offered a second £1000 towards the fitting up and equipment of the laboratories, contingent on the friends of the College contributing an equal amount. We purpose shortly giving an account and plans of these laboratories.

MORE than a quarter of a century has passed since it was decided that the Entomologist's Monthly Magazine should be started. The editors have now resolved to issue a new series, each volume of which will begin in January and end in December. There will be no radical change in the constitution of the magazine, but the number of pages and illustrations will often be increased.

THE result of the poll for a free library at Whitechapel, declared last Saturday night, is interesting and significant. On a register of 6000, there were 3553 affirmative votes and only 935 dissentients. This is the more noteworthy, because about eleven years ago a like proposal was rejected by a majority of

about two to one.

THE following science lectures will be given at the Royal Victoria Hall during January: January 7, "A Visit to the Chief Cities of Italy," by Rev. W. W. Edwards; January 14, "The Bottom of the Sea," by Dr. P. H. Carpenter; January 21, "To Vancouver's Island and back," by Mr. W. L. Carpenter; January 28, "Musical Sounds and how we hear them," by Dr. F. W. Mott.

A SECOND edition of Sir William Aitken's "Animal Alkaloids" (H. K. Lewis) has been published. The work has been carefully revised, and the author's aim has been to bring the book up to the present state of knowledge regarding the important subject to which it relates.

THE first part of a monograph of Oriental Cicadida, by W. L. Distant, has been published by order of the Trustees of the Indian Museum, Calcutta. It is printed in clear type, and includes two fine plates. The monograph, when completed, will evidently be of much scientific value.

M. VAYSSIÈRE has now completed the publication of his "Atlas d'Anatomie Comparée des Invertébrés." It comprises sixty plates, with corresponding letterpress, and is much appreciated by French zoologists.

THE Proceedings and Transactions of the International Agricultural Congress held in Paris last summer have just been issued. A REUTER'S telegram from Madrid says that a shock of earthquake was felt at Granada on the evening of December 16. There was great alarm for the moment, and the people rushed in panic out of the theatre, where a performance was going on at the time. Apparently no damage was done.

THE Pilot Chart of the North Atlantic Ocean for December states that stormy weather has been prevalent during the month of November. Two notable cyclones have occurred; the first moved eastward from Chesapeake Bay on the night of the 9th. On the 11th it was central in about latitude 41° N., longitude 57° W.; and from this position it moved nearly due north-east, and rapidly increased in energy. The other cyclone moved eastward from the New Jersey coast on the 13th, and was central on the 14th in latitude 42° 40' N., longitude 63° 20′ W. This storm attained great violence during the 14th and 15th. After the 16th, gales of varying force occurred along the coast north of Florida. There was very little fog during the month; a dense bank was reported on the 17th on the north coast of Cuba. A number of icebergs are still reported in the vicinity of Belle Isle, and several smaller bergs have been seen over the Newfoundland Banks.

AT the meeting of the French Meteorological Society on November 5, M. Teisserenc de Bort gave an account of his researches on barometric gradients. He distinguished two kinds of gradients, one due to the differences of temperature, and another

1

due to the earth's rotation, and pointed out that these two gradients are always superposed, and that their distinction was a matter of importance, for if the first case predominates (a gradient due to difference of temperature), the wind force may increase and the depression become deeper, while in the second case the depression tends to disappear. He thought it was not impossible to make this distinction, for if we know the force of the wind we might calculate the moment of inertia and the corresponding gradient. He also presented a work on the distri bution of atmospheric pressure over the surface of the globe. He showed that the distribution of pressure over different meridians varies upwards of an inch on the same parallel according to the season. With the view of finding out the arrangement of the isobars in higher regions of the atmosphere, the author has calculated the pressures by formulæ at various heights, from the pressure and temperature observed at the earth's surface, and compared their accuracy by the readings at some mountain stations, and he has found that most of the irregularities in the distribution of the isobars tend to disappear as we reach the higher regions of the air, and to be replaced by inflexions in the opposite sense. A summary of this paper will be found in the Comptes rendus of the French Academy for December 2.

