ON TUE RATE OF II^CREASE OF UNDEllGROUND TEMPERATURE. 87 



temperature of 85°1 F. The mean air temperature at the crest overhead 

 was calculated by the engineer of the tunnel, M. Giordano, by interpolating 

 between the known temperature of the pass of San Theodule and that of 

 the city of Turin, the former being 430 metres higher, and the latter 

 2,650 metres lower, than the point in question. It is thus calculated to 

 be — 2°-6 C. or 27°'3 F. If, according to our usual rule, we assume the 

 ground to be 1° warmer than the air, we have 28°-3 to compare with 85°-l. 

 This gives a rate of 1' in 93 feet ; but, inasmuch as the convexity of the 

 surface increases the distance between the isotherms, a correction will be 

 necessary before we can fairly compare this result with rates under level 

 ground. As a rough estimate we may take § of 93, and adopt 1° in 79 feet 

 as the corrected result. 



* The rocks on which the observations have been made are absolutely 

 the same, geologically and otherwise, from the entrance to the tunnel, on 

 the Italian side, for a distance of nearly 10,000 yards. They are not 

 faulted to any extent, though, highly inclined, contorted, and subjected to 

 slight slips and slides. They consist, to a very large extent indeed, of 

 silicates, chiefly of alumina, and the small quantity of lime they contain 

 is a crystalline carbonate.' 



The St. Gothaed Tunnel (VIII., XI., XII.), which has a length of 

 about 9 miles, has been subjected to much more minute observation, a 

 skilled geologist. Dr. StapiF, having, under Government direction, devoted 

 bis whole time to investigating its geology and physics. He not only 

 observed the temperature of the rock in the tunnel at very numerous 

 points, but also determined, by observations of springs, the mean tempera- 

 tures of the surface of the mountain at various points, and compared 

 these with an empirical formula for air temperature deduced from the- 

 known mean temperatures of the air at Gbschenen, Andermatt, Airolo, 

 and the Hospice of St. Bernard. He infers from bis comparisons a con- 

 siderable excess of soil above air temperature, increasing from 2° C. at the 

 ends of the tunnel to 6° C. at the crest of the mountain over the centre 

 of the tunnel. The highest temperature of the rocks in the tunnel was 

 at this central part, and was about 30°-6 C. or 87° F. The soil tempera- 

 ture at the crest above it was about — 0°'6 C. or 31° F., giving a difference- 

 of 56° F. The height of the crest above sea-level was about 2,850 m., and 

 that of the tunnel at this part 1,150 m., giving a difference of 1,700 m^ 

 or 5,578 feet. The rate of increase here is, therefore, about 1° F. in 100- 

 feet ; and if we apply the same correction for convexity as in the case of 

 the Mont Cenis tunnel, this will be reduced to about 1° F. in 87 feet, as 

 the equivalent rate under a level surface. From combining his observa- 

 tions in all parts of the tunnel, through the medium of empirical 

 formulEe, Dr. Stapff deduces an average rate of 1° F. for every 88 feet 

 measured from the surface directly overhead. Where the surface is a 

 steep ridge, the increase was lesj rapid than this average ; where the sur- 

 face was a valley or plain, the increase was more rapid. As this average 

 merely applies to the actual temperatures, the application of a correction 

 for the general convexity of the surface would give a more rapid rate. 

 If we bring the isotherms nearer by one part in 15, which seems a fair 

 assumption, we shall obtain a rate of 1° F. in 82 feet. 



Collecting together the foregoing results, and arranging them mainly 

 in the order of their rates of increase, but also with some reference to 

 locality, we have the following list : — 



