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The new genus Endosiphonites differs from goniatites and nautilus in the position of the siphuncle, and it agrees with both in the direction of the striae of growth. The whorls, though contiguous, never envelope; and the septa seem usually very nearly simple. Taking D'Orbigny's classification, which being founded chiefly on the position of the siphuncle, must be preferred, we refer this genus to the family Nautilacea, and place it between Nautilus and Lituite.

We come now to consider the species, and the English localities not having been searched with a view to the discovery of these fossils, we have at present only three sufficiently well defined to admit of description. These are figured in Plate VIII. and I have named them as follows:–

(1). Endosiphonites Münsteri nob. PLATE VIII., Fig. 1. This being the largest species, I have named it in honour of the first discoverer of the genus. The individual figured is an extremely beautiful fossil, and, as will be seen from the figure, shows the siphuncle very clearly. It is partially burnt, having been obtained by the fracture of a lump which had passed through a kiln without being reduced to a calx; so that most of the striae of growth are destroyed, although I have no doubt they were before the burning sufficiently clear. It is the only species in which there are decided lobes, and is remarkable for the very large size of the last whorl, the area of the aperture being more than five times as large as that of the corresponding chamber in the former whorl. It is also very flat, the length of the aperture being more than twice its width, and this without any appearance of the shell having been injured or crushed. It measures four inches across.

(2). E. carinatus nob. PLATE VIII., Fig. 2. This species is remarkable for its elliptical form, and for having a keel running along the dorsal margin. Its dimensions are fourteen-tenths by nine-tenths of an inch. It is marked by a series of fine but beautifully distinct striae, which may be clearly seen in some parts of the specimen figured, where in all probability the original shell remains. This is the species alluded to above as having a very large siphuncle, seen in the figure at (a).

Vol. VI. PART III. 3 H

It is also one of those without the very slightest trace of the lobes alluded to by Count Münster.

(3). E. minutus nob. PLATE VIII., Fig. 3. twice the natural size. This very small and pretty species much resembles two of those described by Count Münster, except in the size of the siphuncle, but I have thought it better to give a new name, because of the great importance of this difference. Waved striae may be observed on some parts of the only specimen I have examined, but they are very minute, and required the aid of the microscope to discover them.

It remains now that we consider, from analogy with known genera, how far the animal inhabitant of this new genus may have resembled, in its habits or locality, those of other multilocular shells most nearly allied to it.

What then are those points in the description of the shell that tell most of the history of the animal, and what light is thus thrown on the subject now under consideration ?

It was the opinion of Von Buch, an opinion strengthened by the later researches of Dr Buckland, that the siphuncle must be considered as an all-important organ in the structure of a multilocular shell. It is true that the position of the tube has generally been considered much more than its magnitude, but the size must not be neglected; for assuming Dr Buckland's opinion of its use to be true, viz. that the whole mass of the animal and shell has its specific gravity changed by the pericardial fluid passing into the siphuncle, it is quite clear that the larger this tube in proportion to the area of the septa, the more sudden will be the change of specific gravity, and consequently

the greater the facility with which the animal could alter its depth in the water.

Now in almost all the known species of the family nautilacea, this contrivance is large, well defended, and eminently adapted for resisting external injury, while on the other hand, it is comparatively rare to find a large siphuncle in an ammonite, or any allied genus, and sometimes the tube is found to have dwindled away and become a mere thread. While, however, the siphuncle diminishes in size and importance, the general shape of the shell and peculiar form of the septa indicate an increased capacity for resisting pressure and supporting the weight of a high column of water.

Perhaps, viewing the subject in this light, we may not be far wrong in assuming a natural ground of separation between these two families of cephalopods, since the one appears to have a contrivance for enabling it to swim freely in the ocean, and rise or sink at pleasure, while in the other, there is only as it were the rudimentary appearance of this contrivance; but, on the other hand, additional strength in its habitation, fitting it to dwell more at the bottom of the sea and at considerable depths, and there to keep within necessary limits those crustacea and molluscs, which might otherwise, by their rapid increase, have interfered with the established course of nature.

In applying this theory, if it may be called so, to our new genus, we must necessarily consider separately the group described by Count Münster as having a small siphuncle, and the species now introduced to your notice. In the former, there seems to be a provision for strength, without great power of locomotion; for the septa seem less simple than even in some goniatites, and the lobes must be supposed to increase the resisting power. In the latter there are no lobes, but the siphuncle being so much larger, we may reasonably suppose that the extent of the inhabitant's power of altering readily its depth in the water, must have been in a corresponding degree greater.

The study of comparative anatomy introduces to our notice, in a very striking manner, the strong resemblances in the structure of different animals, and the universal occurrence of what would seem rudimentary attempts at higher and more complete organisation. Such, for instance, are the rudimentary bones in the fins of swimming mammalia, which correspond to the bones of the extremities in man ; and such would seem to be the case in this siphuncle, sometimes very large, then diminishing in size and importance, till it dwindles down to the

merest thread, which can no longer be capable of performing any office in the animal economy.

As an extreme instance of this, I would refer to the fossil represented in Plate VIII., Figs. 5, 6. It is in extremely good preservation, but does not show the slightest appearance of a siphuncle on the dorsal margin, or elsewhere, although it resembles in some respects one of Count Münster's goniatites, named G. subsulcatus. I have had it figured, because it shows very beautifully the singular extent to which the envelopement of one whorl by the rest is sometimes carried, and the marked resemblance which the specimen bears to some of the microscopic genera of D’Orbigny's Foraminifera. Its shape is lenticular, and it measures more than three-quarters of an inch across. In the absence of better information, I am compelled to call it a goniatite, but I cannot help thinking, that for this and many other species also doubtful, it may be found necessary to establish a separate group, founded on the almost total absence of the siphuncle.

In conclusion, I would observe, that among the known, but as yet undescribed fossils of the Silurian System, there is no instance of any species referrible to our new genus; and thus we have another instance of the wide separation denoted even by the zoological character of these ancient formations, which are indeed sufficiently distinct by the known occurrence of intervening deposits. It is the opinion of Professor Sedgwick, that these Cornish rocks, which contain the organic remains described, are the lowest fossiliferous rocks of Devonshire and Cornwall, and far, very far removed in the order of their deposit from the mountain limestone, with which it has been attempted to identify them.


JEsus College,
18th May, 1838.

XX. On a Question in the Theory of Probabilities. By AUGUSTU's DE MoRGAN, of Trinity College, Professor of Mathematics in University College, London.

[Read February 26, 1837.]

THE object of this paper is the correction of an oversight made both by Laplace and M. Poisson, in pages 279 and 209 of their respective works on The Theory of Probabilities.

The reputation of neither of those analysts requires an explanatory eulogium to accompany the detection of an error in their writings, particularly on a subject so liable to cause mistake as the theory in question: I shall therefore proceed at once to the point. Both arrive correctly at the conclusion, that”

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Vr s'F-'a, + Vorow (1) represents the probability that the number of arrivals of A shall fall between v l and v + l, both inclusive, where n (= v 4 wy is the number of trials, and v and w are proportional to the chances of arrival or non-arrival in a single trial. That is, if the number of times which A will happen in n trials be called A., the preceding formula is the probability that u, as deduced from

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will lie between l and + l; on the supposition that p is given, and A, to be found by trial. And both Laplace and M. Poisson immediately infer that the preceding result therefore represents the same probability in the case where A, has been observed, and p is to be

* See the Addition at the end.

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