AT a meeting of the Linnean Society of New South Wales on October 30, Mr. A. Sidney Olliff called attention to the extraordinary abundance of a large Noctuid moth—apparently Agrotis spina, Gu. (A. vastator, Sc.)-during the early part of October in various parts of the country, especially in the vicinity of Sydney, where it appeared in such vast numbers as to cause great consternation amongst those who were not aware that its food in the larval state is confined to low-growing herbage, and that at no stage of its existence does it eat cloth, furs, or feathers. A similar visitation of these moths occurred in October 1867. Mr. Olliff said that Agrotis spina was found in great numbers on the summit of Mount Kosciusko and other high points in the Australian Alps, and added that he was of opinion, after extended inquiry, that this species, and no other, was the true Bugong moth, which formerly formed an important article of food amongst the blacks of the Upper Tumut district.

MR. THOMAS CORNISH, Penzance, recently recorded in Th Zoologist the occurrence of the "Old English" or "Black" Rat, captured at a place about five miles north-east of Penzance. In the current number of the same periodical he says that immediately after that capture a perfectly trustworthy observer saw near Cambourne, at a place ten miles south-east from where the first specimen was obtained, a Black Rat, which was certainly not the ordinary Hanoverian Rat; and at a later time Mr. Cornish saw and handled another specimen, captured in Paul Parish, about three miles south-west of Penzance. "These facts," says Mr. Cornish, "apparently point to an incursion of this animal, which is gregarious certainly, and probably a vagrant in herds, but not a migrant."

MR. J. R. DOBBINS, San Gabriel, California, contributes to the new number of Insect Life (vol. ii. No. 4) a note on the spread of the Australian ladybird. The note is dated July 2, 1889. At that time the Vedolia had multiplied in numbers, and had spread so rapidly that every one of Mr. Dobbins's 3200 orchard trees was literally swarming with them. All his ornamental trees, shrubs, and vines which had been infested with white scale were practically cleansed by this wonderful parasite. "About one month since," says Mr. Dobbins, "I made a public statement that my orchard would be free from Icerya by November 1,' but the work has gone on with such amazing speed and thoroughness, that I am to-day confident that the pest will have been exterminated from my trees by the middle of August. People are coming here daily, and by placing infested branches upon the ground beneath my trees for two hours, can secure

colonies of thousands of the Vedolia, which are there in countless numbers sucking food. Over 50,000 have been taken away to other orchards during the present week, and there are millions still remaining, and I have distributed a total of 63,000 since June I. I have a list of 130 names of persons who have taken the colonies, and as they have been placed in orchards extending from South Pasadena to Azusa, over a belt of country ten miles long and six or seven in width, I feel positive, from my own experience, that the entire valley wiil be practically free from Icerya before the advent of the new year."

COCOA-NUT butter is now being made at Mannheim, and, according to the American Consul there, the demand for it is steadily increasing. The method of manufacture was discovered by Dr. Schlunk, a practical chemist at Ludwigshafen. Liebig

and Fresenius knew the value of cocoa-nut oil or fat, but did not succeed in producing it as a substitute for butter. The new butter is of a clear whitish colour, melts at from 26° to 28° C., and contains o'0008 per cent. water, o'006 per cent. mineral stuffs, and 99'9932 per cent. fat. At present it is chiefly used in hospitals and other State institutions, but it is also rapidly finding its way into houses or homes where people are too poor to buy butter. The working classes are taking to it instead of the oleomargarines against which so much has been said during the last two or three years.

