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from the central meridian, and 10° north of the equator, has its most conspicuous peripheral crest formed of seven principal nearly straight elements, approaching to equality in length, and meeting in points which are situated almost exactly in a circle of 24 geographical miles radius. Here is a very important partial difference, coupled with a very important general agreement.

While Gassendi, with peaks 9000 feet high, projects like a huge narrow wall into the Mare Humorum, and hangs over the interior plain in precipices as steep and many times as high as those over the Atrio del Cavallo, Copernicus, seated in the midst of broad land, on a base of 120 geographical miles, rises in many broken stages, bristling with a thousand silver-bright crests,-a perfect network of rough and complicated ground, crossed by lights and shades, which have a history of their own,--and toward the inside falls off by many irregular terraces, down to an interior plain, as if the whole area had yielded, and the surface had been formed by enormous land-slips. Four sharp notches are traced across the narrow ridge of Gassendi cutting it deeply, like the hollows left by decomposing lava dykes 500 feet broad; one deeper and broader opening unites the inner plain with the outer Mare Humorum, and one far wider opening leads to an accessory crater, over whose awful depth the cliffs, 10,000 to 12,000 ft. high, spread black shadows round some central rocks. In these particulars Copernicus offers a very different aspect. Its high crest, of 10,000 feet, is only cut through by one straight narrow meridional groove, though broken by numerous fissures in other parts, and is in all parts so irregular, partially undulated, and varied with small crateriform points, and enclosed areas, resembling craters, as to offer little analogy to any truncated cone of eruption. The highest summit, on the left hand (west) side-a huge rock-is conspicuous by its broad, deep and extended shade. What suggests a vast lava current, is equally remarkable on the northern slope. Regarding now the central plains of these mountains, we remark in each several low ridges of rather sinuous forms, and several small mounds (half a mile or more across), of which three central digitated masses, not pierced by craters, are the most elevated, and catch the earliest lights of morning which glance over the rocky borders of the basin. Had the drawings been executed at the instant of sunrise on the central meridian line of the basin, these points would have stood up on the soft edge of the light and shade, as bright as the Swiss mountains at sunrise or sunset, but not like them reddened by the optical property of the atmosphere. Gassendi has at least two (I have somewhere a memorandum of more) small craters within the central plain. None such appear in this drawing of Copernicus. In many other lunar mountains the centre is occupied by a crater-formed hill, as Vesuvius stands within Somma; in others the hill remains a smooth rounded mass, but its crater is lost; and a further stage of decay seems to be seen in Gassendi and Copernicus, where the central mass is broken into fragments and sculptured by ramified hollows. May we ascribe these effects to

former action of a lunar atmosphere, now absorbed in the oxidated crust of the moon ? If so, the lunar mountains have a history of water, as well as records of fire, and we must look on the sinuous ridges of the Mare Humorum with eyes accustomed to the gravel mounds of Norway and Ireland ; study the degraded craters after the models of the Eifel ; and map the ‘rillen *' with reference to valleys of erosion as well as of eruption.

In questions of this kind we shall find such drawings as this of the Roman astronomer of priceless value. Studied, scrutinized, enriched with new discoveries, it may be the model for all time to come in this line of research.

It may be followed by two other drawings of the same mountain,—one at the moment when the sun is on the meridian of the central hillocks, to show the light streaks, which hide themselves when the sun is low, and another in the clear afternoon of the lunar day (as much after midday, as this drawing was taken before noon), when every little crack and cavity becomes again distinct, but greatly altered in aspect, and the whole landscape changes under the eye of the observer; the plains growing grayer and softer, and revealing many minute low undulations; the hills looking more and more rugged, and burning with narrower, brighter and more angular tracts of silvery light.

* I have some curious results regarding these beautiful objects."

IV. “A Third Memoir on Quantics." By ARTHUR CAYLEY,

Esq., F.R.S. Received March 13, 1856.

