Elementary Chemistry. By William S. Furneaux, F.R.G.S., Science Demonstrator, London School Board. (London: Longmans, Green, and Co., 1888.) THE main object of this little work is to assist young students intending to sit for the chemistry examination of the Science and Art Department in the new alternative elementary stage. It appears to be, in fact, an illustrated expansion of the detailed syllabus published by the Department in their Directory.

The want of such a work has possibly been felt by 'alternative" many teachers of this or "natural" chemistry, which appears to be rapidly becoming more and more popular with young beginners. There is something truly fascinating in learning these mysteries of common things, and, what is still more important, the knowledge gained has its practical applications in every-day life. In order to afford teachers some idea of the methods recommended of performing the class experiments themselves, the Department have caused to be placed in the western galleries of the South Kensington Museum a complete set of apparatus, as simple and inexpensive as is compatible with the object in view, arranged under the personal direction of the examiners, to illustrate the method of performing each of the experiments indicated in the syllabus. It is to be hoped, therefore, that all who are interested in the teaching of the alternative elementary stage of chemistry, and who can conveniently do so, will avail themselves of this opportunity of comparing the experimental methods there recommended with those which they themselves have previously adopted. One cannot help thinking that many of the methods illustrated by Mr. Furneaux are much too complicated, and it is to be regretted that his book was in the press before the completion of the collection in the western galleries, which was accomplished about two months ago.

The majority of the theoretical explanations leave little to be desired. The ideas of the author, however, as to the nature of the Bunsen flame appear scarcely to accord with more recent investigations, the effect of mixture with an inert gas being entirely overlooked. A. E. T.

Companion to the Weekly Problem Papers. By the Rev. John Milne, M.A. (London: Macmillan and Co 1888.)

THE title of this work gives no adequate idea of its contents. It consists of some 340 pages, which, if about 60 pages be excepted, are devoted entirely to geometry. Besides the author, several other mathematicians are contributors, viz. Mr. R. F. Davis, Prof. Genese, Rev. T. C. Simmons, and Mr. E. M. Langley.

The object of the book seems to be to give prominence to what is here designated "The Modern Geometry of the Triangle." This is seen to consist of a group of pretty theorems which arise from a consideration of the "Brocard points" and the "Lemoine point" of a triangle. The successive chapters bear the titles, " Antiparallels, Isogonals, and Inverse Points," "The Brocard Points and Brocard Ellipse," ""The Lemoine Point and Triplicate Ratio Circle," ""The Brocard Circle and First Brocard Triangle," "The Tucker Circles," "The Cosine and Taylor Circles," ," "The Co-Symmedian and Co-Brocardal Triangles," and "Miscellaneous Theorems and Constructions." They comprise a good and almost complete account of the present knowledge of these subjects.

On p. 180 there is a résum of the bibliography, which has evidently been carefully compiled by the knot of enthusiasts in this country who have followed in the footsteps of M. Le noine M. Brocard, M. Vigarié, Prof Neuberg, M. Catalan, and others. To these investigators on the Continent most of the results here given were known prior to 1881; they were subsequently arrived at independently by mathematicians in England who were unacquainted with the work already accomplished, in the same field of research, abroad. In fact, in the résumé, discoveries, and rediscoveries, and rediscoveries of rediscoveries succeed one another in bewildering fashion. The reasons which have led to the nomenclature in certain cases are difficult to fathom. We find, for instance, a circle associated with the name of one math ematician, when, admittedly, the same circle had been examined by a Continental investigator some years previously, whose name, if name be necessary, it ought

to bear.

66

on

The algebraic portions comprehend sections "Theory of Maximum and Minimum," Theory of Elimination," "Summation of Series," "Binomial Series," and "Algebraical and Trigonometrical Identities."

The book will be chiefly useful to those who take an interest in recent triangular geometry; it will enable them to refer to original sources in Continental mathematical publications, and to follow further developments in English magazines. They will also find collected here most of the leading propositions given in a form which is without doubt both judicious and attractive.

Elementary Hydrostatics, with Numerous Examples and University Papers. By S. B. Mukerjee, M.A. (Calcutta Thacker, Spink, and Co., 1888.)

