desire to examine. Grant that the difference of the two thermometers is not more than 1°,5. It follows from this experiment, that the plate did not allow more than half the calorific rays to pass, whilst the other half contributed to raise its temperature. If we increase the number of plates of the said body, or the thickness of this body, the proportion of the rays absorbed will be greater; for we still suppose it composed of plates similar to the former, each of which absorbs the same proportion of heat. For the sake of simplicity, let us suppose that 100 rays arrive, and that the first plate absorbs one-tenth, the second will not receive more than 100-10=90 rays. The latter will also absorb one-tenth, that is to say, 9. The third will, therefore, receive 90-9-81 rays, and will absorb 8,1; the fourth will receive 72,9 rays, and so on. By expressing these relations mathematically, we may reduce all bodies to the same thickness, and calculate the relative quantity of heat which they have absorbed.

Experiments of this kind, when carefully conducted, not only lead us to recognise the different diathermanity of bodies, but to divide calorific sources into two orders; those which are luminous, such as the sun, the light of a taper, incandescent metals; and those which emit merely dark calorific rays, such as a vessel filled with hot water. Every thing proves that diathermic bodies absorb a much more considerable portion of obscure than of luminous rays. Without seeking to explain this fact, let it suffice us to remark that it is of high importance towards our understanding all that is to follow.

REDUCTION OF SOLAR HEAT DURING ITS PASSAGE THROUGH THE ATMOSPHERE.-If we follow the march of the sun on a fine day, we shall recognise, without the aid of any instrument, that the intensity of its heat diminishes with its height, because the atmosphere absorbs a portion of the luminous rays. As the sun descends toward the horizon, the rays are obliged to traverse a greater thickness of the atmosphere, in order to reach us. At the moment of its setting, its light is so feeble that we can contemplate it with the naked eye. It is the same with its calorific power. Take a lens, when the sun is passing the meridian, and measure the time necessary to inflame tinder, for example; in proportion as the sun approaches the horizon more time will be required to light it, and it will be even impossible when this planet is at a few degrees above the horizon.

In order to measure this reduction accurately, we must

employ a thermometer sufficiently protected against the wind and other influences. De Saussure called this instrument a heliothermometer. Take a box, the interior of which is coated with bodies that are black, and also bad conductors of heat, and which is closed on one side by panes of transparent glass; then place in it a thermometer with a blackened bulb, and adjust the apparatus so that the sun's rays fall perpendicularly on those plates of glass. Herschel proposed a very different apparatus, which he named an actinometer. But the heliothermometer is more easy to construct, and answers the same purpose.

If this apparatus is exposed for a minute to the sun's rays, the thermometer rises. However, a small correction is here necessary. Suppose that the instrument has a temperature lower than that of the medium in which it is placed, the thermometer would rise without the direct influence of the sun; it will then indicate too high a temperature. To find the correction, observations must be made for three minutes. After having arranged the apparatus conveniently, a screen is placed between it and the sun, and the indications of the thermometer are read during this space of time suppose that it has risen 0°,3. The screen is then removed; in the minute, during which it receives the solar rays, it will rise 10,5 for example. The screen is then replaced, and, in the third minute, it will rise, say 0°,1. Thus, under the influence of the circumambient medium, it rose in the first minute 0°,3; in the third minute 0°,1; consequently, in the second minute it must have risen

So that, during the second minute, the sun made the thermometer rise 1°,50°,2 = 1o,3. If the instrument has fallen during the first and the third minute, the mean of those fallings should have been added to the solar action. To avoid errors of observation, the observations are made for eleven minutes. The thermometer is exposed to the solar light during the second, fourth, sixth, &c. minutes; the mean of the five observations is then taken.

Measurements of this kind, when made during days that are perfectly serene, shew that the solar action increases with the height of the sun above the horizon. The following is an example :

7 Vide note f, Appendix, No. II.

In order to deduce from these observations the reduction of solar light in its passage through the atmosphere, we should know exactly the course of the rays in the atmosphere, and the amount to which the thermometer would rise, if it were placed at the limits of our atmosphere; that is to say, if the rays were not weakened. These two elements cannot be exactly determined; but, if we suppose the atmosphere limited by a plane parallel to the horizon, at a height of about 20°, which is true, and if we designate by 1 the shortest distance from the observer to this plane, we may express the length of the course of the sun's luminous rays by multiples of this unity. By repeating the experiment at different heights of the sun, we may conclude approximately the quantity that the instrument would rise, if it were at the limits of the atmosphere. With the instrument that I employed, this quantity was 30,2. Thus, when the height of the sun is 40° 30', only two-thirds of the rays reach the earth; when at 21° 30', only half: the rest are absorbed by the atmosphere, or reflected toward the earth and celestial space.

In order to express this value, which depends on the height of the sun, it is better to seek how many rays would have reached the earth had the sun been at the zenith. If we represent the number of rays that arrive at the atmosphere, during the most serene days, by 100, scarcely 70 or 80 will reach the earth. Thus the fourth are absorbed or reflected by the atmosphere. The total number of rays that reach the ground during a day, is only the half of that which falls on the atmosphere. This is true of a day perfectly serene; but on calculating serene and also cloudy days, we see that the earth does not profit by more than a very small portion of the rays that arrive at the atmosphere.

