same period, from the number of fossils which are common tó the two deposits, and this opinion he has subsequently con firmed in the Anniversary Address recently delivered to the Fellows of the Geological Society.

In a former memoir, when describing the stratum at Ramsholt, the opinion I stated was that it formed part of a deposit, older, geologically speaking, than those shelly strata above it with which geologists were already familiar. Subse quent consideration has tended to strengthen the views which I then advocated, and my object at present is that of testing the importance of those facts which are supposed by some to identify the coralline beds with the other fossiliferous strata.

During the summer of 1835, I entered upon a more minute examination of those localities in which the inferior portion of the crag is most advantageously exposed, and my investigation has been attended with results of a highly gratifying and satisfactory nature. I have procured from Ramsholt every species of coral that has yet been obtained from the more extensive excavations at Aldborough and Orford; while above the coral reefs, which occupy so large a portion of the latter district, I have succeeded in discovering the upper deposit, still retaining those well-marked peculiarities which form a striking contrast to the inferior stratum, and from which even the yet unpractised observer would as naturally separate it as he would the beds of the coralline crag from the London clay on which they repose. My anticipations on this subject have therefore been completely realized, and the true geological position of the Orford crag may now be considered fully established.

The relative position and lithological character of the red crag would during a late period of inquiry have probably assigned it a distinct place in a geological series, and under some circumstances the geologist undoubtedly derives considerable assistance in the classification of fossiliferous deposits from a careful observation of these phænomena. To guide our determination in the instance before us, in addition to these sources we have thrown open to our inspection an extensive series of organic remains; it is from their examination that my own opinions have principally been formed, and it now remains for me to show how far they can be justified.

With this view I shall take a cursory survey of the organic remains at present discovered in the tertiary strata which overlie the London clay in Suffolk and the chalk in Norfolk.

In the coralline crag we find few indications of the exist ence of vertebrated animals; such as are met with belong exclusively to the class of Fish; but the nature of this deposit appears to have been by no means well calculated for the pre

servation of their remains. The only bones of frequent occurrence are those placed within the cavity of the tympanum, and which being of a more solid texture than the rest of the skeleton are found in a very perfect state. These bones belong to an unknown genus, and are peculiar to this part of the crag formation. Teeth of cartilaginous species are occasionally met with, but in the course of my own researches I have never succeeded in obtaining them.

The ocean, however, which deposited the red crag was one evidently swarming with fish; and their mineralized remains, generally consisting of the teeth and portions of the palate, are preserved in great abundance. Among them are the genera Carcharias, Myliobates, Galeus, Lamna, Notidanus, and Platax, &c. Wherever this deposit is detected, some of these genera invariably accompany it. It is here also that we first meet with the higher orders of the animal kingdom. The teeth of the Mastodon, Elephant, Hippopotamus, and other Mammalia are deposited with the Mollusca of this period, and in addition to them I may mentioned the bones of.Birds, which I have recently obtained from several localities.

Turning from the groups of vertebrated animals to those of the Radiata, we naturally revert to that extensive assemblage of Polypifera which characterize so large a portion of the coralline crag, and to which nothing analogous is presented by any other tertiary deposit in this island. The Echinida too, so sparingly distributed in the London clay and upper beds of the crag, are here met with in comparative abundance; fragments and spines are of constant occurrence, and some of the more perfect specimens which have been obtained exhibit the most elegant forms, and are widely removed from known species. There are one or two spots in the red crag where Echini have congregated in myriads, but the species approximate more nearly to those now existing, and with which they may perhaps be identified. The comparison of the Crustacea from the two beds has furnished a corresponding result; but the remains of this group are sparingly met with, and generally in an unfavourable state for examination.

I now proceed to notice that class which among organized beings are thought to furnish the geologist with the most important data in his investigation of tertiary formations, and to which he especially directs his attention when fossiliferous strata of different periods are superposed in the same area, or when he is desirous of ascertaining the probable epoch to which an isolated deposit should be referred.

Mr. Searles V. Wood, who possesses the largest series extant

of British tertiary fossils,states that he has collected 450 species of shells from the crag: of these more than 200 were peculiar to the coralline, 80 peculiar to the upper bed, and 150 were found in both deposits.

Before any conclusions are drawn from this statement, it is of the utmost importance to bear in mind the circumstances under which the fossils of one formation may, by the natural process of degradation, have been imbedded in another. I have before alluded to the fact of secondary shells occurring in the red crag where that deposit is in contact with the chalk; and if causes similar to those now in action were operating at æras antecedent to the present, there is nothing to excite our surprise in this phænomenon. I have been particularly struck with the appearance presented by the fossils in those remarkable masses of transported or protruded chalk which are seen on the beach for a few miles east of Cromer. Many of these enormous fragments are half buried in the stratum of blue clay forming the beach, to which level the elevated portion is by the action of the tides gradually reduced. A platform of chalk is thus formed, which is frequently studded in every direction with Belemnites and Terebratula. As its surface wears away the fossils are brought out in relief, and at length being entirely removed are deposited with the recent Mollusca. The point principally deserving notice here is the introduction of these fossils into the present deposits completely detached from the matrix in which they were imbedded, and which being removed in a finely divided state, would not at a future period be recognised in the form under which it formerly existed.

