connected with the open sea to the south, and the fauna was derived from the direction of Germany. A short account is given of some of the Continental Rhætic formations, followed by a list of Rhætic fossils recorded in England, with the range of each. A consideration of this list enables the author to suggest that the lower limit of the formation should be drawn at the first evidence of Rhætic life after the deposition of the gypsiferous and red or green marls, which (at any rate in their lower part) are certainly of Keuper age. The upper limit may, for convenience, be drawn at an indefinite level where Modiola minima and Pleuromya crowcombeiana become very rare, and the ammonitic and Liassic fauna begins. Further discussion of the lithological, physical, and paleontological evidence leads the author to recognize that the affinities of the Rhætic, thus defined, are rather with the Jurassic rocks than with the Trias. The following zones are suggested, in descending order :

Pecten valoniensis.

Avicula contorta = Black Shales and a limestone-bed.
Bone-Bed.

These zones seem to be fairly constant throughout England, and harmonize well with those of Germany, although they cannot be expected to fit in with the oceanic type of the Alps and the Mediterranean. Further consideration shows that the fossils give evidence of migration, but very little of evolution. The paper

closes with the description of a new species of Anomia and a bibliography.

January 6th, 1904.-Sir Archibald Geikie, D.C.L., D.Sc., Sec.R.S., Vice-President, in the Chair.

The following communications were read :—

1. On a Palæolithic Floor at Prah Sands, in Cornwall.' By Clement Reid, Esq., F.R.S., F.L.S., F.G.S., and Eleanor M. Reid, B.Sc.

Prah Sands lie about 7 miles east of Penzance, and have long been known as exhibiting a good section of head' or rubble-drift, over raised beach, which rests on a wave-worn rocky platform. Recent storms have cleared away the talus at the foot of the cliff, and have exposed, between the 'head' and the raised beach, a Palæolithic land-surface, consisting of loamy soil penetrated by small roots. In and above this occur black seams full of small fragments of charcoal and bone: these are particularly abundant round groups of large flat stones, which seem to have formed ancient hearths. The black seams contain implements made of vein-quartz. For a few feet above this land-surface the angular 'head' consists mainly of loam with fragments of vein-quartz, some of which are worked. This seems to be the first record of Paleolithic man in Cornwall.

2. Implementiferous Sections at Wolvercote (Oxfordshire).' By Alexander Montgomerie Bell, Esq., M.A., F.G.S.

January 20th.-Sir Archibald Geikie, D.C.L., D.Sc., Sec.R.S., Vice-President, in the Chair.

The following communications were read :

:

1. On the Jaws of Ptychodus from the Chalk.' Smith Woodward, LL.D., F.R.S., F.L.S., F.G.S.

By Arthur

2. On the Igneous Rocks at Spring Cove, near Weston-superMare.' By William S. Boulton, Esq., B.Sc., A.R.C.S., F.G.S.

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A traverse from end to end of the exposure at the locality shows that the basalt-mass' varies in structure and appearance, and that it is by no means a simple lava-flow. It may be roughly divided into three portions. Beginning at the cliff-end to the north, the rock for the first 30 yards is a pillowy basalt, with tuff and limestone often occupying irregular spaces between the spheroids of amygdaloidal basalt; then, for about 20 yards, the rock is mainly a coarse agglomerate,' with lapilli and bombs of basalt and limestone; while the remaining 100 yards or so is an ordinary basalt-coulée, with very few and always small lumps of burnt limestone. The limestone below is reddened and altered, and although tuffy-looking, does not contain indubitable lapilli; the limestone above contains lapilli. The pillowy basalt probably represents a river of agglomeratic material carrying finer lapilli, larger and plastic masses of scoriaceous basalt, and lumps of limestone, possibly ejected from a vent. The intervening tuff may present an analogy with the volcanic sand' of the West Indian eruptions. There is no evidence of the quiet deposition of ashy material, but rather of the tumultuous aggregation of a fluxion-tuff taking place under some depth of sea-water. The large and irregular fragments of limestone, oolitic and fossiliferous, found mainly in the lower part of the basalt-mass, have not come in from above through cracks in the lava, but seem to have been picked up while in a soft and powdery state from the sea-bed in which it had been accumulating, and to have been involved with and altered by the volcanic material. The conditions existing in submarine flows appear to be very like those in a sill or intrusive sheet.

