which gives rise to the phenomenon in question. Smith contrived, with profound ability, to account for and calculate the beat independently of the Tartini beat, or whatever it may be called, but the introduction of this by De Morgan has wonderfully simplified the comprehension of the thing.

The accurate rule for finding how many beats per second will result from the concord being any given quantity out of tune; or for finding how much out of tune any concord is when it makes a certain number of beats per second, is remarkably simple.

Let n represent the denominator of the fraction, expressing, in the lowest terms, the true ratio of the concord (e.g. for the fifth 3, n = 2; for the minor sixth %, n = 5, and so on); then let the number of vibrations per second either in excess or deficiency of the number which would make the interval perfectly in tune; also let ẞ = the number of Smith's beats per second :

=

temperament, he has only to calculate the velocity of beats corresponding to the minute error which should be given to each concord, and the required note may be tuned to its proper pitch with a precision and facility which would be impossible by the unaided ear.

The delicacy of this method of tuning would hardly be believed, if it did not rest on proof beyond question. To recur to our example, the difference between 95 and 100 beats per minute would be appreciable by anyone with a seconds watch in his hand; and yet this would correspond to a difference of only of a vibration per second, or in pitch less than Too of a semitone !

This use of beats has been long practised by organtuners to some extent, but its capabilities, as amplified by the aid of calculation, are certainly not appreciated or used as they ought to be.

The third kind of beat is what we may call the overtone beat, and was brought into prominent notice in 1862 by Helmholtz, who uses it for important purposes in regard to his musical theories.

It is known that nearly all musical sounds are com

formulæ.

Take the concord of the fifth,

When this is true the upper note should make 768 vibrations per second to 512 of the lower one; but if it is tuned by equal temperament the upper note will be slightly flat, making 76715. Hence 7085; and as n = 2, we shall get B = 17, i.e. there will be 102 Smith's beats per minute.

Again, suppose we find the concord of the major third give 120 beats per minute (= 2 per second),

how much is it out of tune? As in this case n = 4, we have 9 = 2 = 4;

i.e. the upper note vibrates half a vibration per second either more or less than it ought to do.

The number of beats per second due to imperfections in the various consonances will be as follows, 9 being always the number of vibrations by which the upper note is untrue :

usually the strongest (and by which the pitch of the note is identified), but which is accompanied with several fainter and higher harmonic notes, or, as Helmholtz calls them, overtones. The first of these is an octave above the fundamental, the second a twelfth above, the third a fifteenth, the fourth and fifth seventeenth and nineteenth respectively, and there are others still higher which we need not mention here. The number and strength of the overtones vary for different kinds of sounds, but the five lowest ones are very commonly present and distinguishable. Now, suppose we sound two notes, having such a relation to each other that any of the overtones of one will come within beating distance either of the other fundamental, or of any of its overtones, then a beat will be set up, which is the kind of beat now in question.

A few examples will make this clear. The bass fundamental C shown by a minim in the following example, has its overtone

256

148

261

an octave above, as

In the case of the unison, the Tartini beat and the Smith beat are synonymous, and this identity is the reason why so many writers on beats have gone wrong; they have so often taken unison sounds as the easiest and

simplest for popular illustration, and have either assumed, without further investigation, that the same principles would apply for other consonances also, or have omitted notice of the other consonances altogether.

It will now be easy to understand why beats are capable of such great utility in a practical point of view-namely, as giving a means of measuring, with great ease and positive certainty, the most delicate shades of adjustment in the tuning of concordant intervals. To get, for example, an octave, a fifth, or a third perfectly in tune, the tuner has only to watch when the beats vanish, which he can observe with the greatest ease, and which will give him far more accuracy than he could possibly get by the ear alone. Whereas if he desires to adopt any fixed

Here, if the G is not a perfect concord with the C, the two G's in the treble stave will be also out of tune with each other, and a unison beat will ensue. This is another Helmholtz beat, and a little more complex than the last, as both the beating notes are overtones.

