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a Lancashire pit into anthracite, and even in some parts into graphite.-A paper by Mr. Payne was read, On the Oolitic coalfield of Brora, Sutherlandshire. One of the coalseams, about 3 feet 6 inches thick, is being worked at a depth of from 720 to 300 feet. Mr. Taylor then read three short papers on (1) An analysis of various coals and peats. (2) Specular iron recently discovered in New South Wales. (3) Shale recently discovered at Waitata, New Zealand.Mr. Peach stated that, in the course of preparing these sections, he had made a discovery which may yet prove to be of some service in the Fine Arts, viz., that the pounded dust of such shale as this, an enormous bed of which occurs in New Zealand, yields a colouring material closely resembling sepia, a costly substance.

April 16.--Mr. David Milne Home, F.G.S., president, in the chair. The first paper was read by Dr. Ramsay H. Traquair, Keeper of the Natural History collection in the Edinburgh Museum of Science and Art, On the Structure and Affinities of the genus Cheirolepis. Dr. Traquair submitted the following conclusions at which he had arrived on the matter :(1) That Agassiz was correct in ascribing branchiostegal rays and irregular dentition to the cheirolepis, but the larger teeth are placed in a distinct row internal to the smaller ones, not in the same line as Agassiz described them. (2) That the plates described by Powrie as principal jugulars belong to the shoulder girdle, being in fact the interclavicular plates of Parker; and that cheirolepis has no jugular plates. (3) That the osteology of cheirolepis shows it to be so closely allied to Palæoniscus that it ought to be included in the same family, notwithstanding the minuteness and non-overlapping character of the scales.Mr. George Lyon read a paper On a Species of Griffithides (Trilobite) from a limestone quarry south of Dalkeith, near Edinburgh, and which belongs to a genus extremely rare.-Mr. David J. Brown read a paper On a new Theory of the Formation of Till, or Boulder-clay. The author submitted that till is in reality formed by glaciers, after they enter the sea, tearing up the rocks that form its bed, and grinding them to boulders and mud, and that this mud deposited along with the boulders forms boulder-clay.

VIENNA

Geological Institute, Jan. 7 (anniversary meeting). The Director, Fr. v. Hauer, read the annual report, which states, that during the last year the palace of Prince Liechtenstein has been purchased for the collections, the library, laboratory, and the working rooms of the institute. The staff has been reorganised, and now consists of the Director, Fr. v. Hauer; ViceDirector, Fr. Foetterle; Chief Geologists, D. Stur, G. Stache, and E. v. Mojsisovics; Chief of the Chemical Laboratory, K. v. Hauer; Geologists, H. Wolf and K. Paul; two adjuncts, O. Lenz, the second at present being vacant; two assistants, A. Redtenbacher and K. John; two practitioners, C. Doelter and R. Hörnes.-After mentioning the share which the institute took in the general exhibition of last year, the report announces that geological explorations have been carried on during the last summer in the Bukovina as well as in the Tyrol, whence the examination of the northern chain of the Austrian Alps was finished with the Bregenzer-Wald (Vorarlberg), whilst that of the central chain was continued in the environs of the Oetz valley and the Ortler mountains, and that of the southern chain was begun in the environs of Lienz, in the valley of the Drau. Grateful allusion is also made to the liberal foundation of a capital of 12,000 florins in bonds of the Southern Railway Company, the gift of Albert Schloenbach, of Salzgitter, Hanover, in memory of his late son, the eminent geologist, Urban Schloenbach. The annual interest of this sum will be given to officers or friends of the Geological Institute, to enable them to travel in foreign countries to compare geological observations made in the Austrian dominions with those abroad. The first to whom it has been granted is D. Stur, whose studies on the exact geological position of the Bohemian coal-beds are likely to lead to very interesting results; results, however, which require a comparative study of other coal basins, and chiefly of the rich collections of fossil plants in the Museum of Dresden, for their secure confirmation. -The following specimens have been newly arranged in the museum of the Institute :-The silurian fauna of Galizia; the l'evonian fauna of Moravia; the carboniferous flora of Ostrau Orlau-Karwin, of Schazlar-Schwadowitz, of Kladno-Schlan, of Swina, of Stradonitz, of Radnitz and its environs, of the Pilsen basin, of the Rossitz basin, the flora and the fauna of the old red in Austria, Moravia, and Bo

