AT a small depth (from 12 to 40 feet) below the surface of the earth the temperature is constant throughout the year, and this constant temperature of the soil differs little from the mean annual temperature of the air, except on mountains more than 6,000 feet high. The ground is cooler in summer and warmer in winter than the air above it. For this reason caves were the first habitations of men and cellars are still used for the protection of food supplies from rapid changes of temperature. The fact that the temperature of the earth increases with increasing depth below the surface was first clearly enunciated in 166:], by Kircher. who had obtained his data from Hungarian mining engineers. The first measurements of this increase of temperature were made by Friesleben, Humboldt. Saussure, and others at the commencement of the nineteenth century. “,Ve are now in possession of many good measurements made in various countries. but the results are so discordant that it is difficult to deduce a general law of the increase of temperature. Some of these results are shown in the following table, which gives the geothermic interval, or the increase in depth which corresponds to a rise of temperature of one degree, and also the geothermic gradient, or the fraction of a degree by which the temperature rises per unit of depth. The geothermic gradient is the reciprocal of the geothermic interval. or disprove this theory and introduce order into the apparent chaos of observed results. We have deduced the abnormal temperature gradients mathematically from the known laws of the conduction of heat, taking account of the modifications which the configuration of the earth's surface and the proximity of veins of ore, seams of coal, and volcanic magmas introduce into the simple conditions presented by the sedimentary and unchangeable rocks that underlie the great, low- lying plain of North Germany. Most of the gradients are abnormal because most of the observations were made in tunnels under mountains or in mines of coal or metal. that is, in the vicinity of substances which produce heat in consequence of the oxidizing action of the air, either in gaseous form or dissolved in water. The measurements may be classed according as they were taken: 1. In unchangeable sedimentary rocks under plains remote from mountains and large bodies of water (measurements 1-6). 2. In tunnels under mountains (7-9). 3. Near large bodies of water (11-14). 4. In regions of recent volcanic activity (1,5-16). 5. In coal mines. oil fields, and deposits of oxidiz- able minerals (17-19). The first object of our investigation was purely scientific—the explanation of observed facts with the aid of as few assumptions as possible. The second object was practical—the exact prognostication of the temperatures to be encountered in tunneling, the prediction of volcanic eruptions, and the determination of the existence of hot lavas near the earth's surface. A B 1 C D E F Mean Interval. Mean Gradient. Place. Meters per Deg. C. Feet per Deg. F. Deg. per Meter. Deg. P. per Foot. Remarks. 1. Paruscbowitz (Silesia) 2. Berlin 34. 0 3-2.0. 37.7 62 58 6!) 0.0294 0.0313 0.0266 0.016 0.017 0.015 i * Plai ns in northern and central Germany; non-oxidizable, chiefly sedimentary rocks. Mean (1f seven places in North I Germany \ 354.0 03 0.0290 0.016 39.8 73 0.0253 0.014 ) 5 La Mouillonge 6. India .30.6:-3fi. 7 56 67 0.03326 0.02731 0.018 0.015 1 Plains. Mean for plains exclusive of Ger- ) many \ 33.4 61 0.0300 0.0165 7.:J[ont Cenis Tunnel (middle) 8. St. Gotthard Tunnel: (ai At the mouth in the valley.... (b) At the middle in the mountain.. (J. Simplon Tunnel: (a) At the mouth in the valley.. (b) At the middle in the mountain.. 10. Pribram... Mines of Lake Superior: 50.0 29.4 45.5 28.0 48.7. 59.0 42.O 91 54 83 ;51 89 107 76 0.020 0.034 0.022 0.035.57 O.0200 0.0170 0. 02318 0.011 0.01 0.012 0.020 0.011 0.009 0.013 “1 Measured during the boring of tunnels under mountains. 12. Mines nearer the Jake { 55.0 to (57.0 100 to 122 0.0182 to 0.0150 0.010 to 0.008 Near great lakes or oceans. 13. Calumet and Hecla on peninsula in lake 14. Plains of Utrecht 122.8. 52.0 14.0 224 95 27 0.0081 0.0193 0.068,5 0.004 0.011 0.038 16. Dakota (United States) { 9.0 to 12.8 17 to 23 0.104 to 0.078 0.0.57 to 0.043 Near recent volcanic tertiary ' magmas. 17. Glasgow (coal fields) { 25.5 to 7.8 47 to 14 0.039 to 0.128 0.021 to 0.070 18. Anzin (France) j 20.7 to 15.8 50 to 28 0. 0375 to 0.0651 0.021 to 0.0316 I- In coal and oil fields. 19. Pechelbronn 13.9 25 0.0730 0.040 From this table it appears that the differences between the values are very great. Are these differences attributable to errors in or to unsus pected peculiarities of the various rocks, or is the apparent irregularity subject to definite laws? They cannot be entirely due to errors in measurement. for such causes of error as the heat produced by the drill, or currents of air and water in the borings could scarcely change the temperature by more than 3 or 4 deg. F., which at a depth of 2,000 feet would produce an error of only 7 per cent in the gradient and interval. (In mines. however. the lighting and ventilation and the engines and machines may cause errors of 30 per cent or more.) Many geologists attribute the great variation in the temperature gradient to complex irregularities in the structure of the earth's crust. Some even maintain that the interior of the earth is cold and that the observed elevation