Again, take an interval of a major third, expressing the notes and such of their respective overtones as we require in the same way as before, thus:

600

330

Here, if we suppose the fundamental E to vibrate 165

instead of 160, i.e. five vibrations too sharp, the two upper E's in the treble stave will clash, and a beat will result.

In all these three cases Smith's beats also will naturally be present, and it is curious that in each case when we come to determine the rapidity of the beats, we find it come out the same, whether we calculate it by Smith's formula or by the unison beats of Helmholtz's overtones. We have added the vibration-numbers to the notes, to facilitate the calculation, and we find the number of beats per second to be

each arising from a sharpness of five vibrations in the upper note of the concord.

Hence we may lay it down as a principle that in consonances slightly out of tune, the beat given by the two fundamentals on Smith's plan, and those given by the first corresponding overtones on Helmholtz's principle, are synchronous, and may be considered identical.

The two kinds of beats, however, must not be confounded, as their cause is so distinct. The Helmholtz beats arise from the overtones only, whereas Smith's explanation applies to the fundamental notes, independently of the overtones altogether.

Helmholtz notices (Ellis's translation, pages 302-3) that beats of consonances will occur when sounded by simple tones, but accounts for them in another and very ingenious way, namely, by calling in the aid of the grave harmonics, or, as he calls them, the combination tones.

Taking our first example of the octave consonance given above, when the two notes of 128 and 261 vibrations are sounded together, they will give rise to a combination tone of 123 vibrations, and this, clashing with the 128 note, will give beats at the rate of five per second.

For the next example, the consonance of the fifth, this explanation will not suffice, and Helmholtz has to resort to a cause of the second order, namely, the beat of a grave harmonic, not with an imperfect unison, but with an imperfect octave. Taking our former example, an out-of-tune fifth C and G, of 128 and 197 vibrations respectively; these two notes will give a combination or difference tone of 69 vibrations, or an octave below the C, but out of tune. Then Helmholtz says this lower C will beat with its imperfect octave, on account of a new or second order of difference-tones formed from them, as in the former case.

In a similar but still more remote way, Helmholtz accounts for the beats of other consonances, the fourth, third, &c.

Without questioning the sufficiency of these explanations, I must say they seem to me somewhat far-fetched, and less satisfactory than Smith's, which account for the beats by a more positive and direct method, without calling in the aid of any sounds but the simple fundamental ones. There is at any rate the satisfaction that whichever explanation be adopted, the numerical value of the number of beats per second comes out the same and agrees with the fact; so that in a practical point of view it is immaterial which explanation be adopted.

I have alluded above to one important practical use of beats, namely, in tuning; but there is another use of them, also very interesting, i.e., that they furnish a means of ascertaining the positive number of vibrations per second corresponding to any musical note. This may be done either by the unison or by Smith's beat, and I will give both methods.

For the unison beat :-Take two notes in unison on an organ, a harmonium, or other instrument of sustained sounds, and put one of them a little out of tune, so as to produce beats when they are sounded together. Let V and v represent the vibration numbers of the upper and lower notes respectively. Then by means of a mono

which gives the actual number of vibrations per second of the lower note of the two.

The method of deducing the vibration-number from the Smith's beat was pointed out by Smith himself; but as this method, so far as I know, is not to be found anywhere, except buried under the mass of ponderous learning contained in his work; I give it here in a simple algebraical form. If represents the true ratio of the interval, N the actual number of vibrations per second of the lower note, and M the same number for the upper one, the formula for Smith's beats becomes

n

A METEOROLOGICAL Commission, appointed by the Ministers of Public Instruction, Agriculture and Commerce, Marine, and Public Works, to inquire into the possibility and practicability of a more intimate co-operation being effected among the various meteorological systems of Italy, have just issued their report.

The Commission consisted of fourteen members, including most of the well-known meteorologists of Italy, with Prof. Cantoni as president, and Prof. Pittel as secretary, and met daily at Palermo from Aug. 30 to Sept. 6, 1875. The more important of the conclusions arrived at are these :-That all methods of observing at the stations of the various systems connected with the State be

brought into accordance with those adopted by the Minister of Agriculture and Commerce; that harmonious action be based on the number, quality, and hours of the observations, a preference being given to those stations which from their position will best meet the requirements of local and international meteorology; that the instruments and modes of observing be strictly uniform; that inspection of stations be made at least once every two years, and that the reduction and publication of meteorological results be remitted to a directive council composed of meteorologists elected from the directors of the principal observatories and meteorological institutes, whose decisions will be carried out by a secretary and suitable staff.