The object of the author in the present memoir is chiefly to collect together and put upon record various results useful in the theories of the particular quantics to which they relate. The tables at the commencement relate to binary quantics, and are a direct sequel to the tables in the author's second memoir upon Quantics, Phil. Trans. vol. cxlvi. (1956). The definitions and explanations in the next part of the present memoir are given here for the sake of convenience, the further development of the subjects to which they relate being reserved for another occasion. The remainder of the memoir consists of tables and explanations relating to ternary quadrics and cubics.

V. “Elementary Considerations on the subject of Rotatory

Motion." By W. GRAVATT, Esq., F.R.S. Communicated by the Rev.J. B. READE, F.R.S. Received March 12, 1856.

(Abstract.) The author explains the subject of rotatory motion in a series of propositions by the use of prime and ultimate ratios. He commences with a simple problem, determining the law of the forces by which a particle of matter is deflected into any given course, and pursues the inquiry by a consideration of the effect of these forces as referred to a sphere, going on to the investigation of the character of the motion of any body enclosed within an imaginary sphere, such sphere itself being supposed to revolve upon two axes inclined at any angle to each other. Hence the author determines the position of some point of the circumscribing sphere momentarily at rest, or in other words, of the resultant axis, from which he insists that all centrifugal forces must really be calculated.

His first application of the law thus enunciated is to the motion of the peg-top; and upon the principles he has already laid down, he shows that there is in the first instance rotation round a momentary horizontal axis, calling up rotation round a momentary vertical axis ; and that the ratio of the velocities of these two rotations, together with the length of the peg, determines the angular inclination of the top, contrary to the received explanation as given by Euler and other mathematicians.

The law is further applied to the effect produced upon a falling body by the axial rotation of the earth, in the discussion of which, La Place, in the opinion of the author, has committed two important errors one in denying any deviation towards the equator, the other ; in his calculation of the amount of the deviation towards the east.

This is followed by an investigation of the motion or direction of flight of a cannon-ball or shell fired in a northerly or southerly direction, from which it appears that a large shell will be subject to a deviation from the true line of projection, in consequence of the earth's rotation, amounting to no less than 22 feet.

The author then refers to the well-known experiment of M. Foucault for proving sensibly the rotation of the earth, and shows from calculation that the errors which would be sufficient to vitiate the results in this experiment are so extremely minute and so difficult of avoidance by any perfection of manipulation which can be employed, that its performance cannot perhaps be safely adduced as proving such rotation.

The author illustrated his views by the exhibition to the meeting of a model apparatus, in which the vertical and horizontal motions may be variously combined, but which could not be intelligibly described without a series of complicated drawings unfitted for the compass of a mere abstract.

April 17, 1856.

The LORD WROTTESLEY, President, in the Chair.

The following communications were read :

I. “On the Condition of the Oxygen absorbed into the Blood

during Respiration.” By GEORGE HARLEY, M.D., Teacher of Practical Physiology and Histology in University College, London. Communicated by Professor SHARPEY, M.D., Sec. R.S. Received March 16, 1856.

(Abstract.) The author commences by explaining, that his researches were instituted with the view of ascertaining whether the doctrine maintained by Magnus in regard to the gases interchanged in the lungs during respiration were correct-namely, that the gases in question enter into no chemical combination with the constituents of the blood, either in passing to or from the tissues and organs of the body, but form merely a physical mixture with the circulating liquid. The principal object of the inquiry was to determine the following points :

1. Has blood the property of chemically combining with the respired oxygen ?

2. Which of the constituents of the blood enter into combination with oxygen?

3. Do these constituents, by combining with oxygen, simply become oxidized, or do they also yield carbonic acid gas ?

4. What are the agents which control these changes ?

After describing the method of investigation, and the apparatus employed, the author proceeds to relate a few of the analyses which he considered as the most conclusive. Instead of confirming the view of Magnus, that gases enter into no chemical combination with

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