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THURSDAY, MARCH 30, 1893.

ELECTROMAGNETIC WAVES.

Electrical Papers. Two vols. By Oliver Heaviside. (London: Macmillan and Co., 1892.)

IN

N these two volumes the author has collected the papers on electrical subjects which he has rom time to time contributed to the Philosophical Magazine, the Philosophical Transactions, the Electrician, and other technical journals. The result is a work of some eleven hundred closely printed octavo pages; that is to say, on a rough estimate, it contains in printed matter about half as much again as Maxwell's two volumes on Electricity and Magnetism, and considerably more than the two volumes of Thomson and Tait. When we add that the author brings into action freely (though with perfect mastery) some of the most elaborate weapons of mathematical physics, and that considerable passages are moreover written in a special condensed notation, it will be evident that the task of the reviewer is no easy one. All that we shall here attempt is to give a general idea of the nature of the book, with some reference to its more original features.

The first few articles are devoted to practical questions, such as duplex telegraphy, signalling with condensers, the best arrangement of Wheatstone's bridge, and so on. These are thoroughly readable, and, apart from their technical value, may be commended to mathematical students as containing interesting concrete applications of electrical theory. The rest of the book is partly a commentary on, and partly a development of, the latter part of Maxwell's treatise, and deals mainly with the propagation of electromagnetic effects in space and

time.

It is therefore closely connected with the theoretical work of Poynting and J. J. Thomson on the one hand, and with the practical investigations of Hertz and his followers on the other. At the present time there is no great difficulty in following in imagination the propagation of inductive effects from one conductor to another across the intervening space; and that this should be the case is due in no small degree to the labours of our author, for although probably few readers have been found to follow him step by step, yet many have admired the tenacity with which he attacks problem after problem bearing on his subject, and have gathered valuable ideas and suggestions from his exuberant pages. One of the most noteworthy features in the author's theoretical work is the elimination of the "vector-potential" from Maxwell's equations of the electromagnetic field, with the result that the equations in question are obtained in a "duplex form" in which there is perfect symmetry as regards the parts played by the electric and the magnetic variables respectively, so that the equations are unaltered in form when a reciprocal substitution between the two sets of variables is made. same simplification has been made independently by Hertz. It is of importance for this reason, that the vector-potential is to a certain extent indeterminate. This was indeed insisted upon by Maxwell himself, but, strange to say, he did not always remember his own warning, with the result that more than one most impor

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tant passage of his great work is rendered needlessly obscure. Another function which the author seeks (we think rightly) to relegate to the position of a mere mathematical implement, without physical significance beyond the domain of electrostatics, is the electric potential. There is nothing paradoxical in this, for the original definition of this function postulates a state of equilibrium.

The last paper (but one) in the book forms a sort of crown to the whole. It is entitled "On the Forces, Stresses, and Fluxes of Energy in the Electromagnetic Field," and is reprinted from the Philosophical Transactions for 1892 (A). Unfortunately this paper is by far the hardest to read. Free use is made of the scalar and vector products of Hamilton, but the author is careful to give us his emphatic opinion that quaternions proper are unsuited to the purposes of mathematical physics. This courageous declaration will, we fear, cause a wicked joy in the hearts of many who have struggled in vain with these refractory symbols. For the special system of mathematical shorthand affected by Mr. Heaviside there is much to be said, but for our own part we should prefer to have papers which profess to give new and important results written in the more homely language of "Mr. Cartesian." Another prominent feature in this memoir is the frequent appeal to the principle of " continuity of energy," but this imposing phrase seems to mean nothing more nor less than Maxwell's negation of action at a distance. The author, indeed, takes care to explain that he does not countenance the notion of "identity of energy" which one prominent physicist has attempted to base on a well-known paper by Poynting. It is now generally recognised that the flux of energy in the electromagnetic field is indeterminate. In his treatment of induction in moving media, a very important but most difficult subject, the author is led to at least one definite conclusion of great interest, viz. the existence of a magnetic force acting on a body moved across the lines of electric induction, just as there is an electric force on a body moved across the lines of magnetic induction. This is in conformity with the duplex character of the fundamental equations already referred to. Finally, we must not omit to notice a somewhat startling proposal for a radical change in the system of electric and magnetic units. In the "rational" system advocated by our author, one line of force would emanate from a unit magnetic pole, instead of 4 such lines, so that the force between two poles m,m' at a distance apart would be mm/4m2 instead of mm'/r2 as at present.. The existing system is denounced as containing an absurdity of the same nature as if we were to define the unit area to be the area of a circle of unit diameter.