AT the meeting of the Paris Academy of Jan. 10, General de Nanscuty submitted a report on the project of a physical obser vatory on the top of the Pic du Midi de Bigorre, Pyrenees. As our readers know, a small hotel on the Col de Sencours has been provisionally used for observations since 1873, but amid great difficulty, from avalanches, cold, &c. The Pic is 2,877 metres high, and only 527 short of the highest, but is easily accessible.

THE Observatory on the Puy de Dôme is being rapidly completed, and will be opened this year. A semaphoric system of telegraphy will be used to keep the Observatory in constant communication with Clermont, the chief town of the district, at the foot of the mountain.

THE fourth part of the second series of Mr. William H. Edwards' work on the Butterflies of North America has just been published by Hurd and Houghton, and contains five quarto plates of butterflies, drawn with the utmost excellence by Miss Peart. The forms illustrated are species of Argynnis, Grapta, Melitaa, and Papilio, most of them new species recently described by Mr. Edwards himself.

AN addition to the list of American scientific journals has been made in the form of a Botanical Bulletin, edited by Mr. John M. Coulter, of Hanover, Indiana. At present it is a sheet of four pages, appearing monthly, with the promise of increase in size with increase in subscribers. It is in form and general scope much like the Bulletin of the Torrey Botanical Club.

DR. HOFMANN of Berlin has been elected a foreign associate of the Italian Society of Science in room of the late Sir Charles Wheatstone. This Society was founded in 1782; the Italian members are limited to forty, and at present the Society has only twelve foreign associates, among whom are Sir George Airy, Prof. Cayley, and Sir Edward Sabine. Its rules are numerous, and somewhat stringent.

THE Paris Academy of Sciences at Monday's sitting nominated Prof. Nordenskjöld a Correspondant in the section of Geography and Navigation.

THE Central Section, or governing body of the Geographical Society of Paris, has appointed as its president for 1876 M. Malte-Brun, the son of the celebrated Danish geographer.

THE Geological Society of Paris has elected as its president for 1876 M. Pellat, an amateur geologist, holding a high position in the finance department of Government.

THE warlike habits of the Papuans and their implements of warfare are described in a private letter recently addressed to Dr. Hooker. The writer says that no man leaves his dwelling for his bit of cultivation even without his powerful bamboo bow and a few deadly poisoned arrows. These poisoned arrows are only a few amongst a great number not poisoned, the former being distinguished by elaborate carving and painting, probably to prevent accident amongst themselves. They are each pointed and barbed with human bone brought to almost needle-like sharpness, most carefully and neatly finished; they are poisoned by

plunging in a human corpse for several days. Poor Commodore Goodenough and his men suffered from arrows so poisoned. It is a sort of blood-poisoning that, like other kinds of inoculation, does not develop itself for several days, the slightest scratch being sufficient to render almost inevitable a horrible death. The symptoms are accompanied by violent spasms like tetanus, with consciousness until the last.

CAPTAIN MORESBY'S work on New Guinea and Polynesia will be published shortly by Mr. John Murray. It will include discoveries and surveys in New Guinea and the D'Entrecasteaux Islands, a cruise in Polynesia, and visits to the pearl-shelling stations in Torres Strait of H.M.S. Basilisk, and will be illustrated by a map and wood-cuts. It will be interesting to compare this book of Captain Moresby's with Captain Lawson's "New Guinea," noticed in NATURE some time back.

M. E. QUETELET has called attention to the cold experienced in Brussels in December, 1875, when the temperature fell to freezing every night from 25th Nov. to 6th Dec., falling on the 2nd to 18°5, which is lower than has occurred any time up to the 4th December, during the last forty-two years. In thirteen out of the forty-two years the temperature observations present a relation somewhat analogous to those of 1875. It is remarkable that with this low temperature and a persistent E.N.E. wind, the barometer has continued low and the air humid and constantly cloudy. On the 7th December the temperature fell to 5°9.