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hemia; the cretaceous flora of Moravia and Bohemia; the flora of many tertiary deposits in Bohemia, and of Wieliczka and Swaszawice, in Galizia. In the chemical laboratory, more than 300 analyses and assays have been performed, the library has been augmented by 661 volumes, and the collection of maps by 194 sheets. The progress of the publications appears very satisfactory besides the periodicals, the Jahrbuch, the Mineralogische Mittheilungen and the Verhandlungen, four sheets of the "Memoirs,' were edited, viz., Vol. V., No. 4, On a Fossil Saurian from Lesina, with 2 plates, by Prof. A. Kornhuber ; No. 5, On the Cephalopods of the Gosau beds of the northeastern Alps, with 9 plates, by Dr. A. Redlenbacher; No. 6, Fauna of the beds of Aspidoceras acanthicum, with 13 plates, by Prof. M. Neumayr; and Vol. VI., No. 1, The Fauna of the Flambach and Halstatt beds, with 32 plates, by Dr. E. v. Mojsisovich. Also, a Geological Map of the Environs of Vienna, on the scale of 1:28800, with explanations by Th. Fuchs, and a Catalogue of the Objects exhibited by the Institute at the General Exhibition, have been published. Finally, the most important work has been the completion of M. v. Hauer's large geological map of the Austro-Hungarian empire, printed in colours on the scale of 1 : 576000, the last four sheets of which were published last year. Further communications were made by T. Hirschwald, On the Transformation of Wood into Brown Coal, in the Mine Dorothee, on the Ober-Starz; by S. Nedeljkovic, On the Sanidin-Trachytes of Syrmia; Dr. A. Redlenbacher, Remains of Ursus spelæus from a cavern near Wildalpe, Upper Styria; Dr. G. Stache, On the Fauna of the lower eocene beds of Cosina, in Istria; Dr. C. Doelter, On some Eruptive Rocks in the Transylvanian Erzgebirge.

GÖTTINGEN

Royal Society of Sciences, Jan. 3.-M. Wielen communicated the results of an examination of Greek names of makers inscribed on ancient earthenware lamps in several archæological collections in Athens, Corinth, and Smyrna.-M. Lolling presented a paper on the Theseion and the Hephaisteion in Athens.

RIGA

Society of Naturalists, Nov. 5, 1873.-M. Russwurm furnished some interesting particulars as to the seal-fishing on the Russian coasts. The Baltic supplies annually about 12,000 animals, with a value of 125,000 roubles (the rouble = 35. 1d.); the White Sea and neighbouring parts, 18,000 animals, worth 212,000 R.; the Caspian Sea, 100,000 animals, worth 900,000 R. The Russians (unlike the Finns, &c.) do not eat the flesh of seals, but throw it away. The various species met with, as also the mode of capture, were described.

Nov. 19.-Dr. Gutzeit gave an account of a new official map of Russia, just completed at St. Petersburg.-M. Teich com. municated some observations on the power of scent in butterflies; he thinks they are greatly guided by the sense of smell, which has its seat in the feelers.

Dec. 3.-Prof. Petzholdt read a paper on structural relations of ice and axes of crystals.-Prof. v. Sivers made some obser vations on driftwood collected in the Arctic regions by the recent German expedition.

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TH

HIS, the first volume of the yet young French Society's Proceedings, does it infinite credit. It is a handsome, beautifully printed volume of 1,330 pages, containing upwards of 200 papers, addresses, and lectures on a wide variety of subjects connected with Science, pure or applied. The volume is also well illustrated, some of the plates appended being coloured, a feature which we think the British Association would do well to imitate in its "Proceedings."