A POINT of great importance for the progress of Western science in the Chinese Empire is whether it should be taught in the Chinese or in a foreign language. The subject has been frequently discussed, and quite recently the opinions of a large number of men most prominently engaged in the education of Chinese were collected and published in a Shanghai magazine, the Chinese Recorder. The editor says that nine-tenths of these authorities are of opinion that the Chinese language is sufficient for al purposes in teaching Western science. One gentleman states that Chinese students can only be taught science in their own language, and that the long time necessary for them to acquire English for this purpose is wasted; another says that "science must be planted in the Chinese language in order to its permanent growth and development"; a third sees no reason why the vernacular should not be enough to allow the Chinese student to attain the very highest proficiency in Western science, although he admits that there is at present a want of teachers and text-books. Prof. Oliver, of the Imperial University at Pekin, says he has never found English necessary, but has always taught in Chinese. Prof. Russell, of the same institution, finds Chinese sufficient for popular astronomy. On the other hand, Mr. Tenney says that it can only be for the most popular views of science that the vernacular is sufficient. "It is impossible," he says, "for scholars who are ignorant of any European language to attain any such excellence in modern sciences as to enable them to bear comparison with the finished mathematical and scientific scholars of Europe and America." Thus, he continues, as a medium of thought, any Western language is incomparably superior to Chinese in precision and clearness; the student acquainted with a foreign language has a vast field of collateral thought open to him which does not and never will exist in Chinese, and he can keep abreast of the times, which the Chinese student who must depend on translations cannot do. relation of the Chinese student "to the world of thought is analogous to that of a blind and deaf person in the West, whose only sources of knowledge are the few and slowly increasing volumes of raised type letters which make up the libraries of the blind." As has been said, however, the weight of opinion is against Mr. Tenney.

The

IN a recent number of Humboldt, Herr Fischer-Sigwart describes the ways of a snake, Tropidonotus tessellatus, which he kept in his terrarium in Zurich. It was fond of basking in the

sun on the top of a laurel, from which it climbed easily to a high cherry-tree fixed against a wall, its night quarters. Sometimes, after lying still for hours, it would hasten down into a snall pond (about 4 square yards surface) containing gold-fish, and hide itself for a long time, quite under water, behind some stone, or plants, the tongue constantly playing. When a fish came near, the snake would make a dart at its belly. Often missing, it would lose patience, and swim after the fishes, driving them into some corner, where it at length seized one in the middle of the belly, and carried it to land, much as a dog would a piece of wood. Curiously, the fish, after being seized, became quite still and stiff, as if dead. If one then liberated it, the skin of the belly was seen to be quite uninjured, and the fish readily swam away in the water. The author thinks the snake has a hypnotic influence on its prey (and he had observed similar effects with a ringed snake). It would otherwise be very difficult for the snake to retain hold of a wriggling fish. The snake usually carried off the fish some distance to a safe corner, to devour it in peace.

A SPLENDID find of minerals containing the rare metals of the yttrium and thorium groups has been made in Llano County, Texas (Amer. Journ. of Science, December 1889). The whole district for many miles round consists almost entirely of Archæan rocks, granite being met with everywhere, and forming the common wayside rock. Throughout the granite are dispersed veins of quartz, and it is in these veins, and especially the swellings of the veins, that large masses of rare minerals have been found. The largest of these deposits consist of gadolinite and fergusonite, and of two entirely new minerals, to which the names yttrialite and thoro-gummite have been given. The first discovery of gadolinite in Texas was made in 1886, when a pocket of huge crystals and masses aggregating to about 500 kilogrammes was unearthed. Since that time a more complete prospection of the district has revealed the existence of still larger quantities. The gadolinite is generally found in small lumps weighing about half a pound, but frequently also in much heavier masses, and sometimes in immense crystals. One double crystal was found weighing 42 pounds, and a still larger single crystal weighed no less than 60 pounds. And these immense crystals actually contain over 50 per cent: of oxides of the yttrium metals, as do also the massive varieties. The crust of the gadolinite crystals, which appear to be of monoclinic habit, was generally altered into a brownish-red hydrate of waxy lustre ; but occa sionally, as in case of two particular specimens, the crystals were found in a state of rare beauty and perfection. The new mineral yttrialite, a thorium-yttrium silicate, was discovered associated with and often upon the gadolinite. It was generally altered at the surface to an orange-yellow hydrate of quite different structure to that of the hydrate of gadolinite. One mass of this incrustation was found to weigh over 10 pounds. It contains 46 per cent. of oxides of the yttrium metals. Fergusonite, hitherto an exccedingly rare mineral, occurs in large quantities in the Llano County district, generally in the form of broken interlacing prisms several inches long. Two varieties of it have been identified-one a monohydrated and the other a trihydrated variety. The monohydrated kind forms tetragonal prisms with acute pyramidal terminations, of dull gray exterior, but possessing a brilliant bronze-like fracture. It contains 42 per cent. of yttrium earths and 46 per cent. of columbic acid, Cb2O5. The trihydrated variety is similar, but of a dark brown colour. Associated with the fergusonite is the new mineral thoro-gummite, a hydrated uranium thoro-silicate. This mineral is frequently found in well-developed crystals resembling, and having angles very nearly the same as, those of zircon. It contains 22 per cent. of UO3, 41 per cent. of ThO, and 6 per cent. of yttrium earths. Its probable essential composition is UO,. 3ThO,. 3SiO ̧ . 6H2O. Besides these four minerals of special interest to chemists, many more-such as