THE compiler of this handy little work is Assistant Professor of Mathematics in the Lahore College, who, having been, as is the wont of his order, unable to select from fully to meet the wants of his classes, has culled his elegant extracts from them, and so got what he wanted. This proceeding is a good one for his pupils, and saves them the trouble and expense of purchasing and reading many text-books. The selection is well made, and the compiler suitably acknowledges his indebtedness to the English writers (especially to Dr. Besant's classical work). The subjects handled are definitions and first principles, density and specific gravity, equilibrium of fluids, total pressures and resultant pressures on immersed surfaces, floating bodies, on air and gases, determination of specific gravities, and the application of hydrostatical principles in the construction of instruments and machines. Then follow several papers of problems set in the Calcutta University Examinations from 1860 to 1884; and the book closes with an appendix of formula to be rehistory of the growth of the principles of hydrostatics, membered, and another appendix which gives a short taken for the most part from Whewell's "History of the Inductive Sciences." In the body of the work are given numerous illustrative examples, many of which have been carefully worked out. Putting on one side the manufacture of the book—and herein, perhaps, Mr. Mukerjee is only more honest in making known his indebtedness than late the students on having such a good work in their miny are in the writing of text-books-we can congratuhands, and can indorse the favourable opinion expressed upon it by Prof. T. C. Lewis, Principal of the College. Arithmetic for Beginners: a School Class-book of Commercial Arithmetic. By the Rev. J. B. Lock, M.A. (London: Macmillan and Co., 1888.)

the nu nerous text-books in existence one which seemed

IT is not necessary to report upon this little book at any length. It is founded upon the author's larger work, but modifications as to arrangement and treatment of some of the subjects and as to the examples have been introduced. Then, with an eye to the requirements of the

out example on p. 151 there is an error of some pecuniary magnitude), and the chapter "On Recurring Decim ls, not required by Commercials," finds a place at the close of the text. Mr. Lock is generally so careful in his explanations that we are surprised at his omitting all reference to brokerage in his account of the transferment of stock. Numerous examples are given in the text, and six examination-papers and answers to all questions complete a capital hand-book.

PROF. GREENHILL, in his letter which appears in NATURE of May 17 last (p. 54), has a gain repeated his views on the use of the word weight. He has not, however, replied to the criticisms of those who differ from him (see NATURE, vol. xxxvi. pp. 221, 317).

His opponents wish to know how practical engineers who use the word weight as synonymous with the physicists' mass, treat a problem involving inertia. Prof. Greenhill has not yet given us an example of such a problem taken from some modern text-book of the practical engineer; nor has he yet given us in simple language a definition of weight. Prof. Greenhill some time ago referred me to Kennedy's "Mechanics of Machinery" for such a definition, but I venture to say that there is no such definition to be found in that standard work.

My own idea is as follows: Matter has many properties— inertia, weight (the force with which the earth pulls it), volume, &c. and Newton's great discovery consisted partly in seeing clearly that the universal property of matter by which it must be measured is its inertia, defined as its capacity for resisting change of velocity.

The mass of a body is that which can be ascertained by the operation of massing; such an operation, that is, as the following: To a given lump of matter apply some strain or force, and observe the acceleration produced in the matter by that force; then ascertain by experiment to how many lumps of matter called pounds this same force will communicate an equal acceleration. The weight of a body is that which is ascertained by the operation of weighing. To weigh a body it is placed on a spring balance, and the force of the earth's attraction is observed by showing the compression of the steel spring of the machine.

It happens, however, that the mass of a body is proportional to its weight; consequently it is sufficient to ascertain whether the weights of two masses are equal in order to ascertain that their masses are equal. The weights of two masses are ascertained to be equal by putting them each on one side of a balance, and observing that the force of the earth's attraction on each is the same. Hence the very difficult operation of massing as described above is replaced by the easy operation of weighing.

Prof. Greenhill tells us that "now the invariable unit, the mass, is measured in terms of a variable unit." Is this so? Is it not a fact that those who use exclusively the force of the earth's attraction as the measure of matter, rarely if ever have any conception of the idea of inertia? When the practical engineer has to do with inertia, as in cases of "centrifugal force," he works by formulæ or rule of thumb.

Prof. Greenhill's sentences, "a force equal to the weight of the mass of 10 pound weights," and "the weight of 32 pound weights on the Earth is at the surface of Jupiter a force of 7.1 pounds' weight," are entirely original.

I believe he means to express "the weight of 10 pounds," and the weight of 32 pounds on the earth is a force equal to the weight of 71 pounds on the surface of Jupiter.

Caius College, May 21.

Work and Energy.

JOHN B. LOCK.

WHILE a discussion of the nomenclature of mechanics is going

not of energy. To speak of a foot-pound of energy is quite as incorrect as it would be to speak of a pint of velocity, a yard of acceleration, an acre of momentum, or a pound of duration. There is great need of a short name for the unit of m2. Bardsea, May 21. EDWARD GEOGHEGAN.