The secondary shells in the crag of Norfolk have probably been removed from their original bed by a process similar to that just described. We see no indications of a more violent operation; there are no nodules of chalk accompanying the fossils, which are themselves so completely freed from any adherent matrix that they can only be distinguished from the more recent Mollusca with which they are associated by an attention to specific distinctions, and by the chalk locked up within the cavity of the bivalves.

At the time the formation of the red crag was going forward, the surface of the chalk to a great extent was protected from abrasion by overlying deposits, and wherever this was the case the superior stratum would be the one exposed to denudation, and from which organic remains would be transported. In this way, undoubtedly, have the fossils of the coralline crag, along with those of the chalk, been introduced into a more recent deposit, and the difficulty is now to ascertain the probable amount of admixture. Connected with this

subject there is one circumstance which should not be passed over without consideration: supposing that the disturbing forces were acting with equal intensity over the area of chalk and coralline crag, the effect produced, so far as regards the removal of fossils, would be regulated by their abundance and by the nature of the deposit in which they were imbedded. If, as is really the fact, we find in the red crag six or eight per cent. of fossils belonging to the chalk, we may reasonably infer the presence of a much larger number derived from the coralline beds. Were we to discover fossil shells carried down to the delta of a river the course of which flowed over an equal area of chalk and crag, we should naturally expect that the majority of these transported fossils would belong to the latter formation.

The numerical statements drawn up by Mr. Wood have been made without any reference to the conditions under which a large number of the same fossils have been discovered in the two deposits. However abundant or naturally grouped a shell may occur in the coralline crag, one solitary specimen of that species, or even a fragment having been detected in the upper bed, at once places it on the list of those which are spoken of as common to the two formations; under these circumstances, and taking into consideration the probable extent to which the coralline beds have been broken up, I am only surprised that there should be so large a number as 200 species which are only found in them and have not yet been observed in the rest of the formation.

There are however some Mollusca which are either naturally localized, or occur in the same abundance in both divisions of the crag formation; and setting aside the fallacies which may arise from our erroneous identification of species, we are at liberty to infer from these the probable approximation of the two deposits. It appears, however, that a very large proportion of species may be continued through distinct and very remote geological epochs, for on referring to the tables of M. Deshayes, we find that there are not less than 40 per cent. of species common to the crag and to the formations at this time in progress round the British islands.

Mr. Lyell, when speaking of the newer pliocene formations, observes in vol. iii., page 54, "It will be seen that of two hundred and twenty-six species found in the Sicilian beds only ten are of extinct or unknown species, although the antiquity of these tertiary deposits as contrasted with our most remote historical æras is immensely great. In the volcanic and sedimentary strata of the district round Naples, the proportion appears to be even still smaller.”

It seems then that if instead of 20 or 30 there were 95 per cent. of species common to the red and coralline crag, even then these deposits might be as widely separated as the Sicilian tertiary strata and the formations of the present period!

I have yet to enter upon the most important stage of the present inquiry, that which relates to M. Deshayes's examination of the coralline crag shells, and to the consideration of how far the result affects the opinion I formerly advanced respecting the antiquity of the Ramsholt stratum.

During the last two or three years I have embraced every opportunity of examining the marine and freshwater deposits in the counties of Norfolk, Essex, and Suffolk, and of late my attention has been particularly directed to those views of chronological arrangement which in so comprehensive and elaborate a manner are advocated in the Principles of Geology.' From facts which have fallen under my own notice during the course of my investigation, and from other circumstances which have more recently transpired, I feel confident that a classification of the fossiliferous strata in question, founded upon the proportion of extinct Mollusca which they individually contain, would lead to the most erroneous conclusions.

The sources of error which I have in the present instances detected, will, if clearly established, have a general application in the arrangement of tertiary formations, and will probably materially interfere with the confidence which we might otherwise place in the accuracy of those results which are connected with numerical calculations.

To enter upon a full discussion of this most interesting and complicated subject would greatly exceed the limits of the present communication, and I shall therefore confine myself to those points which are particularly connected with the present inquiry. [To be continued.]

XCI. Theorem respecting Algebraic Elimination, connected with the Question of the Possibility of resolving in finite Terms the general Equation of the Fifth Degree. Extracted by Permission, from a Communication recently made to the Royal Irish Academy. By Professor Sir WILLIAM ROWAN HAMILTON, Astronomer Royal of Ireland*.

Theorem. IF

Fr be eliminated between two equations, of the following forms, namely, 1st, an equation of the fifth degree, of the form

0 = x+Dx + E,

* Communicated by the Author.

(1.)