cyrtolite, molybdite, allanite, tengerite, and a new hydrated thorium-yttrium-lead uranate, termed nivenite-have been found. Altogether, this is the richest find of rare earths which has been heard of for some time, and will probably exert a fresh impetus upon the attempts to set our knowledge of the rare-earth elements upon a surer foundation.

THE additions to the Zoological Society's Gardens during the past week include a Ring-tailed Coati (Nasua rufa 8) from South America, presented by Mrs. Petre; a Common Squirrel (Sciurus vulgaris), British, presented by Mrs. S. Stutterd; a Short-eared Owl (Asio brachyotus) from Hampshire, presented by Mr. E. Hart, F.Z.S.; two Owen's Apteryx (Apteryx oweni) from New Zealand, presented by Captain C. A. Findlay, R. N. R., R.M.S.S. Ruapehu; four Common Vipers (Vipera berus) from Hampshire, presented by Mr. W. H. B. Pain; a Marsh Ichneumon (Herpestes galera) from South Africa, purchased; a Troupial (Xanthosomus frontalis) from Brazil, received in exchange.

(1) This is described in the General Catalogue as "a globular cluster, very bright, small, round, very suddenly brighter in the middle, barely resolvable (mottled as if with stars)." In 1864 Dr. Huggins observed the spectrum, and noted that it was apparently continuous, extending from the orange to the blue, without any traces of either bright or dark lines. It was again observed by Winlock at Harvard College in December 1868, and, strange to say, a bright line spectrum was recorded. "Two distinct bright lines, near each other, and coincident with airlines A 5020 ± and λ 4990; a third faint line λ 4900 ±" ("Harvard College Observations," vol. xiii. Part 1, p. 64). These lines were in all probability the three ordinary nebula lines near λ 500; 495, and 486. Winlock describes the nebula as planetary, and gives exactly the same co-ordinates as those given by Huggins and in the General Catalogue. If both observers really saw the same nebula, the results are highly suggestive of variability; but even then there is the difficulty of the recorded resolvability. It is quite possible that, in the four years which elapsed between the observations, the spectrum changed from an apparently continuous one to a discontinuous spectrum, by some action similar to that producing variability in such stars as Mira, but at the same time a change of brightness would also be expected, and of this there is no record. In any case, the nebula is well worthy of further examination.

(2) This star of Group II. is interesting, as being a connecting-link between stars like a Herculis, in which the bands are very wide and dark, and those like Aldebaran, in which there is a line spectrum with only the remnants of the bands in the red. Dunér states that the bands 2-8 are visible, but all of them are narrow and pale. b, and presumably D, are very strong. Further observations, with special reference to the lines of hydrogen, are suggested.

(3) A star, hitherto described as of the solar type, of which the usual observations are required. If the star appears to be of the same type of the sun or Capella, special attention should be directed to the presence or absence of dark carbon flutings. It is highly probable that stars like the sun, in which there is a photographic indication of carbon absorption, will subsequently cool down and become stars of Group VI., in which carbon

absorption is predominant. If this be the case, all the intermediate stages of mixed metallic lines and dark carbon flutings should be represented amongst the stars.