The French Association, as our readers no doubt know, made a very auspicious start, the number of members amounting to somewhere about 800. There are two classes of members-1st, membres fondateurs, who subscribe one or more shares of the capital of the Association, a share amounting to 500 francs; there are about 250 members of this class, some of whom have subscribed several shares, among the latter being a considerable number of railway and other public companies: 2nd, ordinary members, paying an annual subscription of annual subscription of 20 francs, or a life-subscription of 200 francs; the names of about 50 life-members are in this volume. After an existence of scarcely three months, the Association possessed a capital of nearly 140,000 francs, and an annual revenue of more than 16,000 francs.

The French Association is modelled pretty closely after the older British one, its aim being, according to the rules, "to promote by every means in its power the progress and diffusion of the sciences from the double point of view of the perfection of pure theory and of the development of their practical applications." These ends it proposes to accomplish by means of meetings, lectures, publications, and donations of instruments or money to persons engaged in scientific researches. It appeals for help to all those "who believe that the cultivation of Science is necessary to the greatness and the prosperity of the country."

The Association is divided into four Groups, and each group into several sections; the Groups are-1. The Mathematical Sciences; 2. Physical and Chemical Sciences; 3. Natural Sciences; 4. Economic Sciences. The French Association devotes more attention to the practical application of scientific principles than does the British one; the 1st Group, for example, including Sections of Navigation and of Civil and Military Engineering; the 3rd Group including the Medical Sciences, and the 4th Group Agriculture. This arrangement may at present have some advantages in France, where there are probably fewer special Associations than there are in this country, and because, until the Association gets itself firmly established, it may be advisable to appeal to as many classes of supporters as possible: but we are inclined to believe that it will by and by find that it will serve the cause of Science more effectually by confining its attention to the pure sciences.

VOL. IX.-No. 235

In points of administrative detail, the French follows very closely the British Association. One of its rules ordains that each year the capital fund be increased by 20 per cent. of its revenue. If it prospers in the future as

it has done hitherto, we have no doubt that it will soon have a very large sum at its disposal.

As we noticed pretty fully the proceedings of the Association at the time of its meeting at Bordeaux in Septem|ber 1872, it is unnecessary to notice in detail the papers contained in the volume before us. There will be found in its pages the names of many of the most prominent men of Science in France, and a few belonging to foreign countries, among the latter being Sir Benjamin Brodie and Dr. Gladstone. Two of the published lectures have been published in NATURE in extenso-that of M. Janssen on the Eclipse of December 12, 1871, and that of M. P. Broca on the Troglodytes of the Vézère.

M. de Quatrefages, the first President, in his eloquent and powerful opening address, speaks very highly, and we would fain hope with justice, of the work which has been done by the British Association. "Thanks to it," he says, a part of the population has been reformed. The sons of those fox-hunters, who, as a relief from their rude pastimes, only knew of joys equally violent and material, are now botanists, geologists, physicists, and archeologists."

The President's impressive words as to the sphere of Science at the present day are well worth quoting:"Science is at present everywhere; she is becoming more and more the sovereign of the world. What industry can dispense with the aid of mechanics, and is there any industry which would wish to be bound to the progress already realised by that Science? Is there one which would despise the help of Chemistry? What physician, worthy of the name, would consent to dispense with physiology, that complex science, daughter of chemistry? with physics and with mechanics, any more than with anatomy? What enlightened agriculturist does not understand that the problems of culture and of production are essentially questions of zoology, botany, geology, and chemistry? And in this great city (Bordeaux), one of the queens of universal commerce, what merchant will deny the importance of geography? Science is as indispensable to the military man as to the manufacturer, the physician, the agriculturist. Certainly I am far from denying the part which in war will always fall to courage, to inspiration. But inspiration must be enlightened by study; bravery must be furnished with arms equal to those of the enemy. Revive in imagination Renaud de Montauban or the Roland of legend; place them upon Bayard or Frontin; cover them with their enchanted armour, and dart them against a simple mechanic mounted upon his locomotive. You all know what will be the result of the shock: coursers and paladins will be brayed."

