to prove that the crust is very thick, at least 800 or 1000 miles; and this result, I understand, has been recently confirmed by Professor W. Thomson "On the Rigidity of the Earth."

in a paper 18. These theoretical considerations receive, I think, some confirmation from an examination of the calculated deflection of the plumb-line at stations near the sea-shore. It is for this reason that I have collected the thirteen examples from the Anglo-Gallic and Russian Arcs in paragraph 15, all of which are near the coast. The evidence they furnish, however, is not to be compared in weight with that of the Indian Arc, already considered. In some instances the local attraction of the surrounding country and of the ocean for a certain distance has been calculated, as already stated. These results I will take into account, except the allowances for the ocean as noted at the end of paragraph 15, which I deduct in the fol lowing arrangement of the stations.

The Stations at which the Deflection is towards the Land.

(1) Barcelona, lat. 41 23, S.E. coast of Spain,

Deflection.

+2.20

ย

The Stations at which the Deflection is towards the Sea.

Deflection. "

(3) High Port Cliff, 50 36, S. coast of Isle of Wight, -2.01-0.27=-2.28

The theory I have proposed, that contraction of the crust has formed the basins in which the sea has settled, can hardly be expected to apply so completely to such confined sheets of water as the Mediterranean south of Spain, and the Gulf of Bothnia. Here there may be an actual deficiency of attracting matter in the water, not altogether compensated for by increased density of the crust below. These hollows may have been formed during the breaking up of the crust and subsequent removal of portions by currents, and not chiefly by the contraction of the crust. Thus the deflec tions at the stations (1) and (12) towards the land may be sufficiently accounted for, even if the land about Barcelona and Tornea does not rise sufficiently high to produce them. The deflection at station (2) is small. It seems probable that even if the North Sea has been produced according

to the theory of contraction of the crust, the parts near Dunkirk may have been somewhat hollowed out by the scouring of the tide through the Straits of Dover, so as to give the land, low as it is, every advantage in deflecting the plumb-line south. I have no means of knowing the character of the ground north of station (7) on the coast of Dorset. There is no difficulty, however, in accounting for the north deflection at that place, and even for a greater deflection, if the attraction of the country north of it is as much as the attraction of the land on Burleigh Moor on the north coast of Yorkshire. To this station I shall revert. With regard to stations (9) and (10), I gather the following information from the Ordnance Survey Volume. "At present there are no sufficient data for calculating exactly the disturbance" at Cowhythe (p. 662). It is supposed not to exceed 6" (p. 664); but the calculation is not made for any part of the mountains further south than 50 miles. The south deflection to be accounted for, viz. -3" 11, may in part be thus explained; or, even if, as before, the North Sea is supposed to have been formed by the contraction of the crust, the confined portion between the north coast of Aberdeen and the Orkney Islands may have been formed by the removal of the superficial strata by currents so as to produce a deficiency of attracting matter. So with respect to the other station, Ben Hutig, the unaccounted-for deflection, which is much smaller, viz. -0.60, may be easily explained, as the effect of the land has not been calculated further off than about 3 miles (pp. 660, 661). Thus, on the whole, the deflections at those coast-stations, where it is towards the land, can be pretty well accounted for, without calling in aid the deficiency of attraction of water and supposing that the crust below the ocean is not condensed.

The seven coast-stations of the second list, where the deflection is towards the sea, seem to bear individual testimony to the truth of the theory, that the crust below the ocean must have undergone greater contraction than other parts of the crust. The four stations (3), (4), (5), (6) on the south coast of the Isle of Wight all have deflections southwards; and their magnitudes diminish in the order that the distances from the sea increase,—that order being (3) High Port Cliff, (5) Boniface Down, (4) Week Down, (6) Dunnose (see the Contour Map of Isle of Wight in the volume of Plates accompanying the Ordnance Survey Volume). The amounts of the deflection seem almost to prove too much for the theory. Still they are all in the direction of the ocean, and seem certainly to indicate that there is a redundance of matter, and not a deficiency, in that direction. Blackdown (7) is somewhat further inland than Dunnose is. If, then, the ocean and crust together do really produce the outstanding deflection southward at Dunnose, we shall have to suppose that the north deflection at Blackdown in the first list of coast-stations, arising from the land, is not much less than 2.76+1.73=4·49, which is a little less than the calculated deflection at Burleigh Moor on the coast of Yorkshire, and is therefore not an unlikely amount. The other three coast-stations, (8), (11), (13), all bear out the

VOL. XIII.

Y

theory: though the three deflections are all small, they are towards the sea, the largest of them being at Fuglences, which is very near to the North Cape, and has a large expanse of ocean above it.

19. The least that can be gathered from the deflections of these coaststations is, that they present no obstacle to the theory so remarkably suggested by the facts brought to light in India, viz. that mountain-regions and oceans on a large scale have been produced by the contraction of the materials, as the surface of the earth has passed from a fluid state to a condition of solidity-the amount of contraction beneath the mountain-region having been less than that beneath the ordinary surface, and still less than that beneath the ocean-bed, by which process the hollows have been produced into which the ocean has flowed. In fact the testimony of these coaststations is in some degree directly in favour of the theory, as they seem to indicate, by excess of attraction towards the sea, that the contraction of the crust beneath the ocean has gone on increasing in some instances still further since the crust became too thick to be influenced by the principles of floatation, and that an additional flow of water into the increasing hollow has increased the amount of attraction upon stations on its shores.

The Annual Meeting for the Election of Fellows was held this day.
Major-General SABINE, President, in the Chair.

The Statutes relating to the Election of Fellows having been read, General Boileau and Sir Andrew Scott Waugh were, with the consent of the Society, nominated Scrutators to assist the Secretaries in examining the lists.