(4) A star of Group IV., of which the usual observations are required.

(5) This is a star of Group VI. The three ordinary bands of carbon are visible, band 6, near λ 564, being rather pale. A study of Dunér's catalogue of the stars of this group shows that some of those in which band 6 is pale give secondary bands, whilst others do not. This appears to be mainly, though not entirely, due to differences of magnitude. Comparative observations with the same telescope and spectroscope, with reference to this point, are suggested.

(6) Gore states the period of this variable as 378 days, and the magnitudes at maximum and minimum as 99 and < 13 respectively. The colour is described as trifling, but the spectrum has not yet been recorded. The maximum will occur on December 28. A. FOWLER.

PERIOD OF U CORONE.-Mr. S. C. Chandler (Astronomical Journal, No. 205), from the observations of the period of this star, finds an inequality of the same order as those detected in U Ophiuchi and U Cephei, variables of the Algol type. The period appears to be shortening by 0'0036s. from minimum to minimum. The results depend upon forty-five very unequally distributed minima; thirty-eight, however, lie in the interval 1870-74, and afford a basis to work upon. A larger series of observations is required to elucidate Mr. Chandler's hypothesis, which, however, is quite conformable within the limits of the purely accidental errors of the observations that have been investigated.

IDENTITY OF BROOKS'S COMET (d 1889) WITH LEXELL'S COMET 1770. In the same publication as the above, Mr. Chandler gives some most interesting results of an investigation into the orbits of these comets. The following is a summary of the principal conclusions:

(1) The encounter of the comet with Jupiter in 1886 effected Instead of the a complete transformation of the comet's orbit. present seven years' ellipse, it was previously moving in a large one of twenty-seven years' period.

(2) Several months before reaching its perihelion, it passed, tion, and was deflected into a hyperbolic path about that planet, near the beginning of 1886, into the sphere of Jupiter's attracsatellite of Jupiter. and narrowly escaped being drawn into a closed orbit, as a

(3) At the point of closest approach to Jupiter, May 20, 1886, planet, passing a little outside of the orbit of the third satellite. the comet was distant from it only about nine diameters of the

(4) In 1779, and not before, the comet must have come so near to Jupiter as to pass under his control and experience a radical change of orbit at the point of longitude where Lexell's comet underwent its notable disturbance in that year. Moreever, the elements of Lexell's comet before the disturbance were

strikingly similar to those found for the present comet previous

to 1886.

Taking all the points presented into consideration, the argument for the identity of the two comets is overwhelming. A fuller investigation will be made as soon as the observations for the whole apparition have been received.

SOME PHOTOGRAPHIC STAR SPECTRA.-An examination has been made by Dr. Scheiner of the star spectra photographed at Potsdam (Astr. Nachr., No. 2923). The wave-lengths of lines in the spectra were determined by comparison with the solar spectrum, and as the probable error of the measures is estimated so small as o 005, the identification of the lines seems beyond doubt. The following are some descriptive results :

Cassiopeia. Continuous spectrum; hydrogen lines and D.

bright.

a Corona. The magnesium line at 448 2 appears as a broad line in this star.

a Lyra. Some fine lines, supposed to be due to iron or calcium, are seen, but have not been measured.

Sirius. 91 similar fine lines to those in the above star have been measured, and 43 ascribed to iron. Even more of these lines occur in Procyon.

a Aquila. The spectrum of this star appears almost identical with that of the sun.

B Orionis. The hydrogen and other lines appear broad, but are not diffused at the edges as in a Lyræ and similar stars. 20 lines have been measured from A 400 to A 460.

a Auriga. 291 lines have been measured in the spectrum of this star between λ 410 and λ 470, all of which appear identical with solar lines.

