a considerable extent. The direct heat of the moon, for example, cannot be detected by the finest instruments which we possess; yet from 238,000 observations made at Prague during 1840-66, it would seem that the temperature is sensibly affected by the mere change in the lunar perigee and inclination of the moon's orbit *.

Column VIII. gives the midwinter temperature. It is found by subtracting the numbers in column VII. from 39°, the midwinter temperature. Column IX. shows the midwinter temperature of the centre of Scotland, on the supposition that the Gulf-stream was diminished in volume in proportion to the excentricity. In former papers it was explained how a change of excentricity must affect ocean-currents †.

Sir

I have not given a Table showing the temperature of the summers at the corresponding periods. This could not well be done; for there is no relation at the periods in question between the intensity of the sun's heat and the temperature of the summers. One is apt to suppose, without due consideration, that the summers ought to be then as much warmer than they are at present, as the winters were then colder than now. Charles Lyell, in his 'Principles,' has given a column of summer temperatures calculated upon this principle. Astronomically the principle is correct, but physically it is totally erroneous, and calculated to convey a wrong impression regarding the whole subject of geological climate. The summers at those periods, instead of being much warmer than they are at present, would in reality be far colder than they are now, notwithstanding the great increase in the intensity of the sun's heat resulting from the diminished distance of the sun. If a country is free from snow and ice, then no doubt the temperature will rise during summer as the intensity of the sun's heat increases; but when such a country is enveloped in perpetual snow and ice, the temperature of the summers will never rise much above the freezing-point, no matter what the intensity of the sun's heat may be. The physical reason of this was explained on a former occasion. In a country covered with ice, the direct heat of the sun is often very intense, in fact scorching. It will raise the temperature of the mercury in the thermometer exposed to the direct rays of the sun, but it fails to heat the air. Captain Scoresby, for example, when in lat. 80° 19′ N., found the side of his ship heated by the direct rays of the sun to about 100°,

* See Professor C. V. Zenger's paper "On the Periodic Change of Cli mate caused by the Moon," Phil. Mag. for June 1868.

+ Phil. Mag. for August 1864 and February 1867.

Phil. Mag. for February 1867.

while the air surrounding the ship, was actually 18° below the freezing-point. On another occasion he found the pitch melting on the one side of the ship by the heat of the sun, while water was freezing on the other side from the intense coldness of the air.

The mean temperature of Van Rensselaer Harbour, in lat. 78° 37' N., long. 70° 53′ W., was accurately determined from hourly observations made day and night over a period of two years by Dr. Kane. It was found to be as follows:

:

-28.59

4.03

But although the quantity of heat received from the sun at that latitude ought to have been greater during the summer than in England*, yet, nevertheless, the temperature is only 1°.38 above the freezing-point.

The temperature of Port Bowen, lat. 73° 14′ N., was found to be as follows:

Here the summer is only 2°-4 above the freezing-point.

If we go to the Antartic regions, where the influence of ice is still more felt, we find the summers even still colder. Capt. Sir James Ross found, when between lat. 60° and 77° S., that the mean temperature never rose even to the freezing-point during the entire southern summer; and when near the ice-barrier on the 8th of February, 1841, a season of the year equivalent to August in England, he had the thermometer at 12° at noon, and so rapidly was the young ice forming around the ships that it was with difficulty that he escaped being frozen in for the winter. And on the February of the following year, when he again visited that place, he had the thermometer standing at 19° at noon, and the sea covered with an unbroken sheet of young ice as far as the eye could reach from the mast-head. This extraordinary low temperature at that season of the year was wholly owing to the presence of the ice. Had there been no ice on the Antarctic continent, Sir James would have had a summer

See Mr. Meech's memoir "On the Intensity of the Sun's Heat and Light," Smithsonian Contributions, vol. ix.

hotter than that of England, instead of one actually below the freezing-point.

Now, during the glacial epoch, when Europe was almost covered with snow and ice, the summers could not possibly have been much warmer than they are at present in Arctic and Antarctic regions. In other words, during the glacial epoch the mean summer temperature would be very little above the freezing-point. [To be continued.]

XX. Proceedings of Learned Societies.

ROYAL SOCIETY.

[Continued from p. 68.]

May 28, 1868.-Lieut.-General Sabine, President, in the Chair. HE following communication was read :—

THE

"On the Impact of Compressible Bodies, considered with reference to the Theory of Pressure." By R. Moon, M.A., Honorary

Fellow of Queen's College, Cambridge.

Suppose that we have two rigid cylinders of equal dimensions, which have their axes in the same straight line; suppose, also, that one of the cylinders is at rest while the other moves towards the first with the velocity V in a direction parallel to both the axes; the consequence of the collision which under such circumstances must take place, will manifestly be that half the momentum of the moving cylinder will be withdrawn from it, and will be transferred to the cylinder which originally was at rest.

The mode in which velocity or momentum will thus be collected from the different parts of the one cylinder, and distributed amongst those of the other, is obvious. Exactly the same amount will be withdrawn from the velocity of each particle of the impinging cylinder, and exactly the same amount of velocity will be impressed on each particle of the cylinder struck.

And the reason of this is equally obvious, since, if such were not the case, the particles of each cylinder would contract-a supposition which is forbidden by the very definition of rigidity.