PROF. F. W. PUTNAM, Dr. Packard's late colleague, the Nation announces, has been appointed Civilian Assistant on the U.S. Surveys west of the 100th meridian conducted by Lieut. G. W. Wheeler, and is already occupied in preparing a report on the abundant and very valuable archæological and ethnological material collected by the exploration in Arizona, New Mexico, and California. The report will be profusely illustrated, and the Nation ventures to predict, will be the beginning of our scientific knowledge of the prehistoric civilisation of the abovenamed regions.

A CONVOCATION of the University of London was held on Tuesday, at which, after a long discussion, a resolution was passed affirming the desirability of obtaining a new charter, and declaring that no such charter would be acceptable to convocation which did not enable the University to grant degrees to

women.

THE Ladies' Classes at University College, London, began on Monday last the second term of their eighth session. There was a slight decline in the number of students for the session 1874-75, but the first term of the session 1875-76 showed a considerable Michaelmas term, 1874-75, the whole number of individual advance beyond the highest success hitherto attained. In the students was 199; in the Michaelmas term, 1875-76, just elapsed, the number of individual students was 265. The whole number of tickets taken in Michaelmas term, 1874-75, was 257; in the same term of 1875-76 it was 367.

IN a paper on the Chalk in the Channel district read at the Paris Academy on Monday, Prof. Hebert stated that he expected great obstacles to be met with in the attempt to bore a Channel tunnel.

IT is announced that all communications and notifications in Sciences, to be held at Geneva on Sept. 9, 1877, be sent to the connection with the next International Congress of Medical Committee before June 1, 1876, the time when the Committee will definitely settle the regulations and programme, and appoint reporters. The present president is Prof. C. Vogt, and the secretary Dr. T. L. Prevost.

M. ADOLPHE PICTET, who died at Geneva on Dec. 20 last, at the age of 76 years, was one of the most eminent writers on

ethnology and comparative philology of the present century. In 1839, the French Institute awarded him the Volney Prize for his work on the affinity of the Celtic Languages with Sanscrit. In 1863, this same prize was awarded him a second time for the publication of his great work, "Les Origines Indo-Européenes, ou les Aryas primitifs." M. Pictet was also an eminent man of letters. He was a corresponding member of the Royal Society of Edinburgh.

AN ingenious toy, apparently of Japanese origin, has recently been introduced into London. It consists of a small picture, on paper, of an individual pointing a firearm at an object-bird, target, or second person. By the application of the hot end of a match, just blown out, to the end of the gun, the paper commences to smoulder towards the object aimed at, and in no other direction. When it is reached a report is heard from the explosion of a small quantity of fulminating material. The toys are sold in London by Mesdames Jinks and Ashton, of Glasshouse Street.

ABOUT midnight on the 22nd of December, 1875, two earthquake shocks were felt at Washington, Richmond, Weldon, North Carolina, U.S., and other places in that section. There were two distinct shocks at Richmond, the first continuing about ten seconds, while the other was briefer and not sɔ severe, and was accompanied by a concussion in the air.

THREE distinct shocks of an earthquake are stated to have been felt at Comrie, near Crieff, Perthshire, on Sunday-two at about three in the morning and the third in the afternoon.

