Foot. 



Per 

 English Foot. 



Per 



French Foot. 



l 



Per 



English Foot. ; 



Prof. Forbes, 

 Lord Kelvin, 

 Prof. Everett, 

 Old Thermometers, 

 New Thermometers, 



0-1152 

 0-1156 

 0-1174 



0-1116 



0-1150 



(236-7) 



2351 



(227-9) 



267-0 



252-2 

 237-5 



(125-0) 

 (124-2) 

 (120-4) 



142-0 

 141-1 

 (136-8) 

 133-2 

 125-7 



The numbers enclosed in brackets are not given in the papers of the authors opposite 

 whose names they are placed. 



From the dates of the maxima and minima of the various thermometers we can 

 determine the time necessary for heat to pass through 1 foot of the rock of Calton Hill. 





Mean Depth. 

 Feet. 



Days. 



From old t x and t 2 . 



19-2 



6-2 



new t x and t 2 . 



16-0 



6-6 



old t 2 and t 3 . 



9-6 



6-7 



new t 2 and i s . 



8-0 



6-8 



old t s and t i . 



4-8 



6-6 



new t 3 and t i . 



4-0 



6-8 J 



>- 6 - 6 days. 



To determine the mean annual range at different depths, 1 have plotted the curve, 

 Plate IV., showing the ranges taken from the equations to the annual curves. Accord- 

 ing to theory the range decreases geometrically as the depth increases in arithmetical 

 progression, or the curve is a logarithmic curve. Hence we have log. R = A + Bp, where 

 R is the range at a depth p in feet, A is evidently the logarithm of the range at the 

 surface, where p = and B is a constant fixing the rate of decrease of the range below 

 the surface. This surface range I have taken = 20°, or the mean value shown by the 

 curves. Hence log. 20 = A= 1 "30103. From the point on the curve where the range 



* French foot = English foot x 1-06575 ; (l-06575) 2 = 1-13582. 



VOL. XL. PART I. (NO. 8). 2 D 