MAGNITUDE AND COLOUR OF ARGÛS.-Observations of this variable have been made at Cordoba since 1871, and some comparisons made by Mr. Thome (Astr. Nachr, No. 2922) show that it steadily decreased in magnitude until about the end of 1886, when a minimum of 765 was reached, and it is now about 66. In 1843, Maclear gave the brightness of 7 Argûs as 10, or between that of Sirius and Canopus, so that the variation in magnitude is 8.5, and not 6 as heretofore assumed, this variation, extending over 44 years, gives an average yearly

It will be seen from the foregoing period, that the comet will be at perihelion again in 1890 January 9.87.

ALGOL.-At the meeting of the Royal Prussian Academy of Sciences, held on November 28, Prof. Vogel gave the results he had obtained from photographs of the spectrum of this variable. Prof. Pickering had pointed out, some years ago, that if the variation in stars of the Algol class were due to the transit of a dark satellite across the disk of its primary, producing a partial eclipse, then since in every case yet known the two bodies must be close to each other, and of not very disproportionate size, the primary must revolve with very considerable rapidity in an orbit round the common centre of gravity of the two; and, therefore, be sometimes approaching the earth with great rapidity and sometimes receding from it. Six photographs of the spectrum of Algol-obtained, three during last winter, and three during the November just past-have shown that before the minimum the lines of the spectrum of Algol are markedly displaced towards the red, showing a motion of recession; but that after the minimum the displacement is towards the blue, showing a motion of approach. Assuming a circular orbit for the star, and combining the details given by the spectroscope with the known variation of the star's light, Prof. Vogel derives the following elements for the system of Algol :

It will be seen that the density both of Algol and its companion is much less than that of the sun-less than a quarter, in fact. This is what we might expect, for Algol and all the variables of its class yet examined give spectra of Group IV., and should therefore represent a less advanced stage of condensation than that seen in our sun. This demonstration of the truth of the satellite theory of variation of the Algol type derives also an especial interest from Prof. Darwin's researches on tidal evolution, for assuming, as we well may, that the cause of variation is the same in all members of the class, we now know of nine stars in which a large companion is revolving round its primary at but a very short distance from it, and in a very short space of time. The companion of U Ophiuchi must, indeed, be almost in contact with its parent star.

GEOGRAPHICAL NOTES.

WE regret to have to record the death of Major Peter Egerton Warburton, whose name will always be intimately associated with the history of exploration in Australia. He died at Beaumont, Adelaide, in his seventy-sixth year. His most famous achievement, undertaken in 1873, was the crossing of the continent from a point on the overland telegraphic line to the De Grey River, in Western Australia. Nothing was heard of him for about twelve months, during which he and his party suffered terrible privations in their march across the desert. After the expedi tion, Major Warburton visited England, and was awarded a Gold Medal of the Royal Geographical Society for his efforts towards increasing our knowledge of the interior of Australia. He received the Companionship of the Order of St. Michael and St. George in 1875.

THE death is announced of Cardinal G. Massaja in his eightyfirst year, at St. Georgio a Cremano. For nearly half a century the name of this distinguished explorer has been intimately associated with the progress of geographical discoveries in Abys sinia and the surrounding regions. It was at his suggestion that the Italian Geographical Society organized the Antinori Expedi tion to Shoa, which has resulted in the occupation of a vast region, and the extension of Italian influence over the whole of Ethiopia. His chief work, "I miei trentacinque Anni nell' alta Etiopia," abounds in valuable geographical, historical, and ethnological information on the East African regions for so many years explored and studied by him. The Cardinal was born at Piovà in 1809, and, in 1846, appointed Vicar Apostolic of the Galla nation.

