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ing diagram (fig. 1) of the fluctuations of rainfall, we feel that it would sufficiently prove the impossibility of determining accurately the rainfall at any place except by observations continued over a long series of years at that place, or by differentiation from some proximate long-continued series.

(2) It does not follow that simultaneous observations, even for ten years, giving for example a mean difference between two stations of five inches, prove that the rainfall at the one station is greater than the other by that amount, although if they are not very distant the one from the other it would probably be a safe assumption.

(3) Before mean results can be given with any pretensions to accuracy and finality, they must be corrected for the elevation of the rain-gauge above the ground.

The above remarks sufficiently show that the mere average of the fall of rain measured during ten or more years does not necessarily give the true mean rainfall at that place.

Let us take as an example the highest amount recorded in the Table (Seathwaite), which had during the ten years (1860-69) an average of 154 inches; many persons would say at once that that was therefore the mean rainfall at that station. It is, however, nothing like it. From Table II. and fig. 2 we see that the rainfall over England, generally, during those ten years was 1.5 per cent. above the average, upon which evidence we are bound to reduce the observed mean in that proportion, and then the average becomes 152 inches instead of 154. Even this, however, is not correct; for we pointed out in condition (2) that the same years, or groups of years, are not similarly wet in all parts of the country. Referring, therefore, to Table IV. we find that at the nearest station to Seathwaite, Kendal, the decade in question was 7 per cent. above the thirtyyear mean; hence, on the supposition that the Kendal values are applicable to this station, we have to reduce 154 inches by 7 per cent. instead of by 1:5 per cent., and hence the probable mean comes out 141.8 inches.

Now most fortunately we can test the accuracy of this calculation in three ways.

(1) The mean fall at Seathwaite in the previous decade was 126.98; from the Kendal observations the fall in that decade was 10 per cent. less than

(126.98_11.00 the mean ; therefore ( =141.09 ) we find the probable mean comes

find ° 0.90 out 141.1 from this decade, and 141.8 from that of 1860-69. They thus agree within less than an inch, or one half per cent.

(2) The fall at Seathwaite has now been continuously observed for twenty-six years, viz. from 1845 to 1870 inclusive; the mean of the whole twenty-six years' observations is 140.03.

(3) This value, corrected according to the Table in our 1866 Report, becomes 141.44, agreeing exactly with that indicated by the decades 1850-59 and 1860-69.

This example proves three points :-(1) the great degree of accuracy which is attainable by proper methods ; (2) the care requisite to secure it; (3) the serious errors inseparable from the use of mere arithmetical averages without reference to secular changes.

These observations, however, must of course be taken as general results, and not be construed as having any bearing on the relative rainfall even of proximate stations, the rainfall of which will vary considerably according to local circumstances. Hence it will be seen that the probable average at Seathwaite is 141 inches

instead of 154, or 7 per cent. less. A similar, but generally less correction, may be required for other stations. The figures in Table V. must not therefore be considered as showing the mean fall at the several stations, but only as approximations generally pretty close. The data in our possession, if corrected in accordance with the method explained, would afford more accurate results, but the investigation is altogether beyond our present resources.

Large tracts of Ireland, and even of Scotland, are still without observers ; much has recently been done to remedy these deficiencies, but there are still many localities where observations are very much wanted; we shall gladly receive any offers of assistance from those who have residences or property in those parts, and our Secretary will readily advise them as to instruments.

Third Report on the British Fossil Corals. By P. MARTIN DUNCAN,

F.R.S., F.G.S., Professor of Geology in King's College, London. Introduction.—There can be no doubt that the palæontology of the Madreporaria of the Palæozoic strata is in a condition of profound confusion. When these Reports were commenced, the very excellent descriptions and classification of the Palæozoic Corals by MM. Milne-Edwards and Jules Haime. strengthened by those of M. de Fromentel, appeared to have satisfied paläontologists, and they were received and adopted without much demur. But during the last three or four years a series of more or less important attacks has been made upon the views of those distinguished authors ; consequently opinions respecting many important matters in the palæontology of the Palæozoic corals are in a very unsatisfactory state.