It remains to say a word or two about the style in which the book is written. It is exceedingly fluent, often discursive, and occasionally boisterous, as when the author, introducing the functions called zonal harmonics, remarks that "these are Murphy's P's; not praties, but the functions invented by Murphy"; or again, when in his impatience of vector and other potential functions he gives utterance to the wish to “murder the whole lot." A more serious matter is that the papers in these volumes often overlap, whilst the frequent cross

references make it difficult to detach any one from the rest, or to gather the substance of the author's speculations on any one part of his subject. In the preface he tells us that he had been urged to publish not a reprint, but a systematic treatise. It is, we think, greatly to be regretted that he has not found it possible to take this advice. The labour of compression and of proper co-ordination would no doubt have been great, but it would have been amply repaid by the increased currency given to the author's views. As it is, we fear that the fate of these weighty volumes will be that students of the stamp which Mr. Heaviside would most wish to attract will turn over his pages, picking up a suggestion here and there, will then work out things in their own way, and finally return to the present treatise to ascertain how far their results have been anticipated. And this is really matter for regret, for almost every page bears the impress of a vigorous and original mind, and we cannot doubt that the author's speculations would have exercised a considerable influence on the progress of electromagnetic theory, if it had not been for the disadvantageous form under which they are presented.

THE GREAT SEA-SERPENT.

H. L.

The Great Sea-Serpent. An Historical and Critical Treatise. With Reports of 187 Appearances (including those of the Appendix), the Suppositions and Suggestions of Scientific and Non-scientific Persons, and the Author's Conclusions. With 82 illustrations. By A. C. Oudemans, Jzn. Published by the Author, October, 1892. (London: Luzac and Co.)

IN a large, well-printed volume, Dr. A. C. Oudemans,

Jzn., publishes what he is pleased to call "an historical and critical treatise" about the "Great SeaSerpent," with the reports of 187 appearances, the suppositions and suggestions of scientific and non-scientific persons, and the author's conclusions.

It is impossible, however, to treat this laborious work as a scientific treatise, nor will the author, we trust, be vexed with us when we add that it is the very last form of a work that we would have expected from the pen of the learned Director of the Zoological Gardens at the Hague. for when one gets by practise to know the utter worthlessness of the descriptions given by even well-educated persons of often the most easily diagnosed forms of life--and surely experience of this nature must often have come across Dr. Oudemans's path-one cannot fail to regard as positively hopeless the reconciling of a mass of such crude observations as fill the pages of this book. The very trouble and no doubt anxiety caused by reading over such a pitiful series of records has to some extent affected the author, for he quotes as the motto for his volume the extremely sensible words of a very able biologist, whose chief fault it was not to leave a greater record of his wisdom for posterity, to the effect "That it is always unsafe to deny positively any phenomena that may be wholly or in part inexplicable," meaning thereby to deny a phenomenon because it cannot be explained, and then in the immediately following preface he compares himself to Chladni, who took the trouble to collect all the accounts concerning observations of

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"meteoric stones," and showed the immense number of facts that he had found out about them. In this one word fact-fuct-lies a great world of difference between Chladni's meteoric stones and Oudemans's seaserpents. The meteoric stones could be seen and handled, the sea-serpents are very shy, and it is not advisable to approach them with a steamboat." "Instantaneous photographs of the animal will alone convince zoologists, while all their reports and pencil drawings will be received with a shrug of the shoulders"; this latter sentence, which precedes the preface, makes one shudder at the amount of "reports and pencil drawings" contained in the six hundred following pages.

And yet, perhaps, this work is not altogether without its value. From the middle of the sixteenth century—when Olaus Magnus wrote about "a very large serpent of a length of upwards of 200 feet and twenty feet in diameter, which lived in rocks and holes near the shore of Bergin

until this very present hour all sorts and manners of gigantic forms have been reported about by sailors and others, and even pencil drawings of them have been made, and the collecting together and printing of such a series of records forms as strange a chapter of the science known by the people as has ever made its appearance.