The votes of the Fellows present having been collected, the following gentlemen were declared duly elected into the Society :

Sir Henry Barkly, K.C.B.
William Brinton, M.D.
T. Spencer Cobbold, M.D.
Alexander John Ellis, Esq.
John Evans, Esq.

William Henry Flower, Esq.
Thomas Grubb, Esq.

Sir John Charles Dalrymple Hay,

William Jenner, M.D.

Sir Charles Locock, Bart., M.D.
William Sanders, Esq.

Col. William James Smythe, R.A.
Lieut.-Col. Alexander Strange.
Robert Warington, Esq.

Nicholas Wood, Esq.

Bart.

June 9, 1864.

Major-General SABINE, President, in the Chair.

Mr. W. Sanders; Mr. R. Warington; Dr. Jenner; Mr. J. Evans;

Lieut.-Col. Strange; Mr. W. H, Flower; Dr. Cobbold; Col. W. J. Smythe; Sir J. C. Dalrymple Hay, Bart.; and Mr. A. J. Ellis, were admitted into the Society.

Pursuant to notice given at the last Meeting, MM. Claude Bernard, Jean Bernard Léon Foucault, and Adolph Wurtz, all of Paris, were balloted for and elected Foreign Members of the Society.

The following communication was read:

"Description of the Cavern of Bruniquel, and its Organic Contents. Human Remains." By Professor RICHARD OWEN,

-Part I.

F.R.S., &c. Received May 12, 1864.

(Abstract.)

In this communication the author gives an account of the Cavern of Bruniquel, Department of the Tarn and Garonne, France, in the state which it presented when visited by him in January 1864, and a description of the human remains discovered therein by the proprietor, the Vicomte de Lastic St. Jal, in 1863, and subsequently by the author in January 1864.

The circumstances under which these discoveries were made are minutely detailed, and the contemporaneity of the human remains with those of the extinct and other animals with which they are associated, together with the flint and bone implements, is shown by the evidences of the plastic condition of the calcified mud of the breccia at the time of interment, by the chemical constitution of the human bones, corresponding with that of the other animal remains, and by the similarity of their position and relations in the surrounding breccia.

Among the principal remains of the men of the flint-period described are the following:-1st, the hinder portion of the cranium, with several other parts of the same skeleton, which were so situated in their matrix as to indicate that the body had been interred in a crouching posture, and that, after decomposition and dissolution of the soft parts, the skeleton had yielded to the superincumbent weight; 2nd, an almost entire calvarium, which is described and compared with different types of the human skull, shown to be superior in form and capacity to the Australian type, and more closely to correspond with the Celtic type, though proportionally shorter than the modern Celtic, and the form exhibited by the Celtic cranium from Engis, Switzerland; 3rd, jaws and teeth of individuals of different ages.

After noticing other smaller portions of human cranium, the author proceeds to describe minutely the lower jaw and teeth of an adult, and upper and lower jaws of immature individuals, showing the characters of certain deciduous teeth. The proportions of the molars are not those of the Australian, but of other races, and especially those of ancient and modern Europeans. As in most primitive or early races in which mastication was little helped by arts of cookery or by various and refined kinds of food, the crowns of the molars, especially of m 1, are worn down beyond

the enamel, flat and smooth to the stumps, exposing there a central tract of osteodentine without any sign of decay.

The paper is illustrated by a view and plans of the cavern, and by figures of the principal human remains, and of two implements of bone on which the Vicomte de Lastic had discovered, on removal of the breccia, outline figures of the head of a reindeer and the head of a horse in profile. The description of the various remains of the animals killed for food, and of the flint- and bone-implements applied to that and other purposes, will be the subject of a future communication.

June 16, 1864.

Major-General SABINE, President, in the Chair.

Dr. Brinton; Professor Boole; Mr. T. Grubb; Sir Charles Locock, Bart.; and Mr. Nicholas Wood, were admitted into the Society.

The following communications were read:-
:-

I. "On Complex Binary Quadratic Forms." By H. J. STEPHEN
SMITH, M.A., F.R.S., Savilian Professor of Geometry in the
University of Oxford. Received May 18, 1864.

The purpose of this note is to extend to complex quadratic forms some important investigations of Gauss relating to real quadratic forms. We shall consider in order (I.) the definition of the Genera, (II.) the theory of Composition, (III.) the determination of the number of Ambiguous Classes, (IV.) the representation of forms of the principal genus by ternary quadratic forms of determinant 1. For the comparison of the numbers of classes of different orders, we may refer to a paper by M. Lipschitz (Crelle's Journal, vol. liv. p. 193); and for the principles of the theory of complex numbers and complex quadratic forms, to Lejeune Dirichlet's Memoir, "Recherches sur les formes quadratiques à coefficients et à indéterminées complexes" (Crelle, vol. xxiv. p. 291).

I. The Definition of the Genera.

Let f (a, b, c) be an uneven* primitive form of determinant D, and m=ax2+2bxy+cy2, m'=ax2+2bx'y' +cy' two numbers represented by f. The generic characters of ƒ are deducible from the equation

(ax2+2bxy+cy) (ax+2bx'y' +cy'2)=
(axx'+b[xy'+x'y]+cyy')2 —D(xy' — x'y)2,

* A primitive form (a, b, c) is uneven, semieven, or even, according as the greatest common divisor of a, 2b, c is 1, 1+i, or (1+i)2; i. e., in Lejeune Dirichlet's nomenclature, according as (a, b, c) is of the first, second, or third species. In this paper, when we speak of an uneven, semieven, or even form or class, we shall always suppose the form or class to be primitive. A semieven number is a number divisible by 1+i, but not by (1+i)2.