THE Gazette d'Augsbourg states that a commission which has been visiting the Russian Universities has laid its report before the Czar. The chief recommendations are to increase the Salaries of some of the professors, and to create a few new chairs. THERE are several important papers in this month's part of Petermann's Mittheilungen. The editor himself takes occasion, on the conclusion of the new edition of Stieler's fine HandAtlas, to give a brief history of that work, and to point out the great advances in geography since the last edition was published. The first part of a paper appears, giving some account of Przewalsky's travels in Mongolia and the land of the Tanguts during 1870-73. We believe the author's narrative of this important expedition is being translated into English; a map accompanies the article in the Mittheilungen. A translation from the Russian gives an interesting description of the ruins of Mestorján, in the Turkoman steppes. Some account of the Paris Geographical Congress is given by the delegates from Perthes establishment. A valuable paper by Dr. G. Hartlaub describes the great amount of work done by that indefatigable traveller in China, the Abbé Armand David. Along with a brief summary of discovery in the interior of Australia there is a fine map, showing the routes of Warburton, Forrest, and Giles. SUPPLEMENT No. 44 of Petermann's Mittheilungen contains the first part of a narrative of the expedition which, under the engineer Josef Cernik, in 1872-73, explored the region of the Euphrates and Tigris, for the purpose of estimating its industrial capacities, and to mark out a route for a railway. The narrative will be found to contain much valuable information on the

various aspects of the region visited. We need hardly say the narrative is accompanied by admirable maps.

THE Japanese Government is said to have adopted a singular method for extending a knowledge of the Arabic numerals with their English names; these are printed on cloth, which is sold at a low price to the peasantry.

THE Annuaire of the Bureau des Longitudes for 1876 was published a few days ago with an unusual number of useful tables and a map showing the magnetic declination for all French towns.

M. WALLON, the French Minister of Public Instruction, has abolished the fees of the several examiners in the degree examinations in Law, Medicine, Science, Literature, and Theology. The salaries of the professors and fellows have been raised on a scale varying from 6,000 francs to 18,000 francs, the professors of theology excepted. It is believed that these reforms are preparatory to the gratuitous conferment of degrees, which will be instituted by the new assembly.

We have received the "Transactions" of the Clifton College Scientific Society, vol. ii. part 1, including the period from Dec. 1872 to June 1875. There are a number of very fair papers, though it seems to us that the members generally need to be wakened up and urged to attempt to rival similar societies in some of our other public schools. The" Transactions,” however, contain one paper which alone reflects great credit on the Society, and especially upon its author, R. A. Montgomery. The paper is on the Isle of Unst, in Shetland, and describes, from personal observation, its geology, natural history, antiquities, and scenery, in a manner which would entitle it to a place in the "Transactions" of a more ambitious society. The paper is illustrated by maps and section.

AN important publication has lately been commenced in the form of a Bulletin of the U.S. National Museum, consisting of a series of memoirs illustrating the collections of the museum. It is printed, by direction of e Secretary of the Interior, at the Government printing-office, from materials prepared by the Smithsonian Institution, which, as is known to our readers, has charge of the museum referred to. The first number of the Bulletin consists of a check list of the North American batrachia and reptilia, with a systematic list of the higher groups, and an essay on geographical distribution, as based on the specimens in the National Museum, and as prepared by Prof. Edward D. Cope, the well-known herpetologist and naturalist. The list of species is the first systematic enumeration of American reptiles since the time of Dr. Holbrook, and embraces 101 species of frogs, toads, salamanders, &c., 132 of serpents, 82 of lizards, 41 of turtles and tortoises, and 2 of crocodiles. Each species is accompanied by a reference to some work where it is described or figured. The list of the higher groups embraces those of the whole world, and will form a convenient basis for the arrangement of such collections in public museums.

THE scientific expedition, commanded by M. Mouchez for the survey of the coast of Algeria, will last ten months. During the latter part of the expedition M. Mouchez will resume the exploration of coral reefs, and will be accompanied by M. LacazeDuthiez.

MR. J. CLIFTON WARD has reprinted from the Quarterly Journal of the Geological Society his paper "On the Granitic, Granitoid, and Associated Metamorphic Rocks of the Lake District."

THE tenth edition of the Prospectus of Sir Joseph Whitworth's Scho'arships for Mechanical Science has been issued, containing the papers set at the examinations in May 1875.

ON the 26th of November last, in the French island La Réunion, near Mauritius, a part of a mountain slipped down, seventy-two persons having been crushed by the falling rocks.