A FARM in this neighbourhood was visited yesterday by a flight of about forty sand-grouse (pin-tailed). They were first seen about 6 p.m. feeding on a ploughed field. On rising they took a north-westerly course. A pair which were shot by a gamekeeper are in my possession. The presence of these birds in our country is, I believe, of sufficiently rare occurrence to justify me in asking whether they have been noticed in other districts during the last few days. F. M. CAMpbell. Rose Hill, Hoddesdon, Herts, May 21.

On the Veined Structure of the Mueller Glacier, New Zealand.

THE Mueller Glacier, in the Mount Cook district, has a total length of between six and seven miles, with a breadth of one mile in its lower portion. Like most, if not all, of the New Zealand glaciers of the first order, the lower mile or two is so thickly covered with rock debris that the ice can only be seen in the crevasses. All through the lower portion of the glacier the veined or ribboned structure is well marked, running nearly in the direction of the glacier. But at the terminal face there are two systems of veined structure, with the same strike but crossing one another at angles between 15° and 20°. In one system the blue bands are small, from a half to one inch thick, and separ

bubbles, about twice the thickness of the blue bands. The blue bands are irregular and sometimes anastomose. This system is similar to the veined structure found higher up the glacier.

The second system is formed by large and regular blue bands from three to six inches broad and from two to six or more feet apart. This coarser system is only occasionally developed. The finer system forms a well-marked synclinal curve on the terminal ice cliffs, which are from 250 to 300 feet high.

The ice here contains in places numerous angular stones, principally of slate, scattered irregularly through it, and these fragments always have their broad, or cleaved, surfaces parallel to the smaller system of veins. These stones have no doubt entered the ice through the numerous moulins and crevasses which are found higher up the glacier, but as they are not found in bands nor in pipes, they must have been moved in position by the flowing of the ice, consequently they must originally have been variously oriented, and their present parallelism to the veins is a decisive proof that the smaller system is due to pressure at right angles to the structure. The origin of the coarser system is not so clear. I did not notice it higher up the glacier, as I ought to have done if it had been an older system than the smaller veins. While, on the other hand, if it is a newer system the rock fragments would probably have been oriented parallel with it instead of with the finer system. The clear blue ice is generally supposed to resist melting better than the white ice, and to stand out in ridges; but I observed nothing of this on the Mueller Glacier. Both kinds of ice melt here with about equal rapidity. The grooving of the ice, by runlets of water, is certainly parallel to the structure when that structure is vertical or highly inclined; but the grooves are formed in several layers of both kinds of ice, and it seemed to me that the blue ice melted rather more rapidly than the white ice. I cannot suggest any cause for this difference between the ice of the Mueller Glacier and that of the Swiss glaciers. F. W. HUTTON.

Christchurch, New Zealand, March 22.

On the Rainfall and Temperature at Victoria Peak, Hong Kong.

THE first column of the following table shows the month of the year; the second, the mean rainfall at the Observatory (about 100 feet above the sea) from ten years' records; the third, the mean of the past four years' fall; the fourth, same for Victoria Peak (about 1800 feet above the sea); the fifth, the proportion between the figures in the two preceding columns; the sixth, the height of ascent in feet for one Fahrenheit degree of decrease of temperature (mean of the past four years) ::

I.

cending, even above the open sea; and the defect at the Peak is most noticeable during the raging of a typhoon. The fact that less rain is measured above must, however, be further investigated. It is very doubtful whether it would not be as well to expose the funnels of the gauges 4 feet above the ground, where they would not be so much affected by the rain drifting along the surface of the earth in typhoons, as to have them I foot above the grass, as is the case here.

The last column of the table proves the great variability of the fall of temperature with increasing height. It depends upon the humidity of the air. The astronomical refraction near the horizon must be affected by this, but it is rather doubtful whether the effect should be ascertained by comparing observed refractions with meteorological registers kept on mountains on account of the condensation of moisture which tends to raise the temperature on the top of the hill. But it would appear to be time that some astronomer studied the refraction in connection with daily weather-maps, seeing that the variation of temperature with increasing height is so different in cyclones and anticyclones. Of course near the centre of a cyclone it is scarcely possible to make astronomical observations. Bessel's theory of refraction is considered a failure within 5° of the horizon. Ivory's theory might possibly be made to account for the refraction nearly down to the horizon by observing the value of the constant fin connection with the isobars. It, on the whole, represents the variation of temperature high up in the air as estimated by meteorologists. W. C. DOBERCK, Hong Kong Observatory, February 11.