It will be remembered that the first meeting of the French Association took place while the country was yet sore with the humiliation inflicted upon it by Germany; and very naturally the address of the President, as well as the addresses of many others who spoke, took their tone, to some extent, from this condition of affairs. Still the character of these addresses, though intensely patriotic, is perfectly healthy, the various speakers showing

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that they possessed a clear perception of the most effectual means of raising and advancing their fallen country; they read aright the lessons of the recent war, and declared that Science alone, in its widest acceptance, could be the saviour and elevator of France. And, indeed, there is the greatest hope of a country that has produced men, and that in so great numbers, capable of doing the work the results of which are chronicled in the handsome volume before us; for we are persuaded that this first volume of the French Association's Proceedings will compare favourably with any single volume of the Proceedings of the British Association. The meeting last year at Lyons fully bore out the promise of the first meeting, and we have no doubt that this year's meeting at Lille will be at least equally successful. Let the members of the Association only do all in their power to keep up its high character and carry out faithfully its declared objects, and the beneficial results of its establishment both to Science and to France will, ere long, be evident. As it is, partly no doubt owing to the work of the Association, Science since the conclusion of the Franco-Prussian war has taken immense strides in France; everything taken into consideration, the amount of scientific activity which has recently been developed in that country is very wonderful, and calculated to call forth the gratitude of the friends of science and humanity.

NORTH AMERICAN BIRDS

A History of North American Birds. By S. F. Baird, T. M. Brewer, and R. Ridgway. Vols. i. ii. and iii. Land Birds. (Little, Brown and Co., 1874.)

THE

HE ornithologists of the United States appear to be not less active than those of this country at the present moment. Whilst here we have Gould's "Birds of Great Britain," Dresser's "Birds of Europe," and Newton's new edition of "Yarrell,” all appearing at the same time, so in America Coues's "Key" and Cooper's "Birds of California" are quickly followed by the present important work on the whole of the North American Ornis. For this undertaking Prof. Baird, the well-known AssistantSecretary of the Smithsonian Institution, has obtained the assistance of two very efficient coadjutors, Dr. T. M. Brewer, of Boston, and Mr. Ridgway, already well known for his accurate work in ornithology.

The object of the present work, which aims at a wider grasp than any of its predecessors, is to give an account of what is known of the birds, not of the United States only, but of the whole of the Continent of North America north of the Mexican boundary. Greenland is included on the one side, and the newly acquired United States territory of Alaska on the other, so that many European and Asiatic forms, which have been lately discovered in these two countries, are now for the first time added to the American list.

The materials upon which this undertaking is principally based consist of the very extensive collections of birds from every part of the New World, in the Smithsonian Museum at Washington. The numerous expeditions for exploration and survey sent out of recent years by the Government of the United States into nearly every portion of their enormous western domain have been invariably accompanied by one or more collectors whose contributions have all been deposited in the

stores of the Smithsonian Institution. But besides their collections these investigating naturalists have reaped a rich harvest of facts concerning the life-history of the creatures they have collected, and have deposited their records and journals also in the Smithsonian Archives. From these manuscripts, particularly from the notes of the late Mr. Robert Kennicott, who made most extensive explorations in Western America and in the most northern portion of the Hudsons Bay Territory, many of the most novel facts recorded in the present work have been drawn.

The special value of the researches of Mr. Kennicott and his fellow-workers in the north-west lies in the fact that a large number of the rapacious birds and waterfowl of North America resort in summer to these thinlypopulated districts for the purpose of breeding. Their haunts, not having been previously invaded, much novel information on the nesting habits of the members of these two groups is for the first time published in this work.