THE additions to the Zoological Society's Gardens during the past week include an Emu (Dromaus nove-hollandia) from Australia, presented by Mr. E. J. Dawes; a Palm Squirrel (Sciurus palmarum), a Manyar Weaver Bird (Ploceus manyar), two Nutmeg Birds (Munia undulata), two Amaduvade Finches (Estrelda amadava) from India, presented by Mr. W. D. Baker; a Cinereous Sea-Eagle (Haliaetus albicilla), European, deposited.

SCIENTIFIC SERIALS

THE current number of the Journal of Anatomy and Physiology-the second under the new system-commences with a paper by Dr. G. Thier and Mr. J. C. Ewart, entitled "A Contribution to the Anatomy of the Lens." The fibres of that organ are stated to be composed of a number of flattened bands, termed primary fibres, and to be covered with elongated flat cells resting on a structureless membrane.-Dr. McIntosh describes the central nervous system, the cephalic sacs, and other points in the anatomy of the Lineida, demonstrating that in the Nemerteans the nervous system is highly developed, and that the cephalic sacs are special organs of sense, their internal surface being in direct communication with the surrounding water by the ciliated duct, whilst the fibrous peduncle places their cells in continuity with the central nervous system. The paper is profusely illustrated.-Prof. Rutherford, who has been assisted by M. Vignal, records his experiments on the biliary secretion of the dog. In almost every case the animal had fasted about eighteen hours. Under the influence of curare a tube was tied into the bile duct. The amount of bile which flowed in each quarter of an hour was measured. The cholagogue action of croton oil is shown to be nil; that of podophylline considerable; that of aloes powerful; that of rhubarb well marked; that of senna feeble; that of colchicum considerable, by making the bile watery; that of taraxacum very feeble; that of scammony feeble; that of calomel probably nil; that of gamboge nil; that of castor-oil nil. The memoir, with its valuable diagrams, deserves special attention. Dr. Galabin contributes an article on the pulse-wave in the different arteries of the body. The author, we are glad to see, has modified his previous statement as to the modification of a double wave the result of a single impulse, in the explanation of the predicrotic undulation in the sphygmograph trace. He gives an explanation of this as well as of the predicrotic wave. Some of his arguments are, we think, based on too few facts, whilst others are complicated by their pathological nature.—Mr. D. J. Cunningham has some notes on the broncho-oesophageal and pleuro-oesophageal muscles of man, first described by Hyrtl. -Dr. Stirling contributes a memoir on the summation of electrical stimuli applied to the skin, in which, from an excellent series of experiments on the frog, he demonstrates, according to the view of W. Baxt, that reflex movements can only be liberated by repeated impulses communicated to the nervous centres.-Mr. F. M. Balfour commences a series of papers to ultimately constitute a monograph on the development of Elasmobranch Fishes. Commencing with the ripe ovarian ovum, its description is followed by that of the segmentation, in the volume before us. This monograph will be an invaluable adjunct to that on the hen's egg, by Dr. M. Foster and the same author, and is a most promising production of the Biological school of the University of Cambridge.--Prof. Huxley writes on the nature of the craniofacial apparatus of Petromyzon, a specially favoured region of that author. The plates are unfortunately delayed for three months.-Mr. S. M. Bradley has a note on the secondary arches of the foot.-Prof. Turner, lastly, gives a note on the placental area in the uterus of the cat after delivery, in which he shows that in delivery not all the mucosa of the placental area comes away, its deeper structures being partly left. -Prof. Turner and Mr. Cunningham's report on the progress of anatomy concludes the part.

Archives des Sciences Physiques et Naturelles, Oct. 15, 1875.-In this number is concluded an important paper by Prof. Lemström, of Helsingfors, on the theory of Aurora Borealis, apropos of some phenomena of Geissler tubes. The phenomenon from which he set out was that a Geissler tube is illuminated when near the pole of an electric machine, without the tube touching the poles. Air, at a pressure of 5 to 10 mm., acquires its maximum electric conductivity, and Prof. Lemström conceives the air in the upper regions of the atmosphere, rarefied to about 5 mm., as forming a great conductor concentric with the earth; its height some 3,000 kilometres less at the poles than at the equator, and the electric density (on both conductors) 9 per cent. greater, while the force with which the electricity of the atmospheric conductor is attracted to the earth is 42 per cent. greater (at poles than at equator). Thus there is accumulation of atmospheric electricity at the poles, and the auroras are produced on its combination with that of the earth. The theory regards aurora as a phenomenon entirely of our globe; but the possibility is not excluded of an action of the sun, causing a periodical variation of auroras, through meteorological phenomena, such as evaporation on the

