TABLE NO. 5.-Showing the Excess or Defect of Rain between those periods when the Moon's motion in Declination is changing, and when it is greatest, or when the Moon is in greatest Declination and crossing the Equator.

On the Reduction of Periodical Variations of Underground Temperature, with applications to the Edinburgh Observations. By Prof. W. THOMSON, LL.D., F.R.S.

The principle followed in the reductions which form the subject of this communication may be briefly stated thus :

The varying temperature during a year, shown by any one of the underground thermometers on an average for a series of years, is expressed by the ordinary method in a trigonometrical series of terms representing simple harmonic variations*,-the first having a year for its period, the second a half-year, the third a third part of a year, and so on. The yearly term of the series is dealt with separately for the thermometers at the different depths, the half-yearly term also separately, and so on, each term being treated as if the simple periodic variation which it represents were the sole variation experienced. The elements into which the whole variation is thus analysed are examined so as to test their agreement with the elementary formulæ by which Fourier expressed the periodic variations of temperature in a bar protected from lateral conduction, and experiencing a simple harmonic variation of temperature at one end, or in an infinite solid experiencing at every point of an infinite plane through it a variation of temperature according to the same elementary law. In any locality in which the surface of the earth is sensibly plane and uniform all round to distances amounting at least to considerable multiples of the depth of the lowest thermometer, and in which the conducting power of the soil or rock below the surface is perfectly uniform to like distances round and below the thermometers, this theory must necessarily be found in excessively close agreement with the observed results. The comparison which is made in the investigations now brought forward must be regarded, therefore, not as a test of the correctness of a theory which has mathematical certainty, but as a means of finding how much the law of propagation of heat into the soil is affected by the very notable deviations from the assumed con* By a simple harmonic variation is meant a variation in proportion to the height of a point which moves uniformly in a vertical circle.

ditions of uniformity as to surface, or by possible inequalities of underground conductivity existing in the localities of observation. When those conditions of uniformity are perfectly fulfilled both by the surface and by the substance below it, the law of variation in the interior produced by a simple harmonic variation of tempera. ture at the surface, as investigated by Fourier, may be stated in general terms in the three following propositions: (1) The temperature at every interior point varies according to the simple harmonic law, in a period retarded by an equal interval of time, and with an amplitude diminished in one and the same proportion, for all equal additions of depth. (2) The absolute measure in ratio of arc to radius, for the retardation of phase, is equal to the diminution of the Napierian logarithm of the amplitude; and each of these, reckoned per unit of length as to augmentation distance from the surface, is equal to the square root of the quotient obtained by dividing the product of the ratio of the circumference of a circle to its diameter, into the thermal capacity of a unit of bulk of the solid, by the thermal conductivity of the same estimated for the period of the variation as unity of time. (3) For different periods, the retardations of phase, measured each in terms of a whole period, and the diminutions of the logarithm of the amplitude, all reckoned per unit of depth, are inversely proportional to the square roots of the periods.

The first series of observations examined by the method thus described were those instituted by Professor Forbes, and conducted under his superintendence during five years, in three localities of Edinburgh and the immediate neighbourhood: (1) the trap rock of Calton Hill; (2) the sand below the soil of the Experimental Gardens; and (3) the sandstone of Craigleith Quarry. In each place there were, besides a surface thermometer, four thermometers at the depths of 3, 6, 12, and 24 French feet respectively. The diminution in the amplitude, and the retardation of phase in going downwards, have been determined for the annual, for the half-yearly, thirdyearly, and the quarterly term, on the average for these five years for each locality. The same has been determined for the average of twelve years of observation, conti. nued on Calton Hill by the staff of the Royal Edinburgh Observatory.

The following results with reference to the annual harmonic term are selected for example :

If Fourier's conditions of uniformity, stated above, were fulfilled strictly, the numbers shown in the second column would be all equal among one another, and equal to those in the third column. The differences between the actual numbers are surprisingly small, but are so consistent that they cannot be attributed to errors of observation. It is possible they may be due to a want of perfect agreement in the values of a degree on the different thermometric scales; but it seems more probable that they represent true discrepancies from theory, and are therefore excessively interesting, and possibly of high importance with a view to estimating the effects of inequalities of surface and of interior conductivity. The final means of the numbers in the second and third columns are, for

The thermal capacities of specimens of the trap rock, the sand, and the sandstone of the three localities were, at the request of Professor Forbes, measured by Regnault, and found to be respectively

5283, 3006, and 4623.