L. Agassiz, A. Agassiz, and now Count Pourtales would remove the Tabulata from the list of Madreporaria. Mr. Kent and I doubt the propriety of establishing the Tabulata as a group. Count Keyserling demurred years since at receiving the long septaless Tubulata amongst the Madreporaria, and, after due examination, I agree with him in relegating them to the Alcyonaria,

Working amongst the Rugosa, I have shown that they do not invariably characterize Palæozoic strata, for some of the types have persisted, and no reasonable doubt can be entertained concerning the descent of the Jurassic Coral-fauna from the Palæozoic.

The genus Palæocyclus has been shown not to belong to the Fungidæ, but to the Cyathophyllidæ. Genera with the hexameral arrangement of septa have been found in Carboniferous and Devonian strata.

Lindström's interesting researches respecting the operculated condition of some Palæozoic corals require most careful study and much following up, and the assertion of L. Agassiz respecting the hydroid relationship of those Rugosa which have tabulæ demands further inquiry *.

Ludwig, of Darmstadt, has added to the confusion by not acknowledging the received classification in the least; and in his able enthusiasm (antiGallican enough) he alters generic and specific names, employing sesquipedalian Greek, and even absorbing the original authors (* Palæontographica,' H. von Meyer, 1866).

* G. Lindström, pamphlet translated by M. Lindström from the original Swedish, • Geological Magazine, 1866, p. 356. He notices that Guettard first described an operculum in a rugose coral, and that then Steenstrup saw one in a Cyathophyllum mitratum. Lindström produces evidence respecting the genera Goniophyllum, Calceola, Zaphrentis, Hallia, and Favosites (see also p. 406 et seq.).

Thus he confuses Stromatopora concentrica, Goldfuss, with the Madreporaria, and calls it Lioplacocyathus concentricus. Fortunately Ludwig gives à plate of it (tab. lxxii, fig. 1), and thus proves the total absence of all structures which differentiate the Madreporaria. After thus dignifying a rhizopod, we may be prepared for any thing.

The same author figures a form which is clearly that of Heliolites porosa, and calls it by the extraordinary name of Astroplucocyathus solidus, Ldwg. It appears that this naturalist studied this eminently cellular type from a cast, hence the term solidus. Again, in tab. lxxi. fig. 2, Ludwig delineates a good specimen of Cyathophyllum hexagonum, Goldfuss, 1826, and with surpassing coolness names it Astrophloeothylacus vulgaris, Luwg. He then confounds a species of Lithostrotion and Smithia Hennali, E. & H., in one genus, Astrophloeocyclus, Ldwg.

The student of the Silurian corals will be surprised perhaps to find that, according to Ludwig, Halysites catenularia, Ed. & H., the Catenipora escharoides of Lonsdale, is transformed into Ptychophloeolopas catenularia, Ludwig, doubtless on the principle that having found such a very distinguished generic title, the compiler of it has the right to eclipse the discoverers of the form. Chætetes, which some of us consider to belong to the Alcyonarian group, as it has no septa, Ludwig decorates with the title “ Liophlcocyathus.

In his sixty-ninth plate, fig. 5, there is a very good representation of a coral ordinarily known as Acervularia Troscheli, Ed. & H. This form was inaccurately described by Goldfuss, who called it Cyathophyllum ananas. Now the authorship is settled by this Alexander, who cuts the knot by claiming the species as his own, under the title of Astrochartodiscus ananas, Ludwig !

Then Pleurodictyum problematicum, Goldfuss, is altered into Tæniochartocyclus planus, Ldwg.