earth's surface.-Prof. Schnetzler contributes some observations on Bacteria.-M. Cellerier investigates mathematically the simul taneous movement of a pendulum and its supports; and a résumé is given of the proceedings at the extraordinary session of the Geological Society of France, held in the end of August at Geneva and Chamounix.-In the "Bulletin Scientifique" there is a description of a curious phenomenon observed by M. Gumœlius in Sweden, viz., intercrossing rainbows.

Journal de Physique, November, 1875.-This number contains the second part of M. de Romilly's paper on the conveyance of air by a jet of air or of vapour. He investigates the effects of the jet when driven against the lateral wall of the receiver, the orifices of the discharge-pipe and the receiver forming, if projected on a plane parallel to them, two circles exteriorly tangent. The form and separation of the two instruments are varied.-M. Angot, in another continued paper, gives a good account of Thomson's quadrant electrometer.-There are also short mathematical notes on the verification of the law of Huyghens, by M. Abrin; and elementary demonstration of the formula of La Place, by M. Lippmann, together with the usual amount of matter abstracted from other serials.

SOCIETIES AND ACADEMIES
LONDON

Heat. By T. E. Thorpe, Ph.D., and A. W. Rucker, M.A. Royal Society, Jan. 6.—On the Expansion of Sea-water by (Fellow of Brasenose College, Oxford), Professors of Chemistry and Physics in the Yorkshire College of Science.

The extensive contributions which have recently been made to the physical history of the ocean have shown the desirability of exact knowledge of the relations of sea-water to heat. The authors have accordingly made observations in order to determine the law of the thermal expansion of sea-water.

The only attempt hitherto made to solve this problem which can lay any real claim to consideration is due to the late Prof. Hubbard, of the United States National Observatory. The Directions," 1858, vol. i. p. 237. results of his investigation are contained in Maury's "Sailing

Muncke, nearly fifty years ago, determined the expansion of an artificial sea-water at various temperatures between 0° and 100° C.; but our confidence in the results as applicable to natural sea-water is affected by the circumstance that the solution was

prepared from data furnished by the imperfect analyses of Vogel and Bouillon La-Grange.

The observations of Despretz were confined to temperatures below 13° 27, as the main object of his inquiry was the determination of the point of maximum density of sea-water. The subsequent investigations of Neumann and Rossetti were equally limited, as they were undertaken with the same view.

The water used in the authors' observations was collected from the Atlantic, in lat. 50° 48′ N. and long. 31° 14′ W.; and its specific gravity at o° C., compared with distilled water at the same temperature, was found by the bottle to be 1'02867. already employed by one of the authors in determining the exThe method of experiment was precisely the same as that pansion of the liquid chlorides of phosphorus. It was essentially that already used by Kopp and Pierre; i.e. the expansion was observed in thermometer-shaped vessels (so-called dilatometers), graduated and accurately calibrated.

Three of these instruments and two sets of thermometers were employed. The latter were made by Casella; the length of a degree in different instruments varied between 9 and 13 millims. ; they had been compared (the one set directly, the other indirectly) with Kew standards.

Three perfectly independent sets of observations were made with the water in the state in which it was collected; but as Mr. Buchanan, of H.M.S. Challenger, has found that the specific gravities of different sea-waters lie between the extreme values 10278 and 10240, and since, in order to be of value in the in vestigation of the physical condition of the ocean, the observations on their value and the formulæ of reduction ought to be correct to the fourth decimal place, quantities of the sea-water were diluted with distilled water, so as to have specimens of approximately the specific gravities of 1'020 and 1025; and a third quantity was concentrated by evaporation until its specific gravity was increased to 1033; two series of independent observations were made on the expansion of each solution.

Empirical formulae were calculated to express the results of