THURSDAY, NOVEMBER 21, 1878

MATHEMATICS AT CAMBRIDGE.

Examination for Mathematical

THE Cambridge for a long time enjoyed a high reputation, especially among Cambridge men, who have been accustomed to point to it as the model of what an examination should be. The credit thus claimed has been in past times more or less deserved, but to what extent it is so now is a question on which there may be variety of opinion. Like every other institution, the practical usefulness of which depends upon the ease with which it can adjust itself to external conditions, the Tripos examination must undergo changes to meet cor. responding changes from the outside; and there may come a time when the external conditions operate so powerfully that mere modifications are insufficient, and when the changes made must be both radical and extensive. The old Tripos system has recently been put to a severe strain, and it is admitted on all hands that the result has proved un satisfactory. We propose to inquire into the causes which have brought this about, and to discuss the measures by which it is hoped the evil will be met.

It may be laid down as a fundamental axiom that a university honours examination should be in harmony with the studies of the candidates, and that it should be reasonable in its demands upon them. What the very best students may be expected to answer after faithful work during their] undergraduate course should clearly be taken as a guide in fixing a superior limit to the number and difficulty of the questions. Nor should this estimate be pitched too high, because there are other subjects of interest and study besides mathematics, in which it is desirable that even the best of young mathematicians should engage, and an education based on mathematics alone must necessarily be defective.

If we accept these propositions we must admit that the estimate of what is reasonable towards the candidates was very different fifty years ago to what it is now. One cannot help looking back with regretful eyes on the Tripos questions of that time, so remarkable for their simplicity and elegance, as well as for the happy appreciation of the degree of difficulty such questions should possess. The questions of more recent times, although they are often to be admired from an æsthetic point of view, are in many instances far beyond the reach of any but the very best men, and may be described as being somewhat too difficult and elaborate.

There are obvious reasons why, as time goes on, the questions should become more difficult; still it would be interesting to trace the changes over some considerable period, so as to be able to explain how the Tripos examination has reached its present form. The changes must have been of a gradual character, because the traditions and customs of the examination have been faithfully transmitted from one set of examiners to the next. One can see, however, that if any particular person were to examine often, as has occasionally happened, or if several persons of like tastes were to examine together, we should find the questions displaying a particular bias. Vol. XIX.-No. 473

When this should occur, the studies of the candidates would receive the same bias, and particular branches of mathematics would thus be pushed for a time into undue importance. So much was this the case about the year 1864 that Sir G. Airy, when delivering the Rede lecture in the Senate House, went out of his way to denounce

the excessive attention given in the University to certain branches of pure mathematics.

We can thus imagine the Tripos examination based upon the traditions of its predecessors, yet continuing to grow both in extent and difficulty, and with some of its features perhaps somewhat exaggerated. In 1873 a great change had to be made. The University, feeling it was not creditable to it that so little encouragement should be given to the higher branches, and especially to the great modern subjects of mathematical physics, determined that those subjects should be introduced into the Tripos examination. The additions thus made, besides considerable extensions in the subjects already existing, included, amongst others, Elliptic Functions, Electricity, Magnetism, and Heat.

It was thought that in thus extending the examination the students would have a choice of subjects, and that their course of study would thereby be rendered more interesting than it was before. It was certainly never intended that the burdens under which the Tripos candidate was already staggering, should be increased upon him. But how were these changes met on the part of the students and on the part of the teachers? The imme diate result seemed to be that the best candidates attempted to know something of all the subjects. The examiners in 1874 were careful to watch for indications as to whether the candidates had devoted themselves to special groups, but they reported that there was no evidence to that effect. The University thereupon passed a Grace enacting that the number of questions in the higher subjects should be increased, the object being to supply a sufficient variety so that a candidate who had confined his studies to a limited group might reasonably expect plenty to occupy him in the examination. This provision has continued operative down to the present time, but it does not appear to have produced the salutary effect intended. There is much reason to fear that the best candidates still push their way through most of the subjects, whilst the next best struggle as far in the same direction as they can.

There is then a well-defined evil to be remedied. For no one can deem it a good education where the student is carried, necessarily with rapidity, over a variety of subjects, many of which he must therefore very imperfectly comprehend. What changes in the examination are proposed to the University as a remedy we will presently describe. Meanwhile let us glance at the position of the teachers in their relation to the new state of affairs.