Problem by Vincentio Viviani.

To pierce in an hemispherical dome four windows such that the remainder of the surface shall be exactly quadrable. It was solved by Leibnitz, J. Bernoulli, and others. Viviani himself, in 1692, published the construction, but without proof. Divide the base of the dome into quadrants; on the four radii as diameters trace semi circles, one in each quadrant; the four right semi-cylinders, of which these are the bases, will pierce the dome in the required windows. The following simple proof, for which I am substantially indebted to Prof. Francis W. Newman, would probably interest many readers of NATURE:

OXYZ is quarter of dome; AB, generator of cylinder meeting OX = OB; angle CDB =XOA = 0; DC = DB = OA = R cos 0; dome in B; BCD, plane parallel to base. Radius of dome = R = OB. cos BOA = OA = R. cos 0; .. BOA = 0; .. arc EB = R@ ; Z

I'47 2'97 I'66 2'30

4'63

1'56

288

March

3'53 341 3.60

I'06 489

6:55 7.89

9'19 1'16 407

May

9.82

4.86

6:29 1'29

309

16.71 1.16

259

August

16.93

September..

9.89

7'98

B

October...
5'06 2'57
November.... 1'04 0'77
December 0'49 0'97

7:01 0.88 2'06 I'19 1.54 267 I'21 125 278

283 0.80 281

Year 85'52 79'96 93'27 I'17 310 The rainfall at the Peak exceeds the record at the Observa' ory by about one-sixth of the whole amount, and this appears to be due to the circumstance that the mountain presents an obstacle to the wind from whatever side it blows, in consequence of which the air is forced to rise, and being thereby cooled it precipitates more moisture in the form of rain. Even when the air is moderately dry at sea-level its temperature may be decreased below the dew-point in the course of such a rise. The comparatively great rainfall in hilly districts must be attributed to this, for a hill must of course exercise its influence at a distance all round. Our rainfall would therefore be smaller if there were no hills in this neighbourhood. But during the months of September and October less rain is collected at the upper level. This is explained by the circumstance that most of the rain in those months is due to typhoons, when the air is everywhere as

arc BC= 0. R cos 0. Element of surface of window is BC. (EB) R20. cos. . de; .. surface of window is the integral of this from 0 to 0. Integrating by parts, and taking limits, surface of window = R2 (= 1); .. the remainder of the surface XYZ is R2, which is exactly quadrable. Q.E.D. Cor. The quadrable part of the quarter-dome is equal to the surface of the semi-cylinder which is within the dome. For, if AB %, and arc XA == Re, element of surface of the cylinder is . ds = R. sin e. de; .. the entire surface within the dome is the integral of this from 0 = 0 to 0 = π, viz. R2. A general discussion of Viviani's problem may be seen in Lacroix, "Traité du Calcul Differentiel et du Calcul Intégral," tome ii. pp. 219–22. EDWARD GEOGHEGAN.

2

Bardsea, May 2.

SUGGESTIONS ON THE CLASSIFICATION OF THE VARIOUS SPECIES OF HEAVENLY BODIES.1

VI.

ON THE CAUSE OF VARIATION IN THE LIGHT OF BODIES OF GROUPS I. AND II.

I. GENERAL VIEWS ON VARIABILITY.

IN my former paper I referred to the collision of meteor-swarms as producing "new stars," and to the periastron passage of one swarm through another as producing the more or less regular variability observed in the case of some stars of the class under consideration.

I propose now to consider this question of variability at somewhat greater length, but only that part of it which touches non-condensed swarms; i.e. I shall for the present leave the phenomena of new stars, and of those whose variability is caused by eclipses, aside.

It is not necessary that I should pause here to state at length the causes of stellar variability which have been suggested from time to time. It will suffice, perhaps, that I should refer to one of the first suggestions which we owe to Sir I. Newton, and to the last general discussion of the matter, which we owe to Zöllner ("Photometrische Untersuchungen," 76 and 77, p. 252).

Newton ascribed that special class of variability, to which I shall have most to refer in the sequel, as due to the appulse of comets.

"Sic etiam stellæ fixæ, quæ paulatim expirant in lucem et vapores, cometis in ipsas incidentibus refici possunt, et novo alimento accense pro stellis novis haberi. Hujus generis sunt stellæ fixæ, quæ subito apparent, et sub initio quam maxime splendent, et subinde paulatim evanescunt. Talis fuit stella in cathedra Cassiopeia quam Cornelius Gemma octavo Novembris 1572 lustrando illam cœli partem nocte serena minime vidit; at nocte proxima (Novem. 9) vidit fixis omnibus splendidiorem, et luce sua vix cedentem Veneri. Hanc Tycho Brahæus vidit undecimo ejusdem mensis ubi maxime splenduit; et ex eo tempore paulatim decrescentem et spatio mensium sexdecim evanescentem observavit” (“Principia," p. 525, Glasgow, 1871).