But if, instead of being perfectly rigid, each cylinder is in the slightest degree compressible, a variation in the effect will occur.

As before, momentum of finite amount will be transferred from the one cylinder to the other, but the mode of collection of the velocity withdrawn from the one, and the mode of distribution of that injected into the other, will no longer be the same as before.

In order that the moving cylinder may not be reduced to absolute rest by the collision, it is obvious that the cylinder originally at rest, or a portion of it, must be moved out of the way, so as to allow of the continuance, even in a modified degree, of the other's

motion; and this can only be effected on the terms of a transference of velocity or momentum taking place from the one cylinder, or part of it, to the other cylinder, or part of it.

But when the cylinders are compressible, we are freed from two conditions which obtain when the cylinders are rigid.

In the first place, it is no longer necessary to suppose, neither should we be justified in assuming, that the velocity abstracted from each particle of the impinging cylinder, or transferred to each particle of the cylinder struck, is the same; on the contrary, all experience tells us that, in bodies susceptible of compression, compression is always produced by collision-in other words, that variation of velocity, in the parts about which the collision takes place, is the immediate and invariable concomitant of collision.

In the second place, when the cylinders are compressible, it is no longer essential to suppose that the effect of the collision will be to withdraw velocity from every particle of the impinging cylinder, and to impart velocity to every particle of the cylinder struck. Undoubtedly such may be the case if the cylinders are short, if they are possessed of only a moderate degree of rigidity, and if the velocity before impact of the impinging cylinder is considerable. But if the cylinders be long, while the velocity of the impinging cylinder is of moderate amount, the contrary may occur. The condition that the cylinder originally at rest shall not oppose an immediate insurmount able barrier even to the modified motion of the other may, obviously, be sufficiently satisfied if a motion of contraction is imparted by the collision to a definite portion of the second cylinder.

But when the cylinders are compressible, equally as when they are rigid, the collision must cause the instantaneous abstraction of velocity or momentum, either from the whole of the impinging cylinder, or from a definite part of it, and the instantaneous communication of the velocity so withdrawn, either to the whole of the cylinder struck, or to a definite part of it.

We have hitherto assumed the velocity of each particle of the impinging cylinder to have been originally uniform. Let us now sup. pose, however, that immediately before impact a counter velocity of variable amount is impressed on the different parts of the impinging body, so that, at the instant of impact, before taking account of the effect of collision, the velocity at any point of the impinging body may be expressed by V-V1,-where V is constant, but V, has the value zero at the surface of collision, and thence gradually increases as we recede towards the other extremity of the cylinder, so that V–V1, which expresses the velocity of the impinging cylinder before impact, has its greatest value at the surface of collision, and diminishes as we recede therefrom.

It is clear that, in the case we are now considering, the collective momentum abstracted from the impinging cylinder by the collision will be less, and finitely less, than that which was abstracted by the collision in the former case, in which the velocity of each particle of the impinging cylinder was supposed uniform and equal to V.

For, if M be the momentum lost by collision when the velocity before impact is uniform and equal to V, it is clear that when the velocity before impact is represented by V-V,, the quantity V, may be such that the momentum before impact may be finitely less than M; from which it follows inevitably that the amount of momentum lost by collision in this latter case must be less than M.

Let us now vary the data by supposing that the velocity before impact increases instead of diminishes as we recede from the surface of collision, so that at the moment of impact, before taking account of the effects of collision, the velocity at any point of the impinging cylinder is represented by V+V, instead of V-V1.

It is clear that the momentum abstracted by the collision in this latter case will be greater, and finitely greater, than in the case where the velocity before impact is uniform and equal to V. Let the additional momentum abstracted in this case be M,, the whole momentum so abstracted being represented by M+M1.

Let us now make a final variation in the conditions of the problem, by supposing that at the moment of impact, and irrespective of the impact, a velocity equal and opposite to V is communicated to each particle of the impinging cylinder, so that at that instant, without taking account of any action of the one cylinder upon the other, the velocities of the two cylinders along their surfaces of contact will be equal, or, rather, will be alike zero, at the same time that at every other point of the impinging cylinder there will be a variable velocity V, increasing in amount as we recede from the surface of contact.

In estimating the effect of the cylinders being in contact under the circumstances last described, it is clear that the abstraction from each particle of the impinging body of the velocity V can only be regarded as preventing the transference to the second cylinder of so much of the momentum M+M, as that velocity, if it had constituted the entire velocity before impact of the impinging body, would have given rise to, viz. M,—and that the momentum M,, whose appearance in the expression M+M, is due to the fact of the first cylinder having been originally endowed with the variable velocity V1 in addition to the constant velocity V, will still continue to be transmitted to the second cylinder from the first.

We are thus led to this singular and, doubtless, pregnant conclusion, that in a continuous material system in which there is neither discontinuity of velocity nor discontinuity of density, all the consequences of collision may occur, viz. the instantaneous transmission of a finite amount of momentum from one part of the system to another, provided we have discontinuity in the tendency to compression in the different parts of the system.

The author has endeavoured, in former communications to the Royal Society, to show that when the velocity in a fluid diminishes in the direction to which the motion tends, the slower particles will offer a resistance to the motion of the faster particles, which the received theory fails to take into account. The foregoing speculation