It must be admitted that the great changes made in 1873 found the college lecturers unprepared. There were only one or two of them who ventured to expound the new subjects to college classes. The students were therefore compelled to depend upon the private tutors, and thenceforth the selection of groups became difficult, if not impracticable. The fact we have just mentioned was, in For the truth, a misfortune in more ways than one. new subjects, and, indeed, the higher subjects generally

D

It is impossible to touch on all the points which suggest themselves in connection with this question, but we may point out in conclusion that the examination in Cambridge has to adapt itself to two classes of candidates, viz. There is the class who may be called professed mathematicians, because they spend their lives in cultivating mathematical science and in teaching it to others, and there is the class who abandon their mathematics as soon as their undergraduate course has terminated. Of the former class we believe that their tastes and the necessities of their position will alike carry them beyond the subjects of the first examination. In the case of the second class, which is a large one, it is undoubtedly a wise thing to restrict their studies within the limits of the easier subjects. For under the present system, in their eagerness to secure good places they attempt subjects which are either beyond their powers or their opportunities, and so fail to gain the advantages which a strict mathematical training is supposed to afford.

"CRAM" BOOKS

Notes on Physiology, for the Use of Students Preparing for Examination. By Henry Ashby, M.B. (London: Longmans, Green and Co., 1878.)

THI

HIS book, being a fairly creditable and careful specimen of its kind, seems to offer a fitting opportunity for denouncing the whole class of "cram" books of which it is a member. It purports to be notes on physiology, compiled originally, while the author was a demonstrator in the Liverpool School of Medicine, for the use of those students of the school who were preparing for the primary examination of the College of Surgeons; and it is confessedly based upon Foster's "Physiology" and the two chief anatomical text-books used in England. It is a small 18mo of about 230 pages, clearly printed in a large type, and it contains a number of condensed and dogmatic statements in all departments of physiology. It is, we rejoice to be able to say, written perspicuously and compiled with evident care. Most of what Mr. Ashby has read in Foster he has accurately digested and dogmatised. But though he has thus almost disarmed criticism as to his particular book, the book still remains infected with the vices of its class; it is a delusion and a snare to the student; and we heartily wish Mr. Ashby's talents had found a worthier object for their exercise. "Notes" are undoubtedly of the greatest value to a student-nay, they are indispensable, if he is to acquire a large view of his subject; but they are only valuable when the student has compiled them himself from the larger text-books, or, better still, from original memoirs, or when he bas seen them digested and set down, so to speak, before his eyes by his teacher. Each of the sentences in his book Mr. Ashby doubtless could and would make the text of a lucid explanation in his lectures or demonstrations. He would lay before his hearers the different views of observers on different physiological questions, as he had learnt them, and, balancing the evidence, he would abstract for them a trustworthy judgment in a careful and concise statement: and the student who took down his notes, on re-reading them, would have the whole discussion refreshed in his mind with more or less

But if this were all we might be content to let books like this sink to their own level; their inutility would lead to their speedy death. But while the good student would never for a moment think of reading notes that he had not made himself, or if he did read those of another, would quickly find out the cause of their uselessness to any one but their author, the bad student is misled to believe that 230 small pages of fair-sized type contain the whole of the physiology that he needs; he looks through the list of contents and finds set down there almost every physiological fact and problem of which he has ever heard, and he naturally concludes that he has only to equip himself with this little book in order to cope

with his examiner.

Mr. Ashby's book, admirable for the purposes of his own students, is useless or worse than useless to the students of any other teacher; published to the world, it is like a creature in an improper medium, and we are constrained to wish that, with all similar books, it may quickly meet the usual fate of creatures so circumstanced.