Besides Messrs. Baird, Ridgway, and Brewer, whose names appear on the title-page, we are informed in the preface that two other well-known American naturalists have contributed to the present work-Prof. Gill having furnished a portion of the introduction, and Dr. Coues the tables of the orders and families.

The work is profusely illustrated by woodcuts, besides containing a series of illustrations of the heads of all the species, drawn upon separate plates. The woodcuts contain the outlines of the principal characters of every genus, embracing the shape of the bill as seen from above and from the side, the comparative lengths of the wing and tail feathers, and the outline of the tarsus and toes; besides reduced but well-executed and highly-characteristic whole figures of many of the species.

The tendency of the American ornithologists of late years has been rather to unduly augment the number of species by raising slight local variations in form and structure to specific rank. In the present work rather the opposite tendency is manifested, and we are not sure that it is not in some instances carried too far. For instance, the whole of the Purple Martins, of the genus Progne, recently divided by Prof. Baird into seven or eight species, are now treated of as one; and the different species of Redpole Linnets of Dr. Coues are again reduced to their primitive number. As, however, the distinctive characters, such as they are, are invariably stated with accuracy and precision, it does not really make much difference whether the forms are actually classed as species or varieties.

The three volumes of this elaborate work now before us contain the whole of the Land Birds. A fourth volume, shortly to be issued and to be devoted to the Water Birds, will complete the undertaking. There can be no doubt, as will be at once apparent to anyone who consults the work, that it is of a most complete and exhaustive character, and that it will fully sustain the well-known reputation of Prof. Baird and his fellow-labourers.

OUR BOOK SHELF

Our Common Insects. By A. S. Packard, jun. (Naturalist's Agency, Salem, Mass.)

IN this fully illustrated little work Mr. Packard, the author of the excellent and much larger "Guide to the

Study of Insects," gives a short and popular account of entomology generally, by taking a series of types from amongst the best-known North American insects, and describing them in detail. We should have liked to find some of the descriptions rather more explicit, as they might have been, without any alteration in the size of the volume, if some of the illustrations had not been so frequently repeated. In a work like Euclid there is no doubt considerable advantage in having the figures so placed that it is not necessary to turn over the pages in referring to them, especially when it has to be read by boys; but when space is short and the subject of such general interest, we cannot help feeling that their repetition, three times in more than a single instance, is quite uncalled for. The author's own work at the development of Insecta, which he has published in the " Memoirs of the Peabody Academy of Science," enables him to take a larger view of his subject than that held by most. This is particularly indicated in the very suggestive chapter entitled "Hints on the Ancestry of Insects," in which the researches of Ganin, Lubbock, Brauer, Haeckel, and Müller are all brought to bear on such questions as the relation of the Zoca form of the embryonic Crustacean to the similarly undeveloped and generalised, here termed Leptus, form of Insecta, in which the configuration is ovate, the head is large, bearing from two to four pairs of mouth-organs resembling legs, and the thorax is merged with the abdomen; this general embryonic form characterising the larvæ of the Arachnida, the Myriapods, first-named of these authors on the development of Platygaster error, an ichneumon parasite, in the author's mind tend to confirm the theory held by him that the ancestry of all the Insects, including the Arachnids and Myriapods, should be traced directly to the worms. We recommend this small book to all interested in the progress of this branch of invertebrate zoology.