There is but little necessity of insisting on the need of experience in seeing ere one can describe what is seen, nor on the need of a power of describing what one correctly sees so that the description may be applicable, nor need one wonder that such powers of seeing and describing were not to be found united in the many seagoing worthies whose extraordinary narratives crowd the pages of this volume. But what to say about the capacity for belief to be found in the compiler of this work, who concludes his task by naming a form he has never seen, Megophias megophias (Raf.) Oud., and further thinks that a Phylogenetic table, which he gives, “will in a practical manner show the rank which, in my opinion, sea-serpents occupy in the system of nature"?

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This volume contains an account of the "literature" on the subject of sea-serpents; a detailed record of the various accounts and reports concerning observations of sea-serpents chronologically arranged and thoroughly discussed; and criticisms on the papers written on the same subject; next the various explanations hitherto given, and lastly the author's own conclusions-these he divides into "fables, fictions, exaggerations and errors, and what he is pleased to call "facts." Among the fictions he regards the belief that the sea-serpent "casts its skin, as common snakes do, and that it is born on land"; among the exaggerations that it has "a tail fully a hundred and fifty feet in length"! among the errors "that there are two species of sea-serpents, or that there are several species of them all belonging to the same genus"; or that "it ever takes [mistakes] a boat for one of the other sex."

As to the facts, which may be-it is well to note"inferred from what is reported," we find enumerated among them the external characters of the sea-serpent. its dimensions, form, and skin. Of its internal charac ters "it is not astonishing that we don't know much," yet it is clear "that if the animal opens its mouth there

is an opportunity to learn something about its teeth, tongue, &c.," and so we get a series of "inferred" facts about them. We have further details of its colours, sexual differences, a very full account of its "physiological characters," some of its "psychical characters," concluding with its enemies, its repose, its sleep, and its death.

Enough has been written to prove that this volume is not without a certain amount of interest. We have found it a rather troublesome task to read it through, but to open its pages at random one is sure to be arrested by some startling phase of belief or by some marvellous narration, and the first half of the book very certainly deserves to be described as a conscientious compilation. It is written in most excellent English.

PUBLIC HEALTH.

A Treatise on Public Health and its Applications in Different European Countries. By Albert Palmberg, M.D., Medical Officer of Health for the County of Helsingfors in Finland. Translated from the French edition, and the section on England edited by Arthur Newsholme, M.D. (Lond.), D.P.H., Medical Officer of Health for Brighton. (London: Swan Sonnenschein and Co., 1893.)

AL

LTHOUGH scarcely more than a year has elapsed since the issue of the Swedish edition of this work, translations of it have already appeared in French, English, and Spanish. A book which within so short an interval has attained to such a pitch of popularity may be admitted to have practically established its claim to rank amongst the important contributions towards the literature of the subject with which it is concerned. Extensive indeed as is the ground travelled over by the author, yet so ably has the material been handled, that we feel it to be a matter for regret that the writer was unable to deal with the hygienic administration of all, instead of a portion only, of the important European countries. The sanitary administrations of England, Scotland, France, Germany, Austria, Sweden, and Finland are detailed; but the description of the Public Health service of Russia, Denmark, Norway, Holland, and Italy is omitted. Not having visited these countries, and studied the subject by a personal inquiry on the spot, Dr. Palmberg very wisely preferred not to deal with them at all, rather than run the risk of making inexact statements concerning them

In treating of the various countries, the plan which the writer has followed has been first to give a brief summary of the sanitary laws in force, and then to describe in detail the methods adopted in the capital towns for carrying out these regulations. Of all countries England claims the largest share of attention, Dr. Palmberg assigning to her the chief place amongst the nations for the excellence of her Public Health administration, and the care with which all matters connected with hygiene are attended to. The chapter on England contains a good résumé of our principal sanitary laws, together with a summary of the model bye-laws of the Local Government Board. The description of sanitary apparatus is excellent, the text being plentifully supplied with illustrations. Notwithstanding the limited space which is allotted to each

country, the author is nevertheless able to introduce a mass of detail relating to practical sanitation which we believe would be looked for in vain even in our standard text-books on hygiene. We may instance as examples of this the paragraphs on the scavenging of London, and the disposal of rubbish and street refuse; the description of the preventive measures adopted in this country for the limitation of the spread of infectious disease, together with an account of the ambulance service and hospital ships; the explanation of the methods adopted for the ventilation of some of our important public buildings; the excellent résumé of school hygiene, for which we have no doubt the author is deeply indebted to Dr. Newsholme ; and the summary on industrial hygiene, although the author is rather inclined to repeat many of his remarks under this head when describing “the sanitary provisions as to industries." Dr. Palmberg's admiration of English sanitation is pronounced, and in commenting on our appreciation of the beneficent results of good ventilation, we find him giving vent to the quaint statement that “even in cold weather the windows of high houses are opened, children and adults without fear of chill breathing the pure air"!