To render matters easier to the student, Ludwig associates Acervularia luxurians and Cyathophyllum helianthoides in one genus, Astroblascodiscus, and of course places his name after the species. Then Cyathophyllum cæspitosum becomes, under the same lexicographic hands, Astrocalanocyathus cospitosus, Ludwig! In another place Cyathophyllum helianthoides, Goldfuss, just mentioned under the term Astroblascodiscus, appears as Astrodiscus. Lonsdale's Cystiphyllum cylindricum is turned into Liocyathus catinifer, Ldwg.

This author, moreover, appears to hold a brief against the belief in the quadrate arrangement of the septa in the Rugosa, and, in a manner which is excessively arbitrary and artificial, terms such and such septa primaries, so as to reduce the cycles to sixes. In spite of the evidence of great industry given by Ludwig, I cannot accept his classification, nor do I find his hypothetical septal readings consistent with facts. Nevertheless, Ludwig has contributed to our knowledge of Permian corals, and has discovered some species of genera hitherto supposed to characterize the Carboniferous formation in the Upper Devonian of Germany.

The nature of this Report must therefore be very different to those already presented to the Association. Those reports relating to the Corals of the Mesozoic strata were essentially founded upon observed facts, and upon data which had been more or less before the geological world for years; the generalizations embodied in them were established upon very satisfactory details. But in the present instance there is much uncertainty; there are

vast accumulations of details to be worked out without the existence of a satisfactory classification, and, in fact, the whole subject of the Palæozoic Madreporaria is in too transitional a state for an exhaustive report to be made upon them.

In presenting this Report, therefore, I hope the Association will consider that I have not yet completed my task, and that it will allow me to continue my work and to present other reports when occasion offers. No further grant will be required, as the future reports will deal more with the results of other labourers than with my own.

The present Report is divided into four parts.

I. The consideration of the alliances of the Neozoic and the Palæozoie Coral-faunas.

II. The classification of the Perforata.
III. The classification of the Tabulata.
IV. The Rugosa.

In order to avoid useless repetition of well-known facts, I have referred to them by giving their bibliography, except when they are contained in inaccessible works.

I. The Palæozoic corals of Great Britain have been the subject of many admirable works ; they have been largely treated of in the - Monograph of the British Fossil Corals' (Palæontographical Society) by MM. Milne-Edwards and Jules Haime, and by M‘Coy in Sedgwick's great work. Phillips, Lonsdale, King, Sam. Woodward, Parkinson, Martin, Fleming, Portlock, Sowerby, and Pennant have described species in their well-known works, and Kent, James Thomson, and I have contributed some information on the subject of the Scottish corals. But, with the exception of the labours of the last three persons, the literature of the Palæozoic Corals will be found very accessible in the monograph already noticed; any omissions, and a considerable number of new species will be published in my Supplement to that monograph, which I trust will appear year after year, especially as the Supplement to the Mesozoic Corals is now complete (Palæontographical Society).

The vertical range and the horizontal distribution of the species of corals have been worked out by Robert Etheridge, F.R.S., in a work which is now in course of publication (Cat. of Brit. Fossils).

MM. Milne-Edwards and Jules Haime classified the British Palæozoio Corals amongst the sections Aporosa, Tabulata, Tubulosa, and Rugosa. The great section Perforata is not represented in the British strata, but it is in the equivalent American beds.

The only representative of the Aporosa in their classification was one of the Fungidæ, Palæocyclus being the genus. It is a Silurian form, and no others of the family have been discovered in the other Palæozoic rocks. The genus has been the subject of a memoir in the Philosophical Transactions, 1867, where its rugose affinities are pointed out, and its cyathophylloid nature also. But the Aporosa are nevertheless represented in the Devonian and Carboniferous rocks by the genera Battersbyia and Heterophyllia (Phil. Trans. 1867).

The alliances of these forms and of some of the Rugosa with the Jurassic Coral-fauna have been noticed in my Supplement to the Brit. Foss. Corals (Pal. Soc.), part “ Liassic," and in the Essay in the Phil. Trans, of 1867*.

