80 EEPORT — 1882. 



be independent of the temperature, and be the same all the year round. 

 By ' conductivity ' we are to understand the ' flux of heat ' divided by the 

 ' temperature-gradient ; ' -where by the ' flux of heat ' is meant the quantity 

 of heat -which flows in one second across unit area at the depth considered, 

 and by the ' temperature-gradient ' is meant the difference of temperature 

 per foot of descent at the depth and time considered. 



Convection of heat by the percolation of water is here to be regarded 

 as included in conduction. If the conductivity as thus defined were the 

 same all the year round, the increase of mean temperature per foot of 

 depth would be independent of the annual range, and would be the same 

 as if this range did not exist. 



As a matter of fact, out of six stations at which first-class under- 

 ground thermometers have been observed, five show an increase down- 

 wards and one a decrease. The following are the results obtained for the 

 depths of 3, 12, and 24 Trench feet :— 



Brussels, three years .... 

 Edinburgh (Craigleith), five years 



„ (Gardens), five years . 



„ (Observatory), seventeen years 



Trevandrum, India, three years 

 Greenwich, fourteen years 



In calculating the mean temperature at 12 feet for Trevandrum, we 

 have assumed the temperature of May, which is wanting, to be the same 

 as that of April. 



Omitting Trevandrum, and taking the mean values at 3 and 24 

 French feet, we find an increase of -656 of a degree in 21 French feet, 

 which is at the rate of 1° for 32 French, or about 84 English feet. 



3. Another question which it has sometimes been necessary to discuss 

 is the influence which the form of the surface exerts on the rate of 

 increase of temperature with depth. 



The surface itself is not in general isothermal, but its temperature is 

 least where its elevation is greatest; the rate of decrease upwards 

 or increase downwards being generally estimated at 1° F. for 300 feet. 

 This is only about one-fifth of the average rate of increase downwards in 

 the substance of the earth itself beneath a level surface. If the two rates 

 were the same, the isotherms in the interior of a mountain would be 

 horizontal, and the form of the surface would have no influence on the 

 rate of increase of temperatui'e with depth. The two extreme assump- 

 tions that the surface is an isotherm, and that the isotherms are hori- 

 zontal, lie on opposite sides of the truth. The isotherms, where they 

 meet the sides of the mountain, slope in the same direction as the sides of 

 the mountain, but to a less degree. Probably the tangents of the two 

 slopes are generally about as 3 to 4. ^ 



Further, if we draw a vertical line cutting two isotherms, the lower 

 one must have less slope than the upper, because the elevations and 

 depressions are smoothed off as the depth increases. 



The practical inference is that the distance between the isotherms (in 

 other words, the number of feet for 1° of increase), is greatest under 

 mountain crests and ridges, and is least under bowl-shaped or trough- 

 shaped hollows. 



The observations in the Mont Cenis tunnel, and the much more com- 

 plete observations made by Dr, Stapfi" in the St. Gothard tunnel, fully 