FROM the Berlin Correspondent of the Daily News we learn that a full account of the ascent of Kilimanjaro by Dr. Hans Meyer and Prof. Purtscheller has been received at Berlin. It is dated "Marangu Jagga, October 9." The journey from Zanzibar to Uawela took exactly a fortnight. On September 25 the travellers reached Marangu. On October 2 they encamped, with a Pangani negro, on the ridge of the plateau, at a height of 14,450 feet. At 2.30 a.m. they started for the lava-ribs surrounding the valley of glaciers to the south about 1200 feet above. At 7 o'clock, on the right side of the valley, at an elevation of about 16,500 feet, the first snow was seen under cover of the rocks. The higher they went, the more clefts and fissures the field of ice had. The travellers say :-" After great exertions we reached, at 1.45, the snow-line, and it was seen that the highest peak, which was formed of rocks jutting out of the snow, was about one and a half hour's march to the left. After resting a day and a half we set off, on October 5, to bivouac in the Lava Cave, at a height of about 15,200 feet, and on the next day we repeated the ascent. The peaks were gained without particular difficulty, and on the central and highest one, 19,680 feet above the sea, the German flag was planted." Dr. Meyer proposes to call this peak Kaiser Wilhelm Peak. The view from here on to the Kibbs Crater-which is 6600 feet broad and 660 feet high, and the lower half of which is encased in a mighty belt of ice, whilst a volcanic cone of about 500 feet rises in the centre-is magnificent. The beauties of the landscape in the Kilimanjaro region seem to be quite extraordinary. On October 10 the Kimawensi was to be ascended. The two travellers enjoy the best of health.

THE double number of the Bollettino of the Italian Geographical Society for October and November, which appears some weeks behind time, is largely devoted to African subjects, and more particularly to the north-eastern region, which is rapidly becoming an "Italian colony." Captain D. Stasio publishes a summary of Don Francesco Alvarez's "Travels in Ethiopia" in the sixteenth century, enriched with valuable notes and additions. Alvarez, a priest attached to an embassy forwarded by Portugal, in 1520, to the Emperor of Abyssinia, shows himself a careful observer of men and things, and his work, which was included in Ramusio's "Navigationi et Viaggi" (Venice, 1588), abounds in details regarding the political, social, and economic relations of that region in the sixteenth century. Giulio D. Cocorda brings to a conclusion his important series of papers

on the South African gold-fields, which include much information on the present condition of the whole of South Africa as far north as the Zambesi. The observer points out that, while the Delagoa Bay and other lines of communication are much discussed, the fine artery of the perfectly navigable Limpopo is entirely neglected, notwithstanding Captain Chaddock's navigation of it a few years ago. The writer remarks that "this river flows mainly through regions under the influence or protectorate of England; the Transvaal people on the one side, and those of Matabeleland on the other, would certainly be glad to avail themselves of this outlet for their produce. As it traverses only a small tract of Portuguese territory about its estuary, I hope and believe that Portugal will not be allowed to treat the Limpopo as she is now attempting to treat the Zambesi. The subject is of such importance that it cannot fail soon to be brought before the British Parliament." Referring to the negotiations at present going on in connection with the Swaziland question, he observes, in the same spirit:-"The Swazi people must, sooner or later, yield either to the Transvaal or to England, and if to the former, it must be to the entire detriment of British interests. England, as the suzerain power in South Africa, should be the first in the field, both in her own interest and in that of her other colonies and subjects. If she does not assume the protectorate of Swaziland, besides losing the control of a vast and rich mineral district, she will deprive the colony of Natal of all further hope of expansion. If she ignores her responsibility in this matter, and allows the Transvaal Republic to absorb Swaziland, she will add another to the long list of blunders that threaten to destroy all prospect of consolidating a dominion as large as Canada, and may end disastrously for British interests in South Africa.'

A FRENCH traveller has just achieved a feat of great interest. Captain Trivier, equipped by the newspaper La Gironde, started some eighteen months ago for the Congo State. He went up the river to Stanley Falls, and thence proceeded to Central Africa and the Lake region, accompanying caravans. He has just arrived at Mozambique.

The

Globus reports that during the past summer M. Thoroddsen, the well known student of Iceland, has carried out a journey in the waste region known as Fiskivötn, lying between Hecla and the Vatna Jökul, which has hitherto been unvisited for the most part by any inquirer. To the east and north of Hecla he discovered a new obsidian region. Crossing the Tunguaa, he went to the Fiskivötn group of lakes, all true crater lakes. district between this and the Vatna Jökul has absolutely no plant-life whatever; it consists of lava-fields, and plains of volcanic sand. In it he found a lake, Thorisvatn, the second largest in the island. Thence, after a day's journey through an utterly desolate district, he reached the hitherto unknown source of the Tunguaa. To the south of this he discovered, between three ranges of hills, previously unknown, a new and very long lake.