Hence, according to position (3), stated above, the thermal conductivities are as follows:-

These numbers do not differ much from those given by Professor Forbes, who for the first time derived determinations of thermal conductivity in absolute measure from observations of terrestrial temperature. In consequence of the peculiar mode of reduction followed in the present investigation, it may be assumed that the estimates of conductivity now given are closer approximations to the truth. To reduce to the English foot as unit of length, we must multiply by the square of 1'06575; to reduce, further, to the quantity of heat required to raise 1 lb. of water by 1o as unit of heat, we must multiply by 66 447; and lastly, to reduce to a day as unit of time, we must divide by 3651. We thus find the following results :

These numbers show the quantities of heat per square foot conducted in a day through a layer of the material 1 foot thick, kept with its two surfaces at a difference of temperature of 1 degree, the unit of heat being, for instance, the quantity required to raise 1000 bls. of water by Toth of a degree in temperature.

On the Establishment of Thermometric Stations on Mont Blanc.
By Professor TYNDALL, F.R.S.

I proposed to the Royal Society some months ago to establish a series of stations between the top and the bottom of Mont Blanc, and to place suitable thermometers at each of them. The Council of the Society thought it right to place a sum of money at my disposal for the purchase of instruments and the payment of guides; while I agreed to devote a portion of my vacation to the execution of the project. At Chamouni I had a number of wooden piles prepared, each of them shod with iron, to facilitate the driving of it into the snow. The one intended for the summit was 12 feet long and 3 inches square; the others, each 10 feet long, were intended for five stations between the top of the mountain and the bottom of the Glacier de Bossons. Each post was furnished with a small cross-piece, to which a horizontal minimum thermometer might be attached. Six-and-twenty porters were found necessary to carry all our apparatus to the Grands Mulets, whence fourteen of them were immediately sent back. The other twelve, with one exception, reached the summit, whence six of them were sent back. Six therefore remained. In addition to these we had three guides, Auguste Balmat being the principal one; these, with my friend Dr.

Frankland and myself, made up eleven persons in all. Though the main object of the Expedition was to plant the posts and fix the thermometers, I was very anxious to make some observations on the diathermancy of the lower strata of the atmosphere. I therefore arranged a series of observations with the Abbé Vueillet, of Chamouni; he was to operate in the valley, while I observed at the summit. Our instruments were of the same kind; and in this way I hoped to determine the influence of the stratum of air interposed between the top and bottom of the mountain upon the solar radiation. Wishing to commence the observations at an early hour in the morning, I had a tent carried to the summit. It was 10 feet in diameter, and into it the whole eleven of us were packed. The north wind blew rather fiercely over the summit; but we dropped down a few yards to leeward, and thus found shelter. Throughout the night we did not suffer at all from cold, though the adjacent snow was 15° Centigrade, or 27° Fahr. below the freezing-point of water. We were all, however, indisposed. I was, indeed, unwell when I quitted Chamouni; but I fully expected to be able to cast off the indisposition during the ascent: in this, however, I was unsuccessful; my illness augmented during the entire period of the ascent. The wind increased in force towards morning; and as the fine snow was perfectly dry, it was driven upon us in clouds. Had no other obstacle existed, this alone would have been sufficient to render the observations on solar radiation impossible. We were therefore obliged to limit ourselves to the principal object of the expedition-the erection of the post for the thermometers. It was sunk 6 feet in the snow, while the remaining 6 feet were exposed to the air. A minimum thermometer was screwed firmly on to the cross-piece of the post; a maximum thermometer was screwed on beneath this, and under this again a wet and dry bulb thermometer. Two minimum thermometers were also placed in the snow; one at a depth of 6, and the other at a depth of 4 feet below the surface; these being intended to give us some information as to the depth to which the winter cold penetrates. At each of the other stations we placed a minimum thermometer in the ice or snow, and a maximum and a minimum in the air. The stations were as follows:-the summit, the Corridor, the Grand Plateau, the glacier near the Grands Mulets, and two additional between the Grands Mulets and the end of the Glacier de Bossons. We took up some rockets, to see whether the ascensional power or the combustion was affected by the rarity of the air. During the night, however, we were enveloped in a dense mist, which defeated our purpose. One rocket was sent up, which appeared to penetrate the mist, rising probably above it; its sparks were seen at Chamouni. Dr. Frankland was also kind enough to undertake some experiments on combustion: six candles were chosen at Chamouni, and carefully weighed. All of them were permitted to burn for one hour at the top; and were again weighed when we returned to Chamouni. They were afterwards permitted to burn an hour below. Rejecting one candle, which gave a somewhat anomalous result, we found that the quantity consumed at the top was, within the limits of error, the same as that consumed at the bottom. This result surprised us all the more, inasmuch as the light of the candles appeared to be much feebler at the top than at the bottom of the mountain. The explosion of a pistol was sensibly weaker at the top than at a low level. The shortness of the sound was remarkable; but it bore no resemblance to the sound of a cracker, to which, in acoustic treatises, it is usually compared. It resembled more the sound produced by the expulsion of a cork from a champagne-bottle, but it was much louder. The sunrise from the summit exceeded in magnificence anything that I had previously seen. The snows on one side of the mountain were of a pure blue, being illuminated by the reflected light of the sky; the summit and the sunward face of the mountain, on the contrary, were red, from the transmitted light; and the contrast of both was finer than I can describe. I may add, in conclusion, that the lowest temperature at the summit of the Jardin during last winter was 21° Cent. below zero. We vainly endeavoured to find a thermometer which had been placed upon the sum mit of Mont Blanc last year.

