5 66 



NATURE 



{Oct. 5, 1882 



diate vicinity showed a tenperature 9°"0 R. at the bottom 

 Thi» is direct evidence that the water near the top of the great 

 bore hid been warmed 2° R., or 4^° F. by convection. 



Suggestion -. for observations in filled-up bores will be found 

 in the eleventh report, but they have not yet taken a practical 

 shape. 



D. Questions affecting Deductions from Observa- 

 tions — I. In many instances the observations of temperature 

 have been confined to considerable depths, and in order to 

 deduce the mean rate of increase from the surface downwards it 

 has been nepessary to assume the mean temperature of the 

 surface. To do this correctly is all the more difficult, because 

 there seems to be a sensible difference between the mean tempe- 

 rature of the surface and that of the air a few feet above it. 



In the third report some information on this point is given, 

 based on observations of thermometers 22 inches dee,) at some 

 of the stations of the Scottish Meteorological Society, and of 

 thermometers 3 (French) feet deep at Greenwich and at Edin- 

 burgh. These observations point to an excess of surface-tern 

 perature above air-temperature, ranging from half a degree to 

 nearly two degrees, and having an average value of about one 

 degree. 



Dr. Schwartz., Professor of Physics in the Imperial School of 

 Mines at Schemnitz, in sending his observa'ions made in the 

 mines at that place, remarks on this point : — 



"Observations in various localities show that in sandy soil-, 

 the excess in question amounts, on the average, to abou' half a 

 degree Centigrade. In this locality the surface is a compact 

 rock, which is highly heated by the sun in summer, and is protected 

 from radiation by a covering of snow in winter ; and the conform 1- 

 tion of the hills in the neighbourhood is such as to give protection 

 against the prevailing winds. Hence the excess is probably greater 

 here than in most places, and may fairly be assumed to be 

 double the above average." 



Some excellent observations of underground temperature at 

 small depths were made at the Botanic Gardens, Regent's Par 1 .;, 

 London, for the six years 1871-76, along with observations of 

 air-temperature, and have been reduced by Mr. Symons. They 

 are at depths of 3, 6, 12, 24, and 4S inches beneath a surface of 

 grass, and their joint mean derived from readings at 9 a.m. and 

 9 p.m. for the >ix years is 49-9, the mean for the 4S inch ther- 

 mometer being 5005. The mean air-temperature derived in 

 the same way from the readings of the dry-bulb thermometer is 

 49 6. Hence it appears that the excess of soil above air is in 

 this ca e about o°'4. 



Quetelct's observations for three years at Brussels (p. 4S of 

 his "Memoire") make the earth, at depths less than ij foot, 

 colder than the air, and at greater depths warmer than the air. 



Caldec itt's observations for three years at Trevandrum, in 

 India, make the ground at the depth of 3 feet warmer than the 

 air by 5° 7 F. 



Dr, Stapff, in his elaborate publicitions on the temperature of 

 the St. Gothard Tunnel, arrives at the conclusion that the mean 

 temperature of the soil on the surface of the mountain above the 

 tunnel Is some decrees higher than that of the air, the execs 

 increasing with the height of the surface and ranging from 2° or 

 3° C. near the ends of the tunnel, to 5° or 6° in the neighbour- 

 hood of the central ridge. 



2. Connected with this is the question — Whether the menu 

 annual temperature of the soil increase; downwards from the 

 surface itself, or whether, as is sometimes asserted, the increase 

 only begins where annual range ceases to be sensible — say at a 

 depth of 50 or 60 feet. 



The general answer is obvious from the nature of conduction. 

 Starting with the fact that temperature increases downwards 

 at depths where the annual range is insensible, it follows 

 that heat is travelling upwards, because heat will always pass 

 from a hotter to a colder stratum. This heat must make its way 

 to the surface and escape there. But it could not make its way 

 to the surface unless the mean temperature diminished in ap- 

 proaching the surface; lor if two snperposed layers had the 

 same mean temperature, just as much heat would pass from 

 the upper to the lower as from the lower to the upper, and 

 there would not be that excess of upward flow which is necessary 

 to carry off the perennial supply from below. 



'I bis reasoning is rigorously true if the conductivity at a given 

 depth 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 tempera- 

 ture per foot of descent at the depth and time c onsidered. 



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 

 underground thermometers have been observed, five show an 

 increase downwards, and one a decrease. The following are the 

 results obtained for the depths of 3, 12, and 24 French feet : — 

 3 feet. 12 feet. 24 feet. 



Brussels, three years 51-85 53-69 53-71 



Edinburgh (Craigleith) five years ... 45'S8 45-92 46-07 

 ,, (Gardens) five years ... 46-13 48-76 4709 



,, (Observatory), seventeen 



years 46-27 46-92 47"l8 



Trevandrum (India), three years ... 85-71 86"I2 — 



Greenwich, fourteen years 5°'92 50'6l 50*28 



In calculating the mean temperature at 12 feet for Trevandrum, 

 we have a-sumed the temperatu-e 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 

 34 English fee'. 



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 tempe- 

 rature is least where its elevation i- greatest ; the rate of decrease 

 upwards or increase downward- 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 

 temperature with depth. The two extreme assumptions that the 

 surface is an isotherm, and that the isotherms are horizontal, lie 

 o 1 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 le-s 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 in- 

 crease), 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 complete observations made by Dr. Stapff in the St. 

 Gothard tunnel, fully bear out these predictions from theory. 

 The discussion of the former occurs in the fourth report, p. 15. 



As regards the St. Gothard tunnel, Dr. Stapff reports: — 

 "The mean rate of increase downwards in the whole length 

 of the tunnel is '0206S of a degree Centigrade per metre 

 of depth, measured from the surface directly over. This is 1° 

 F. for 88 feet. Where the surface is a steep ridge the increase 

 is less rapid than this average ; where the surface is a valley or 

 plain the increase is more rapid." 



4. The question whether the rate of increase downwards is 

 upon the whole the same at all depths, was rai-ed by rrof. 

 Mohr i 1 his comments upon the Sperenberg observations, and is 

 discussed, so far as these observations bear upon it, in the 9th 

 and I Ith reports. 



Against the Sperenberg observations, which upon the whole 

 show a retardation of the rate of increase as we go deeper, may 

 now be set the Dukinfield observations begun by Sir William 

 Fairbairn, and continued by Mr. Garside. Taking Mr. Gar- 

 side's observations, and assuming a surface-temperature of 49°, 

 the increase in the first 19S74 feet is at the rate of l°in 79-5 

 feet ; in the next 420 feet it is at the rate of 1° in 70 feet, and in 

 the last 283A feet it is at the rate of 1° in 51! feet. I 



From a theoretical point of view, in places where there is no 

 local generation of heat by chenical action, the case stands 

 thus:— 



The flow of heat upwards must be the same at all depths, and 

 this flow is equal to the rate of increase downwards, multiplied 