and the true Insects. The elaborate observations of the

The Transactions of the Academy of Science of St. Louis, vol. iii. No. I. (St. Louis, U.S., 1873.) THIS Volume contains a journal of the proceedings of the Society from March 1868 to January 1873, and a few papers in extenso. The latter are :-Notes on the Genus Yucca, by G. Englemann; On the new Genus in the Lepidopterous Family Tineidæ, with Remarks on the Fertilisation of the Yucca; and Supplementary Notes on Pronuba yuccasella, by C. V. Riley; Descriptions of North American Hymenoptera, by B. D. Walsh ; Atmospheric Electricity, by Dr. A. Wislizenus, being the yearly report of atmospheric electricity, temperature, and humidity, from observations made at St. Louis; Catalogues of Earthquakes for 1871, by R. Hayes; and On the Occurrence of Iron Ores in Missouri, by J. R. Gage. Mr. Hayes, on the basis of the recorded earthquakes from 1739 to 1842 has found that the "largest maxima occurred in the years of the heliocentric conjunction and opposition of Jupiter and Saturn, with but three exceptions, and in these cases the increase began in those years, but the maximum was not reached till the following year." He suggests that these planets induce electric currents which call into action those forces to which the causes of seismic phenomena are usually ascribed."

LETTERS TO THE EDITOR

[The Editor does not hold himself responsible for opinions expressed by his correspondents. No notice is taken of anonymous communications.]

Herbert Spencer and à priori Axioms

MR. HERBERT SPENCER (vol. ix. p. 461) has "ended what he has to say on the vexed question of the origin of physical axioms" by laying down

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By speaking of it as an “immediate corollary," I presume that Mr. Spencer means that Newton's Second Law of Motion is the proposition obtained by substituting for the general term, cause, the particular term, force, and for the general term, effect, the particular term, motion generated; so that, according to Mr. Spencer, this law simply asserts "a definite quantitative relation between a force and the motion generated by that force." But surely the quantitative relation asserted by Newton is not only definite, but is further the special relation of proportionality; so that, if the law is an immediate corollary of an à priori asrelation between cause and effect is that of direct proportionality," sumption, the assumption must be that "the exact quantitativ e or in more familiar words, that "effects are proportional to their causes." Perhaps this is what Mr. Spencer meant to assert. At any rate let us admit it as a definite basis for reasoning, and endeavour to deduce some consequences from it.

"The cause of a stone falling when left to itself is its weight; but the greater the cause, the greater the effect,' therefore the greater the weight of the stone the more quickly will it fall, and thus of two stones let fall from the same height, the heavier will reach the ground sooner than the other.' Something of this kind, it may be presumed, was the argument of Aristotle and his followers before the age of Galileo: and how on d priori principles is it to be refuted? Of course it is disposed of at once by the simple observation that the same force does not produce the same motion in different masses: but independently of some such observation or experiment, it seems to me impossible to deny that it may be true, though even an à priori philosopher might show that, as other alternatives are conceivable, it is not necessarily true. As a matter of historical fact, Galileo refuted it once for all by the "consciousiy-made experiment" of letting two different weights fall simultaneously from the leaning tower

of Pisa.

But it may be said that the above argument is hardly "definitely quantitative." Let us then examine Newton's Second Law of Motion as an "immediate corollary" of our priori assumption. Here the cause is "the motive force impressed," and the effect "the alteration of motion." But then the question arises-how are the quantities of this cause and effect to be measured? Newton carefully defines quantity of motion as proportional to mass and velocity jointly; that is, he measures it by momentum. From another point of view it would have been correct to measure quantity of motion by kinetic energy or vis viva, that is, as proportional to mass and the square of the velocity jointly. Further the "alteration of motion" might be measured either with respect to a given time or to a given space. Newton implies the former, and consequently the explicit statement of his second law is that "the momentum generated in a given time by an impressed force is proportional to that force." Substitute for this "the momentum generated in moving through a given space," or "the kinetic energy generated in a given time," and the law becomes untrue. Substitute the kinetic energy generated in moving through a given space," and we have a law which is true, but not that which Newton asserted as his second law. Now among these four alternatives how is our à priori philosopher to decide? He might perhaps analyse them further and show that some of them are inconsistent with the others, and I believe he might reduce the questions to be decided to still simpler ones; but I fail to see (in common, I believe, with everyone who has thoroughly grasped the fundamental principles of rat mechanics) how, without recourse to consciously-made observations or experiments, he could arrive at a certain conclusion.