GENERAL PHYSICS.

A Proposal of a General Mechanical Theory of Physics.

By J. S. STUART GLENNIE, M.A.

The approach of a planet to a sun, iron to a magnet, one particle to another, may be the effect of, or conceivable only as the effect of a pull of the sun, the magnet, or the first particle; but such a pull, however useful as a temporary metaphysical, or metaphorical conception, is mechanically an absurdity: such approach can be mechanically conceived only as the movement of the planet, the iron, or the second particle in the direction of least pressure as between the sun, the magnet, or the first particle, and some third body.

་་

A somewhat extensive colligation of physical facts has led to the conviction that, by further experimental and mathematical research, attractions and repulsions will be found explicable as expressions of the relations of the pressures between three bodies, a general mechanical theory of physics established, and thus the “ persuasion" of Mr. Faraday and the profoundest scientific thinkers, "that all the forces of nature are mutually dependent, having one common origin, or rather being different manifestations of one fundamental power," demonstrated as a truth.

The mechanical conceptions and explanations of phenomena with diffidence offered in this paper, are as yet given, less as a theory, than as a proposal of a way in which a general mechanical theory may be established. And the following is a summary of, perhaps, the principal of these conceptions and modes of explanation. Atoms are conceived as mutually determining centres of pressure.

Thus, atoms are not conceived as particles in a medium or in space, at distances from each other determined by the proportions of the hypothetical forces of attraction and repulsion, but as in contact with, and pressing against each other, while their centres are at distances determined by relations of inward and outward pressure.

For convenience of representation and mathematical calculation, atoms may also be defined as centres of lines of pressure; the comparative length of these lines being taken to represent, not the absolute, but the relative development of the force of the atom.

Matter, or that which resists our force, is conceived as a form of force; and the idea of force is explained by the conceptions of

Equilibrium-the state of equality among the opposing pressures of a system of atoms (defined as above) or bodies (defined as aggregates of atoms).

Motion-the effect of a difference of polar pressures on an atom or body; determined in direction by the resultant of greatest pressure; in degree (or velocity) by the ratio of such difference; and as uniformly accelerated, varyingly accelerated, or uniform, according as that ratio is constant, varyingly, or uniformly inconstant.

A line of motion-the direction of the transmission of pressure relatively increased at one point, and correspondingly decreased at all others.

Heat and specific heat-the former is conceived as an expression of the relations of the mutual pressures of bodies, the latter, of atoms.

The solid, liquid, and gaseous states appear deducible from certain conditions of relative pressure between three bodies or atoms.

From the condition of equal transmission in all directions, it follows that, in a system with that condition, an increased pressure in any direction will be, as it were, broken up; hence the ratio of resistance at any point will be greater than if the pressure had been directly transmitted; it will be radially transmitted; and will diminish according to the law of the inverse squares.

The phenomena of static electricity appear explicable as the results of the pressure on each other of heterogeneous bodies, or bodies of less and greater power of resisting pressure. Hence the outward pressure of the one is increased, of the other diminished; and hence positively and negatively electrified balls may be represented, the former as having its own, the latter the lines of pressure of the medium increased. The poles of dynamic electricity are the ends of a line of motion,-points of greater and less pressure.

The relation of magnetism and electricity is the mechanical consequence in a medium of the lateral diminution of pressure increased at a point.

Conduction and insulation, magnetism and diamagnetism are corresponding