With regard to another class of variables he makes a suggestion which has generally been accepted since.

"Sed fixæ, quæ per vices apparent et evanescunt, quæque paulatim crescunt, et luce sua fixas tertiæ magnitudinis vix unquam superant, videntur esse generis alterius, et revolvendo partem lucidam et partem obscuram per vices ostendere. Vapores autem, qui ex sole et steHis fixis et caudis cometarum oriuntur, incidere possunt per gravitatem suam in atmosphæras planetarum et ibi condensari et converti in aquam et spiritus humidos, et subinde per lentum calorem in sales et sulphura et tincturas et limum et lutum et argillam et arenam et lapides et coralla et substantias alias terrestres paulatim migrare.”

Zöllner, in point of fact advancing very little beyond the views advocated by Newton and Sir W. Herschel, considers the main causes of variability to be as follows. He lays the greatest stress upon an advanced stage of cooling, and the consequent formation of scoriæ which float about on the molten mass. Those formed at the poles are driven towards the equator by the centrifugal force, and by the increasing rapidity of rotation they are compelled to deviate from their course. facts, and the meeting which takes place between the molten matter, flowing in an opposite direction, influence the form and position of the cold non-luminous matter, and hence vary the rotational effects, and therefore the

These

'The Bakerian Lecture. delivered at the Royal Society on April 12, by J. Norman Lockyer, F. R.S. Continued from p. 6o.

luminous or non-luminous appearance of the body to distant observers.

This general theory, however, does not exclude other causes, such as, for instance, the sudden illumination of a star by the heat produced by a collision of two dark bodies, variability produced by the revolution of a dark body, or by the passage of the light through nebulous light-absorbing masses.

If the views I have put forward are true, the objects now under consideration are those in the heavens which are least condensed. In this point, then, they differ essentially from all true stars like the sun.

This fundamental difference of structure should be revealed in the phenomena of variability; that is to say, the variability of the bodies we are now considering should be different in kind as well as in degree from that observed in bodies like the sun or a Lyræ, taken as representing highly condensed types. There is also little doubt, I think, that future research will show that, when we get short-period variability in bodies like these, we are really dealing with the variability of a close companion.

II. ON THE VARIABILITY IN GROUP I.

That many of the nebulæ are variable is well known, though so far as I am aware there are no complete records of the spectroscopic result of the variability. But bearing in mind that in some of these bodies we have the olivine line by itself, and in others, which are usually brighter, we have the lines of hydrogen added, it does not seem unreasonable to suppose that any increase of temperature brought about by the increased number of collisions should add the lines of hydrogen to a nebula in which they were not previously visible.

The explanation of the hydrogen in the variable stars is not at first so obvious, but a little consideration will show that this must happen if my theory be true.

Since the stars with bright lines are, as I have attempted to show, very akin to nebulæ in their structure, we might, in their case also would be accompanied by the coming reasoning by analogy, suppose that any marked variability out of the bright hydrogen lines.

This is really exactly what happens both in ẞ Lyræ and in y Cassiopeia. In ẞ Lyra the appearance of the lines of hydrogen has a period of between six and seven days, and in y Cassiopeia they appear from time to time, although the period has not yet been determined.

III. ON THE VARIABILITY IN GROUP II. This same kind of variability takes place in stars with the bright flutings of carbon indicated in their spectra, o Ceti being a marvellous case in point. In a Orionis, one of the most highly-developed of these stars, the hydrogen lines are invisible; the simple and sufficient explanation of this being that, as I have already suggested, the bright lines from the interspaces now at their minimum and containing vapours at a very high temperature-teste the line-absorption spectrum now beginning to replace the flutings-balance the absorption of

the meteoritic nuclei.

Anything which in this condition of light-equilibrium will increase the amount of incandescent gas and vapour in the interspaces will bring about the appearance of the hydrogen lines as bright ones. The thing above all things most capable of doing this in a most transcendental fashion is the invasion of one part of the swarm by another one moving with a high velocity. This is exactly what I postulate. The wonderful thing under these circumstances then would be that bright hydrogen should not add itself to the bright carbon, not only in brightline stars, but in those the spectrum of which consists of mixed flutings, bright carbon representing the radiation.