The heat that the earth receives from the sun radiates into space; but, as it is dark heat, it is probable that it experiences a much greater difficulty in traversing the atmosphere than do the luminous rays of the sun. When the transparency of the air is disturbed by vapours, the dark and also the luminous rays experience a still greater resistance in their progress; but if they prevent the heating of the soil

by the rays of the sun, they also oppose its cooling by radiation.*

TEMPERATURE OF THE EARTH AND OF SPACE.

-Hitherto, we have considered the sun as the only source of heat that warms our globe; but Fourier has shewn that there exist two other very influential causes, namely, the proper heat of the earth itself, and also that of space. Although their action cannot in any degree modify the indications of the thermometer, it is, however, well to analyse it briefly.

If we bury thermometers in the ground, at different depths, and so that their bulbs shall be in contact with the earth, the annual variations will be smaller as the instruments are

M. POUILLETL devised two instruments, much more perfect than that of HERSCHEL, for estimating the quantity of solar heat absorbed by the atmosphere. One is the direct pyrheliometer, the other, the lenticular pyrheliometer. The latter is composed of a lens 24 or 25 cent. in diameter, with a focal distance of 60 or 70 cent., in the focus of which is a plated vessel, containing about 600 grammes of water, in which the bulb of a thermometer is plunged. The form of the vessel and the arrangement of the lens are so combined, that, for all heights of the sun, the rays fall perpendicularly on the lens, and on the surface of the vessel; which latter is covered with lampblack, and is intended to receive them in the focus and to absorb them. (For the description of these two instruments, vide Les Comptes rendus de l'Académie des Sciences, t. vii., p. 24 [1838]; and Eléments de Phys. t. ii. p. 528, and fig. 375 and 376.)

Numerous experiments made with these two instruments have led to the following results:-When the atmosphere has every appearance of perfect serenity, it yet absorbs nearly one-half of the total quantity of heat which the sun emits toward the earth; and it is the other half alone of this heat which falls on the surface of the earth, and which is more variously distributed, according as it has traversed the atmosphere with greater or less obliquity.

If the total quantity of heat, which the earth receives from the sun in the course of a year, were uniformly spread on its surface, and employed without any loss to melt a bed of ice, which should envelope the entire globe, it would be capable of melting a bed thirty-one metres thick.

Mr. FORBES Communicated to the Royal Society of London, on the 26th of May, and the 2d of June, 1842, the results of the correspondent experiments which he had made in September, 1832, with M. KAEMTZ, at Brienz, and on the Faulhorn, upon the transparency of the atmosphere. The dif ference of level was 2119 metres. The following are some of the results, which are as new as they were unexpected.

1st. The bundle of calorific solar rays, on entering into our atmosphere, is composed of two sorts of rays; the one easily absorbable by the atmosphere, the other absolutely refusing all extinction; the former form nearly 0,8 and the latter 0,2 of the total number.

2d. The law of the extinction of the rays of the first order is a geometrical progression (according to the hypothesis of BoUGUER, KAEMTZ, &c.), such that the vertical transmission through the atmosphere, taken from its base (the level of the sea) to its superior limit, reduces the eighty absorbable rays to thirty-three.

It follows, from this new theory of Mr. FORBES'S, that the portion of the heat which is not absorbed in the case of vertical transmission, instead of being 75 per cent of the extra-atmospheric heat, is only 53 per cent. (Vide Phil. Mag. Sept. 1842.)—M.

more deeply buried in the earth. At about six or seven metres, the instrument is stationary for the whole year, and indicates a degree of temperature which approaches closely to that of the annual mean. This temperature increases the more we penetrate into the soil. Experiments made in mines and in artesian wells put this general fact beyond doubt. The nature of the soil and local circumstances modify the law of increase, which varies between twelve and thirty-five metres for one degree centigrade.

In all countries, the temperature increases with the depth. To say that this increase has no limit is what experience cannot teach us, and we are reduced to conjectures. Some philosophers admit an indefinite increase : it would follow from this, that, at a depth of about 3200 metres, a temperature of boiling water would be found; and the centre of the earth would be composed of matter in the state of fusion, or in the gaseous state, the heat of which would surpass all that the imagination can conceive. Add to this that the globe, having been formerly in the liquid state, has been cooled by radiation alone. The surface became cool first, and one part of its loss was repaired by the heat that was transmitted from within outwards. This transmission took place without cessation; but it has been calculated that this quantity of heat is insignificant, in comparison of that which comes to us from the sun. It was much greater before man existed on the earth. At certain geologic epochs, all the points of the globe were hotter; and this explains to us why we find in high latitudes fossil vegetables and animals, the analogues of which cannot at the present moment live any where but within the tropics.

At first sight, it seems incredible that the nucleus of the globe is incandescent, while at the surface we do not feel this heat. This fact is only explained by the want of conductibility in the rocks that compose the crust of the earth. Volcanos have made us familiar with phenomena of this kind. The lava that runs from the crater of a volcano possesses so great a heat that it almost melts all metals; but a crust is soon formed on its surface; it breaks, and its fragments swim in the current of lava like blocks of ice on a river. They solidify so quickly, that travellers have been able to traverse the liquid lavas by walking over them. If the current is stopped, these fragments, by uniting, form a solid crust, which prevents the mass from becoming cold; and, after several years, a notable heat is found in the centre of these streams. Gemellaro observed on Etna a