of temperature is due to local and very irregular generation of heat. Most geologists. however, assume that the earth's interior is hot and ascribe the great variation in the observed temperatures and gradients to differences in the thermal conductivity of the rocks and to the influence of subterranean water courses. the arrangement of strata. and other causes that cannot be directly determined. Dr. Thoma and the writer have- endeavored to prove For the purpose of our calculations it is indifferent whether the observed temperatures are due to the cooling of a molten interior (as Kant, Laplace, Fourier, and Poisson assumed), to mechanical action (Mallet), to chemical and radioactive processes (Himstedt), or to all of these combined. Our only assumptions are that the mean of the results obtained in a region remote from mountains and large bodies of water represents the normal value and that Fourier's differential equation of the conduction of heat is true and applicable. We have calculated the gradients and temperatures under mountains and valleys with the following results: Distance Ol,pd r'alcu'atecj Tunnel. from Mouth, Temperature. Tempt rature, Meters. Dell'. C. Deg. C. St. Gotthard 700 to 900 13.S to 15 14.9 to 15 St. Gotthard 3.500 25.9 25.9 St. Gotthard... &50I0 U.7 ,32.1 St. Gotthard 9500 25.3 25.9 Mont Cenis Middle 29.5 30.4 Simplon Middle 52.0 49.0 The agreement is so close that it is evidently possible to calculate in advance the temperatures to be encountered in tunneling with quite sufficient accuracy for practical purposes. Great effect has been ascribed to the dip and the order of strata, but our experiments on the thermal conductivity of various wet rocks (all the Alpine strata are saturated with water) in various directions prove. that this effect is very small. The cooling or heating effect of streams of water depends on the extent of surface that they wash. The springs of St. Gotthard are too small and compact to have an appreciable effect except in their immediate vicinity. Near large masses of water the geothermic interval is greatly increased and the gradient correspondingly diminished by the conductivity of the water. A lake covering 400 square miles to a depth of 600 feet can diminish by one-half the gradient at a depth of 1.600 feet and a distance of six miles from the lake. The best examples of this influence of water are offered hy the mines of Lake Superior. The geothermic interval is 76 at the Osceola mine five miles from the lake, 100 to 122 at mines nearer the lake, and 224 at the Calumet and Hecla mines on the Keweenaw peninsula. From the measurements of the interval in recent volcanic regions not containing ores or coal the depth at which molten lava occurs may be computed. From the formulm for an ellipsoidal mass of a diameter exceeding six miles and the temperature gradient deduced from observations near the surface at Neuffen, in the vicinity of a tertiary crater and basaltic overflows, we find a temperature of about 1,500 deg. F. at a depth of four or five miles. Our calculations also indicate that variations in the activity of a volcano must be reflected in the temperature gradient of the vicinity, and that three observations of the temperatures at' depths of 16 feet and 50 feet should suffice to determine to a fair degree of accuracy the location ar:d form of the subterranean mass of liquid lava. Unfortunately, we have no records of this character. I have devised an apparatus costing from $75 to $150, for the purpose of registering the changes in the mass of lava by means of the variation of the geothermic interval, and thus, perhaps, predicting volcanic erup- t'ons. Over veins of coal and some other minerals the temperature gradient is high, while below them it soon attains the normal value. The same results are given by the mathematical theory applied to deposits of spherical or ellipsoidal form. We find that a spherical mass of J 00 meters radius, with its center 400 meters below the surface, would increase the temperature gradient immediately above it from 0.0.30 to 0.050, if the generation of heat in the mass is 3,400 gramme-calories per second. This is equivalent to a yearly combustion of 100 grammes of carbon and hydrocarbons on each square meter (approximately 3 ounces per square yard) of the surface of the mass. This calculation shows that no very great production of heat is required to cause a considerable change in the observed temperature. Hence, it is theoretically possible to cool mines by refrigerating chambers suitably distributed beneath and beside the galleries, if the chambers are sufficiently large and numerous and well insulated, so that all the heat which they absorb is taken from the rock The temperatures and gradients in the interior of the coal or ore can also be computed, but each case will differ from the rest. From the foregoing considerations it is evident that the abnormal temperature gradients can be explained very simply and without the introduction of new hypotheses, by the varying production of heat in coal seams, the proximity of volcanic masses, and the cooling effect of large bodies of water. The mathematical method, instead, offers to the mining engineer and tunnel constructor a very valuable means of calculating the temperatures of shafts and tunnels in advance with a fair degree of accuracy, when something is known of the geological conditions.—Translated for Scientific American Supplement from Umschau.