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May we not say ten that these great à priori principles, whatever value they may have in a "System of Philosophy,” are of little avail in any special science, and that the "axioms" of such science, however much they may involve these principles, are not mere "immediate corollaries" therefrom?

If not intruding too much on your space, I am tempted to apply to Mr. Spencer's great principle of the "Persistence of Force" the same mode of treatment as I have applied above to the principle that "effects are proportional to their causes."

Mr. Spencer distinctly refuses to identify this principle with the great physical principle of the Conservation or the Persistence of Energy, the firm establishment of which undoubtedly marks one of the most important epochs in the history of Science. Force, in Mr. Spencer's use of the term, includes numerous species of which energy is but one. I feel sure that every mathematician and physicist would protest against the inclusion under one term of magnitudes of such different kinds as statical force and energy, or the work done by such a force; but not to dwell on this, I believe that Mr. Spencer would certainly acknowledge as one of his species, that which (in my view) is alone properly termed Force, namely, such as can be measured in terms of the weight of a pound or a gramme. What then does Persistence of Force of this kind mean? Does it mean that the numerical sum of the intensities of all the Actions and Reactions throughout the universe is constant? If so, it is untrue: for, to take a simple illustration, if a weight be supported, first by a single string, and then by two strings not vertical, the tensions are quite different in the two cases, and there is no equivalence between those which disappear, and those which are introduced in passing from one to the other. If not, we must take account of the directions of our forces, and then, if it mean anything, it appears to be but the expression of Newton's Third Law that "action and reaction are equal and contrary" in this form :-"The algebraical sum of all the forces throughout the universe is persistently zero.' Το every mathematician, at any rate, this assertion and the assertion that "the sum of the energies of all kinds throughout the universe remains persistently of the same definite numerical amount are assertions of facts of such different orders, that to class them together is rather to introduce confusion of thought than to establish a grand general principle.

I have offered the above remarks because it appears to me only fair to the author of the article on Herbert Spencer in the British Quarterly Review to show that it is felt by others, who have made a study of the fundamental principles of rational mechanics, that his strictures on Mr. Spencer's treatment of those principles are in all essential points fully justified, however much they may wish that the expression of those strictures had been in some instances modified in its tone. The Park, Harrow, April 20

ROBERT B. HAYWARD

I THINK it is positively due, not only to the writer of the now famous article in the British Quarterly Review, but to Newton's memory and to Science itself, that the correspondence which has been going on should not seem to terminate as a drawn game, at any rate in the opinion of some bystanders, who may from their antecedents be presumed competent to judge.

That Mr. Spencer will ever be convinced is, I suppose, hopeless; I at any rate am not going to try to convince him. But I can assure the British Quarterly Reviewer that he has my very deepest sympathy in his argument with an antagonist who is at once so able a master of fence as Mr. Spencer, and yet is so intensely unmathematical, it would seem, as to pass from "exact quantitative relation" to "proportionality;" or as to talk of the effect of a force, without defining how the effect is to be measured, without feeling the slightest difficulty.

Nor does it seem that Mr. Frankland, in NATURE, vol. ix., p. 484, is quite justified in his conclusion that the truth lies between the two opposite views. And his own view is in fact entirely coincident with the Reviewer's, except, perhaps, on a point which is not relevant to the controversy, viz. how far the experimental proof of the so-called physical axioms is complete.