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February 3rd.-Sir Archibald Geikie, D.C.L., D.Sc., Sec.R.S., Vice-President, in the Chair.

The following communications were read:—

1. On a Deep-Sea Deposit from an Artesian Boring at Kilacheri, near Madras.' By Prof. H. Narayana Rau, M.A., F.G.S.

The village of Kilacheri is about 6 miles due south of the railway-station of Kadambattur. Here permeable beds of sandstone and felspathic grits dip at low angles seaward, and are overlain by impervious clays and shales. The boring, after penetrating the upper clays and sandstones, passed through carbonaceous shales, and at a depth of about 400 feet reached a blue homogeneous rock, effervescing with acid and showing radiolarian tests under the microscope. Most of the latter display the inner

reticulate structure in thin sections, and some of them, when isolated, show radiating spines as well; they are, however, not capable of specific determination. One or two specimens of foraminifera have also been seen. The deposit underlies beds of the Upper Gondwána Stage. The bed also contains palagonite, volcanic glass, pumice, mineral-fragments (such as plagioclase, quartz, augite, and possibly hornblende), and black metallic spherules of iron and manganese. The last sometimes partly fill the radiolarian tests, and sometimes encrust the pumice and palagonite; they give the manganese-reaction with a borax-bead. The author concludes that the deposit is of truly abysmal origin, similar to those described in the Challenger Reports; and he points out the remarkable interest of such an occurrence in Peninsular India, a region which appears to have been a land-area since Palæozoic times.

2. The Rhætic Beds of the South-Wales Direct Line.' By Prof. Sidney Hugh Reynolds, M.A., F.G.S., and Arthur Vaughan, Esq., B.A., B.Sc., F.G.S.

After a reference to the literature of the subject the following exposures are described: the Stoke-Gifford and the Lilliput or Chipping-Sodbury sections. From the first section the Bone-Bed is completely absent. The beds here rest upon tea-green marl, and are covered by the Cotham Marble. A section to the east of Lilliput Bridge shows two large rounded hummocks of Palæozoic rock projecting into the Rhætic, and in both cases the Black Shale is deposited on it in an arched manner, forming an anticline of deposition. There is also a very rich Bone-Bed at the base, which is not uniformly distributed. The upper beds correspond with those of Stoke Gifford. In correlating these rocks with those of neighbouring areas, a table of general sequence is given, in which the Lower Rhætic is divided into three and the Upper into two stages, which are correlated with the notation of Richardson and Wilson. This is followed by a range-table of the typical Rhætic mollusca: Cardium rhæticum and C. cloacinum, Schizodus Ewaldi, Pecten valoniensis, and Avicula contorta. Palæontological notes on the invertebrata and vertebrata follow. New species of Anomia, Plicatula, Modiola, and Cardinia are described; notice is given of other Rhætic mollusca; and a range-table is appended of the commonest mollusca that occur at Sodbury and Stoke Gifford. The reptiles, amphibia, and fishes referred to are all known species. A general account is given of the distribution of the Bone-Bed in the Bristol district. In Somerset, except at Emborough and Watchet, no true Bone-Bed has been recorded; in the district immediately north of Bristol there is a single, well-marked BoneBed at the base of the Black-Shale Series, or very slightly above it; while in the Gloucester district the principal Bone-Bed tends to lie at a greater distance from the base of the Black Shales. For these reasons, the authors think that the principal Bone-Beds in the various sections cannot be regarded as homotaxial equivalents.

IT

XXXVI. Intelligence and Miscellaneous Articles.

NOTE ON "." BY R. CHARTRES.

T could be easily shown that if two numbers are written down at random the probability that they will be prime to each

other =

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This affords a simple and interesting method of obtaining an approximate value of .