France, the author informs us, has no general sanitary law, most of the sanitary regulations in force consisting of ministerial decrees, orders of prefects and councils of health. Corresponding to this laxity of sanitary control, the great sanitary improvements which have been from time to time introduced have not been followed in Paris by a continuous fall in mortality, as in the case of the other European capitals. As the author very rightly remarks, the time is past when it can be supposed that good sense and administrative capacity merely suffice for the regulation of the Public Health. The drainage of Paris is exhaustively treated, the sewerage of the town being dealt with in detail, the writer in the course of his description pointing out that the system in use is objectionable, inasmuch as it allows deposits of sand to occur, and necessitates the maintenance of an army of 850 men to keep the sewers clear, the workers themselves at the same time having a relative mortality from typhoid fever twice as great as that for all Paris. Moreover, owing to the friction of the enormous deposits of sand in the sewers the wear and tear on the latter are great, and compel frequent repairs.

The sanitation of Germany and Austria is dealt with in the same thorough spirit as pervades the rest of the book and calls for no special remark.

In the description of the general regulations in force in Sweden relating to hygiene in towns, we think, however, that these laws might with advantage have been more systematised, much after the plan that the writer has adopted in dealing with Finland.

The translation is remarkably well done, and with one exception is quite free from the sort of mistake usually met with in English editions of foreign works. The instance we refer to occurs on page 380, where the author, in describing the forms of stove ordinarily employed in Germany, makes use of the following words :--" Although the construction differs from that of the English ventilating stoves made by Douglas Galton and Boyle and Son."

Dr. Palmberg's book is undoubtedly a valuable one, and should prove of the utmost utility to all interested in

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THIS quite recently published new edition of this most charming and useful book has been so completely altered as to be at first sight scarcely recognisable, and we are glad to record that all these alterations have been improvements, the result of a determination on the author's part never to give up the effort of making it better. the present edition the old plates, many of which contained but feeble portraits of plant life, have been broken up, and in their places we find delightful pictures of some of our best loved flowering shrubs and plants, at one time represented as growing over walls or cottage porch, or again by the lake or riverside. All of these are perhaps not equal in execution, but it has seldom happened to us to see so large a number of illustrations with so few that are below a high standard. Such delightful woodcuts as those of the double flowering hollyhock, the Alpine pink, or of Rodgersia podophylla brighten up the pages and add much of interest to this book. So familiar is this volume to most lovers of plants, of which the fact of three editions within ten years is a satisfactory proof, that it seems almost needless to explain that the first portion of it is devoted to a series of chapters on such subjects as design and position of a garden, on the wild garden, the Alpine garden, on spring, summer, and autumn flowers, and we note even on "Pergolas," the illustration of this latter being from Venice. Alas! in these northern countries our sunshine scarcely ever needs a shade. The whole of the first portion of the book is rewritten, and many new illustrations are given, such as the "primrose garden in a small clearing of a birch wood" in Surrey, the group of "Solomon's seal at the foot of a wall," and others too numerous to mention.

The second and much larger portion is devoted to a list, arranged in alphabetical order, of all those plants that have been grown successfully in the gardens of Great Britain and Ireland, and of some few that may be expected to grow there. Like the rest of the volume, this part too has been very thoroughly revised and brought up to date. To every one in the possession of a garden, or having the care of one, we would say study this "English Flower Garden," for you cannot do so without profit.

and composite numbers, squares, cubes, square roots, &c., Bessel's coefficients for interpolation to the fifth differences, binomial coefficients for interpolation, also for fifth differences, and lastly a useful table of the errors of observations, from which we can at a glance determine the ordinates of the probability curve, values of probability integrals, &c. An explanation, preceding the tables themselves, shows how they may be advantageously used, and the author offers the reward of "a dollar" for the first notice of a mistake "to promote the detection of errors."