MR. DAUVERGNE has, says the Times of India, completed an adventurous journey in the regions of North-West Cashmere. His course was from Leh northwards to the Kilian Pass, in Kashgaria, and then northwards across the Pamir to the Upper Oxus. He reached Sarhad in safety, and after six days' halt there, crossed the Hindu Kush by the Baroghil Pass, as he did not wish to visit Chitral. He then turned eastwards, and after a trying journey through the snow, crossed the Ishkaman Pass, north of Yasin. Thence he travelled southwards by the Karambar Valley, and eventually reached Gilgit, a short time after Captain Durand had started for Chitral. Mr. Dauvergne reports that the Russian explorer, Captain Grombc hevsky, whose attempt to reach Kafiristan was noticed some time ago, was stopped at Kila Panjah on the Oxus, by the Afghan

authorities.

THE ST. PetersburG PROBLEM. THIS celebrated problem, which is first mentioned before 1708 in a letter from the younger Nicholas Bernoulli to Montmort, has been frequently discussed by Daniel Bernoulli | (1730) and other eminent mathematicians. It may be briefly stated as follows:

A tosses a coin, and undertakes to pay B a florin if head comes up at the first throw, two florins if it comes up at the second, four florins if it be deferred until the third throw, and so What is the value of B's expectation?

on.

The chance of head appearing at the

Ist, 2nd, 3rd, 4th 1, 1,

I, 2, 4, 8

2,

nth throw is

1". A promises to pay for head

I

2- florins, hence B's expectation is 2"-1/2" = florin.

Hence the total value of B's expectation is an infinite series, each term of which is a shilling, or it is infinite.

This result of the theory of probability is apparently directly opposed to the dictates of common-sense, since it is supposed that no one would give even a large finite sum, such as £50, for the prospect above defined.

Almost all mathematical writers on probability have allowed the force of the objection, which they have endeavoured to evade by various ingenious artifices all more or less unsatisfactory. The real difficulty of the problem seems to lie in the exact meaning of infinite and value of the expectation.

Since the infinite value of the result is only true if an infinite number of trials are paid for and made, all such considerations as want of time and the bankruptcy of A or B are precluded by the terms of the question.

The value of B's expectation is frequently confused with how much he can or ought to pay for it; thus Mr. Whitworth ("Choice and Chance," p. 234) finds that if B have 1024 florins, he may give very little more than 6 florins for the venture. This ingenious, solution seems to have no reference to the original problem, which has been modified by Mr. Whitworth's introduction of the word "advantageously " (p. 232).

B can pay for his expectation in three ways: (i.) a sum before each toss; (ii.) a sum before each series of tosses ending with head; (iii.) a sum for the total result of A's operations.

Mr. Whitworth apparently assumes the first method of pay ment, and shows that the larger B's funds are the more he may safely pay for each toss, since he can continue to play longer. Many mathematicians take the second method of payment. "However large a fee I pay for each of these sets, I shall be sure to make it up in time" ("Logic of Chance," p. 155).

It is easy to show in this case also that what may be safely paid before each series increases with the number of series.

Suppose a very large number of tosses made, about half would come up heads and half tails; each head would end a series, when a fresh payment must be made by B. Suppose the tosses limited to one series, if B pays one florin he cannot possibly lose, if he pay anything more he may lose by head coming up the first time, and the more he pays the greater will his chance of loss be, since the series of tails must be longer to cover it. But, however large a finite sum he pays, he is not certain to lose, e.g. head may not come up till the hundred and first toss, when he would receive 2100 = = 1,267 650,600 228,229 401,496 703,205 376 florins. If the sets are limited to one hundred, about 50 heads would probably come up the 1st toss.