* The PalastRÆACEÆ. Genera Battersbyia and Heterophyllia (Phil. Trans. 1867, p. 643 et seq., P. M. Duncan).-The so-called cænenchyma of Battersbyia inæqualis, Ed. & 11, is like that of Battersbyia grandis, nobis, and B. gemmans, nobis. It is really nothing

I do not consider that the Tubulosa belonged to the Madreporaria, but that they were Alcyonarians.

It is very certain that some Aporose, Perforate, and Rugose corals have tabulæ, and that their existence cannot remove the forms from their received zoological position into the separate section of Tabulata.

Thus the well-known Aporose coral of the deep sea, Lophohelia pro

more than portions of Stromatopora which enclose the corallites and grow simultaneously with them.

I have altered the generic characters of Battersbyia, in consequence of a careful examination of the old and the two new species. It is as follows:--Corallum fasciculate and branching; corallites tall, cylindrical, unequal in size and distance; septa numerous and following no apparent cyclical order.

Endothoca very abundant: it is vesicular, and there are no tabulæ. Epitheca, costa, and canenchyma wanting. The wall is stout, and the septa spring from wedge-shaped processes. The columellary space is occupied by vesicular endotheca. Gemmation extracalicular and calicular from buds having only five septa. There are three species :

Battersbyia inæqualis, Duncan.) Deronian Limestone;
- grandis, Duncan. } found in pebbles,
gemmans, Duncan.

and not in situ. In Battersbyia gemmans the buds which develop more than five septa grow into coral. lites, which are destined to bud again from the external wall, and the buds which develop five septa produce other buds from their interseptal loculi; the buds thus developed resemble the corallites with more than three septa. This curious alternation of gemmation has not been noticed in any other genus.

The genera Battersbyia and Heterophyllia (Phil. Trans. loc. cit.) have much in common. They have a stout wall, a vesicular and disse pimental endotheca, delicate septa, very irregular in their number, and neither tabular epitheca nor a quaternary septal arrangement.

The genus Battersbyia has nothing to ally it to the Rugosa or the Tabulata. Heterophyllia has in some of its species the solitary septum or vacancy which is so often observed in the Cyathophyllidæ. Its costal wall and endotheca connect it with the Mesozoic and recent Astræidæ.

The singular septal development of Battersbyia is witnessed in the fasciculate Liassic Astræids. The pentameral arrangement of the Battersbyian septa is not unique, for Acanthocænia Rathieri, D’Orb., of the Neocomian has only five septa, and so have the species of Pentacænia, all of which are from the same great formation. The proper Liassic and some of the Lower Oolitic Thecosmiliæ and Calamophylliæ represent and are allied by structure to Battersbyia. The highly specialized characters of the Heterophylliæ, especially of H. mirabilis, could hardly be perpetuated during great and prolonged emigrations, so that the genus appears to be without representatives in the secondary rocks. Its alliance to Battersbyia, however, is evident enough.

The genus Heterophyllia, M.Coy, was examined by me in 1867, and the study of several new species of it rendered a fresh diagnosis requisite.

The following description of the diagnosis appeared in my essay on the genera Heterophyllia, &c., already noticed : . The corallum is simple, long, and slender. The gemmation takes place around the calicular margin, and is extracalicular. The septa are either irregular in number and arrangement, or else are six in number and regular. The costæ are well developed, and may be trabecular, spined, and flexuous. The wall is thick ; there is no epitheca, and the endotheca is dissepimental.”

The genus may be subdivided into a group with numerous septa, and a group with six septa.

In the first the rugose type is faintly, and in the last the hexameral arrangement is well observed.

The dense wall and the dissepimental endotheca prove that the type of the Mesozoic Coral-fauna was foreshown.

The endotheca varies in quantity in the different species, and it resembles the tabular arrangement; but even when this is the case and the cross structures are well developed and numerous, they do not stretch over the axial space, so as to shut out cavities as if they were doors; they do not close in the whole of the visceral and interlocular

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