Catalogue of the British Echinoderms in the British Museum (Natural History). By F. Jeffrey Bell, M.A. (London: Printed by Order of the Trustees.) DURING recent years many additions have been made to the collection of echinoderms in the British Museum; and, as Dr. Günther explains in his preface to the present volume, much time and labour have been given to the study and arrangement of these additions. It seemed expedient, he says, to prepare, together with the nominal list of the specimens, a complete account of the species hitherto found in British seas. All students of the subject will congratulate themselves on the fact that this decision was arrived at, for the result is that they are now provided with a handbook which will enable them to identify, without much difficulty, any specimens that may come in their way. Mr. Bell, in beginning the preparation of so full a catalogue, had before him a task of no small difficulty, and in the manner in which he has discharged it he has displayed great patience, insight, and knowledge. A number of well-printed plates add largely to the value of the work.

LETTERS TO THE EDITOR.

[The Editor does not hold himself responsible for opinions expressed by his correspondents. Neither can he undertake to return, or to correspond with the writers of, rejected manuscripts intended for this or any other part of NATURE. No notice is taken of anonymous communications.]

The Hatching of a Peripatus Egg.

IN NATURE, vol. xliv. p. 468, I briefly described sone eggs of the larger Victorian Peripatus, which were laid by specimens kept alive by me in the winter (Australian) of 1891. At that time, following previous authority, I identified the species which laid the eggs as P. leuckartii. It appears now, however, that the real P. leuckartii – at any rate, in New South Wales is undoubtedly viviparous, and our oviparous Victorian species is, therefore, probably distinct. (It may be remembered that in NATURE, vol. xxxix. p. 366, I suggested this probable distinction on account of the remarkable pattern of the skin usually exhibited by the fifteen-legged Victorian_form.) Notes on the oviparity of the larger Victorian Peripatus, Further particulars on this subject are given in my "Further generally known as P. leuckartii," and in the literature cited therein. In that paper I described two embryos, removed from eggs which had been laid for about three and eight months respectively. In the latter case I showed that the embryo was possessed of the full number of appendages, and was in all re

Logarithmic Tables. By Prof. George William Jones. spects a perfect young Peripatus, differing externally from the (London: Macmillan and Co., 1893.)

THIS book of tables, which we notice has reached its fourth edition, will be found to serve the purpose for many computations which require an accuracy extending only to four or five places of decimals. The tables throughout seem to be well arranged, and the figures neatly printed, thus fulfilling two important requirements from the computer's standpoint. In addition to fiveplace logarithms there is a table to four-places, together with four-place trigonometric functions, a table of useful constants, and an addition-subtraction table. Among others we may mention a five-place table of natural sines, &c., with a six-place table of their logarithms, prime

adult only in the smaller size and less deeply pigmented skin On the strength of these observations I claimed to have definitely proved that the larger Victorian Peripatus at any rate somedevelopment outside the body until perfect young animals are times lays eggs, and that these eggs are capable of undergoing produced. I am now able to add some further information.

For some time only one egg (belonging to the original lot, for none have since been obtained) remained in the hatching box. The shell of this egg had changed to a dark brownish colour, and latterly an embryo had been visible through the shell, coiled up inside. The egg was lying on a small piece of rotten wood, which rested on the glass floor of the hatching box. Os 1" Proceedings of the Royal Society of Victoria," vol. v. p. 27. Annals and Magazine of Natural History, 1892.

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January 3, 1893, not having opened the box for some days, I made an examination. The egg was in its former position, so far as I could tell, but the shell was split on one side and the young Peripatus had escaped. This young Peripatus was found lying dead on the glass floor of the hatching box, 25 mm. distant from the shell. It must have crawled off the rotten wood and along the glass to the position in which it was found. It was only about 5 mm. in length, so that, even assuming that it moved in a perfectly straight line, it must have crawled for a distance five times its own length. To the naked eye the young animal appeared of a pale greenish colour. It could not have been dead for very many days, but decomposition had already set in, and the animal was stuck to the glass on which it lay. It was impossible to remove it without considerable injury, but I ultimately succeeded in mounting it in Canada balsam, and it is impossible, even in its present condition, to doubt that it really is a young Peripatus, for the characteristic jaws and claws are well shown. I also mounted the ruptured egg-shell, and found that the characteristic sculpturing on the outside was still clearly visible.

This egg, then, hatched out after being laid for about seventeen months (from about July 1891 to about the end of December 1892). I cannot believe that under natural conditions the embryos take so long to develop. At any rate it now appears certain that the larger Victorian Peripatus lays eggs which may hatch after a lapse of a year and five months.

The University of Melbourne, February.