Having asked three friends to write down at random five pairs of numbers, I found in each case three pairs out of the five were 6 3

prime to each other, giving

= or 2=10.
9
5
π

2

I did the same with fifty students with the following result:6 sets of five pairs had only one pair prime to each other

9

16

13 6

Total 50

two pairs

three

De Morgan obtained a very fair approximation by using Buffon's Problem, that if a needle be allowed to fall on a plane ruled surface, the probability of the needle cutting one of the lines twice the length of the needle

times the distance between the lines

OBITUARY NOTICE: DR. WILLIAM FRANCIS.

DR. WILLIAM FRANCIS was born in London on the 16th of February, 1817. He was educated at University College School and St. Omer. He left St. Omer in 1834 and proceeded to Crefelt, but in the autumn of the same year went to Gera, where he remained for about two years. In 1836 he returned to England and spent a year at the London University (University College), afterwards devoting some time to learning the printing business under Mr. Richard Taylor, to whom he had been apprenticed some time previously. He then went to Berlin, and thence to Giessen, where he studied under Liebig, and did much original work, chiefly on the salts of molybdenum. He took his degree of Doctor of Philosophy at Giessen in 1842.

He early developed a taste for Natural History, and during his stay at Gera he devoted much of his time to entomological study and pursuits. While in England, in 1837, "fresh from the teachings of Ehrenberg, and profoundly influenced by the spirit of scientific research which then, as now, prevailed in Germany," he "suggested to Mr. Richard Taylor the establishment of a journal

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in which, while its pages were freely open to the original contributions of English naturalists, special attention should be paid to the researches of Continental observers; and the result was the starting of the Annals of Natural History,' with which, subsequently, the well-known Magazine of Natural History' of Loudon and Charlesworth was amalgamated." His name first appears on the wrapper as co-editor in 1859. As Editor of the Annals' he became acquainted with most of the leading naturalists, and made many life-long friends, his indebtedness to whom he warmly acknowledges in the Preface to the Sixth Series.

While in Berlin and Giessen, Dr. Francis, in conjunction with his friend and fellow-student Henry Croft, forwarded every month a series of reports to the 'Philosophical Magazine' on the progress of chemical science on the Continent; but the space available in that Journal being limited, they, on their return to England, started the Chemical Gazette' in 1842. Croft was compelled to relinquish the editorship before the fourth number appeared, being appointed Professor of Chemistry at King's College, Toronto; and the Gazette' was carried on by Dr. Francis alone until 1859, when the pressure of other work compelled him to relinquish the task, and the 'Gazette' was incorporated with the then newly founded Chemical News.'

In addition to furnishing translations of foreign scientific papers to the Philosophical Magazine,' he also translated many papers for Taylor's Scientific Memoirs,' in the conducting of which, moreover, he had a very large share, although his name did not appear on the titlepage. He also translated Beckmann's History of Inventions' for Bohn's Scientific Series.

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In 1851 his services to the Philosophical Magazine' over many years, both in furnishing translations and in conducting the Journal, were acknowledged by the appearance of his name on the wrapper as co-editor, where it remained until his death. During the whole period of fifty-three years he took an active part in the management of the Magazine. His acquaintance and, in many cases, warm personal friendship with scientific men both in Great Britain and on the Continent, his sound judgment, and tact made his services in this capacity invaluable.

In 1841 he was elected Associate of the Chemical Society, becoming a Fellow in the following year. He was also a Fellow of the Linnean Society (1844), of the Royal Astronomical (1851), of the Geological (1859), and of the Physical (1876).

In 1852 he joined Mr. Richard Taylor as partner in the firm of Taylor and Francis, printers and publishers. He was one of the oldest members of the Stationers' Company, having taken the Livery in 1841.

In 1862 he married Isabella Gray, daughter of Mr. Taunton, M.R.C.S., of Hatton Garden, but became a widower in 1899. For some few years previous to his marriage Dr. Francis had lived at Richmond, and for the rest of his life continued to reside there for the last thirty-one years at the Manor House, where he died on the 19th of January last.