Will it comfort the Reviewer if I tell him some of my own experience? I, too, read Spencer after my degree; and on the first reading of the "First Principles" came to the sad conclusion that I had not understood any mathematics properly; so much fresh light seemed to be thrown on them. I read it again, and more critically, and doubted whether Spencer was quite correct. I read it again, and concluded that he was wrong in his physics and mathematics. I ought to add that I too was, like the Reviewer,

A SENIOR WRANGLER

I AGREE SO fully with the chief contents of Mr. Frankland's letter (vol. ix. p. 484), that I wish to call his attention to one point in which his letter seems to me calculated to mislead. He says, "the pure empiricists argue that because certain observed results coincide with the results of calculation, therefore the assumptions on which the calculation was based must be true. Now without doubt the demonstrative character of this

inference vanishes entirely under Mr. Spencer's searching criticism. But it seems to me that a high probability remains." Now, in the name of pure empiricists, must protest against our being supposed to think that anything "must be true" in any other sense than that there is a "high probability" of its truth. I cannot refer to a better exponent of our views on this point than Prof. Clifford, to whom Mr. Frankland himself refers. And the idea of our having to thank Mr. Spencer for showing that the inductive proofs of the laws of motion (or of any other physical truths) are not demonstrative in any other sense than the above is quite new to us. What Mr. Spencer has done is to bring up instances of this so-called imperfectness in the demonstration as evidences that no à posteriori proof of the proposition can exist, when in point of fact they are specially characteristic of such a proof.

Those of your readers who have examined Mr. Spencer's ingenious proof of the second law of motion, contained in his last letter to NATURE (vol. ix. p. 461), will not ascribe my not immediately answering his letter to any difficulty in so doing.

THE AUTHOR OF THE ARTICLE IN THE BRITISH
QUARTERLY REVIEW

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I take the liberty to enclose to you the new Inch Ordnance map of Arran, to which my letter in vol. ix. p. 441 referred. You will see that as "a matter of fact" the map does not give two outlets, but only one.

I need not ask for your valuable space in reference to Mr. Christie's own "matters of fact," since my views with reference to them are printed in the Athenæum of July 22, 1865. He will see there that I have not only "walked up the north stream from Loch Ranza," but also by Glen Catacol and Glen Dzeven, and a third time from Corrie by Glen Sannox over the waterparting. Also that I have sounded the whole of this little pool of bog-water by walking it, bare-legged, without being over my knees in the deepest part, which was at the south end, where the only outlet is to Glen Iorsa.

I shall have the pleasure to communicate with Mr. Thelwall in reference to his obliging letter. GEORGE GREENWOOD [The Ordnance map forwarded to us by Colonel Greenwood gives only one outlet to Loch-na-Davie.-ED.]

As this subject appears to me to possess an interest apart from the issues hitherto in question, I trust you will allow me a little of your space.

From the fact that lakes do not ordinarily occupy the crest of a watershed, it would d priori appear more likely that a double outfall, if it exist, should lie in or towards adjacent districts than connected with opposed valley systems. The following instance, which I observed in Norway last summer, is, in view of Colonel Greenwood's letter (NATURE, vol. ix. p. 441), worth mentioning. The lake exhibiting it lies about two miles inland (N. W.) from the elevated coast which faces Trondhjem, and is named Stor Lake; its length-nearly parallel to the Trondhjem fjord-is about seven miles, its greatest breadth about two. Like many Norwegian lakes, it presents a facies different to what we are most familiar with in Britain. Instead of occupying a single valley-basin, it consists of a chain of minor basins strung along separated from its neighbours by the subsided walls of the valley an axis of depression (probably a pre-existing valley), and each of which it is the cup-like enlargement. The form of Stor Lake is irregular, with long arms or creeks extended (obliquely to its longer axis) into the mouths of the valleys. In such lakes it might be expected now and then that the effluent waters should pass out at more than one of these channels, and in Stor Lake such is the case. One stream is discharged from one of the component basins, nearly at right angles to the lake's greatest length, the other issues along the depression on which I have said the basins are "strung"-bead-like. The former opening is of post-glacial date, and is superseding the original one for several reasons:-(1) it flows along the strike of a homogeneous bed of schist, whereas the other cuts across beds of various textures, and (2) its volume is greater. Its rival bears evident traces of

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