ARTHUR DENDY.

A Simple Rule for finding the Day of the Week corresponding to any given Day of the Month and Year. A RULE was lately mentioned to me by a friend for finding, almost by inspection, the day of the week for any given year and day of any month in that year, during the present century. The basis of the rule is so obvious, when once the rule is stated, as to require no demonstration, but it struck me as so ingenious as to be worth while communicating it to you in case you deemed it worthy of insertion. I also append a very easy method of extending the rule to any date subsequent to the introduction of the Julian intercalation either in the past or future, except indeed for the eighteenth century, in which the introduction of the new style requires a special treatment.

The nineteenth century rule above alluded to is this. Each of the 12 months has its special numerical constant, thus:Jan. Feb. Mar. Ap. May June July Aug. Sept. Oct. Nov. Dec. 3 6 6 2 5 2 3 1 3 6 I

Write down four columns thus A | B | C│ D Under A enter day of month, under B constant for that month, under C year of century, under D greatest multiple of 4 in the year of century.

Add together the numbers under these heads, divide by 7, and the remainder is day of week; except that in Leap Year I must be subtracted for any day before February 29. Example.-June 18, 1815 (Battle of Waterloo) :

:

-

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0 15 3 36 February 1, 1892 :

36

I Sunday.

7

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A

December 25, 1892:

Sunday Ans.—3—1 = 2 or Monday.

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Remr.

141

I Sunday.

7

B C 25 1 92 23 141 To extend the rule to any future century, we have only to alter the monthly constants, adding 5 to each for each added century after the present, and 1 for each century, an exact multiple of 4, in the interval.

Thus for the thirty-first century. Number of added centuries is 12, and there are 3 centuries, succeeding multiples of 4 (twenty-first, twenty-fifth, and twenty-ninth). Therefore add 5 × 12 +3=63, or omitting multiples of 7, add o.

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For centuries anterior to the eighteenth we must first of all find by special method what the monthly constants would have been throughout the eighteenth century without the change of style, and then subtract 6 for each century short of the eighteenth.

It may easily be seen that the constants throughout the eighteenth century would have been without change of style. Jan. Feb. Mar. Ap. May June July Aug. Sept. Oct. Nov. Dec. 2 5 5 I 3 6 I 4 O 2 5 O For the eleventh century subtract 7 x 6 or 42, i.e. since this is multiple of 7 subtract o, and we get the same repeated.

For the seventeenth subtract 6, and remember that when the result is negative we must replace it by the defect of the corresponding positive number from 7, and we get

3 6 6 2 4 0 2 5 I 2 5 1 Example.-Battle of Hastings, Oct. 14, 1066.

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WITH reference to Prof. G. H. Darwin's notes (NATURE, March 16, p. 460) on the investigations of M. Roche as to the smallest distance from its primary at which a satellite can exist, does not the distance given-viz. 2:44 times the radius of the primary-refer to the case of the satellite having the same density as its primary? In Note 3 Prof. Darwin warns the reader that Roche's limit depends, to some extent, on the density of the planet. Suppose the density of the planet to remain the same while that of the satellite is taken at double. In this case the tidal or differential influence of the planet, on the two halves of the satellite will have doubled, while the gravitational attraction of the two halves of the satellite on each other will have become fourfold; and generally, the power of the planet to pull the satellite asunder will be inversely as the density of the satellite, and directly as the density of the planet.

An alteration of the size of the satellite does not much affect the question, because both forces are thereby equally altered, so long as the satellite is very small in comparison with its distance from the planet.

Seeing that the tidal or differential influence of a planet on its satellite is inversely as the cube of their distance apart, perhaps it would be correct-as far as gravitational influence alone is concerned-to state the limit at which a satellite can exist as being equal to 2:44 R X

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As an interesting case of the same problem from a different point of view, suppose two very small equal spheres in contact, and a third much larger sphere placed in line with their centres, all three having the same density; then, when the distance of the point of contact of the small spheres from the centre of the large one is 2:52 times the radius of the large one, the attraction of the two small spheres for each other just balances the differential influence of the large one tending to draw them asunder. The effects of variation in density and size being the same in this case as in the former.

It would probably be interesting to many of your readers to have Prof. Darwin's views as to whether it is a reasonable supposition that a small satellite, such as Jupiter's fifth, is likely to have the same density as Jupiter; and whether the meteorites forming Saturn's ring are likely to be of so small density as

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