After this we need not say much about the book itself. On the whole it is well done. The histological sections are decidedly the weakest. The "ossification of bone" (p. 29), and the "development of tooth " (p. 107) might as well have been omitted altogether, as put in so meagrely. The extremely important histological researches of Heidenhain on the pancreas seem to be ignored on p. 16, where "probability" only is allowed to the elaborating functions of glandular epithelia. The pigment layer of the eye on p. 17 is assigned to the choroid coat instead of to the retina, and again on p. 194. No nucleus is given to striated muscular fibres on p. 81. On p. 179 Prof. Ferrier's name is put down at the end of a paragraph as if he were the prime authority for certain facts regarding the corpora quadrigemina, which we rather owe to Flourens, Longet, and Goltz. These errors are not of vital importance, and some of them have probably been due to inadvertence. But there are two more mistakes which are of greater weight, and show the danger of mere book-making. On p. 34, where the properties of muscle are discussed, we find that "On contraction . . . O is absorbed and CO2 given off." This is left unexplained here and in the rest of the book. What Mr. Ashby doubtless meant was that during contraction more arterial blood passes into muscle, and more O is taken up than during rest, while CO2 is at the same time emitted; but, in the above unguarded way of statement, the fundamental fact of the independence of the actual absorption of O and disengagement of CO2-a fact of the utmost moment in our conceptions of muscular work-would seem to be passed over. Again, on p. 168, under nervous conductivity, we have the curious statement that "the axiscylinder probably conducts the impression, the medullary sheath acting as a sort of insulator to prevent the currents from becoming mixed and confused"—a physical explanation which no physiologist would now for a moment think of offering.

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. No notice is taken of anonymous communications. [The Editor urgently requests correspondents to keep their letters as short as possible. The pressure on his space is so great that it is impossible otherwise to ensure the appearance even of communications containing interesting and novel facts.]

66

The Divisibility of the Electric Light THE English and American periodicals devoted to electrical science now announce, on authority," that the electric light discovered by Edison is a light by incandescence. If this be true there is nothing new or startling either in the discovery of the light or of its divisibility. Lighting by incandescence has been studied for a long time; indeed, it has been studied much more thoroughly than any other kind of electric lighting. Thirtythree years ago a method of producing and sub-dividing the light was patented in England by a Mr. King. The light was produced by heating to white heat in a vacuum, by means of the electric current, either platinum or carbons; and, the specification adds, "when the current is of sufficient intensity, two or a larger number of lights may be placed in the same circuit." For some years after this discovery several improvements on King's invention were patented in America, France, and England; "but," says M. Fontaine, none of these appear more complete, more explicit, and more practicable than King's; it is, then, useless to continue our nomenclature." The principle of lighting by incandescence, although not neglected or forgotten, seems to have made but little progress until 1871, when M. Lodyguine showed an experiment in the Admiralty Dockyard in St. Peters. burg, when he divided the circuit into no less than two hundred lights. This naturally made a great sensation at the time-as great a sensation as that caused by Mr. Edison's telegram of the 7th ult. The Academy of Science awarded to M. Lodyguine the large Lomonossow prize of 50,000 roubles. A company was formed in St. Petersburg with a capital of 200,000 roubles, and the excitement in Europe was then almost as great as has been witnessed in England lately. It was soon found, however, that Lodyguine's discoveries, like those of his predecessors in the same field were, after all, impracticable, and that his illimitable division of the light, however ingenious, was only a fanciful experiment. Every penny subscribed to the company referred to was lost, and Lodyguine's great discovery is now, where it was then-in his laboratory.

It has, however, been urged that these early inventors of the electric light knew only of the galvanic battery as a generator of a powerful current, and that had they known of the Gramme machine, or other dynamo- or magneto-electric machine, the results might have been different. The remark, however, only applies to King and the improvers who immediately succeeded him. The great division of the light by Lodyguine, to which reference has just been made, was in a circuit produced by two "Alliance" machines. Even, however, if such were not the case, there are at present before the world, in more or less detail, four recent inventions for the production of a divided light by incandescence. These are the inventions of M. Reynier, of M. Arnaud, of Mr. Edison, and most recent of all, M. Werdermann. From the

way in which these discoveries-if they are discoveries have been ushered into the world, it is found that great claims are made on their behalf, and there are, therefore, naturally great expectations on the part of the public in regard to them. It cannot be urged now in mitigation of the shortcomings of the incandescent light, as it has been urged in the past, that it has not had a fair trial, on the ground that the lamps in existence were imperfect in conception, and complex in construction. The lamp of M. Reynier seems admirable in its way, and if light by incandescence were to be the light of the future, the claims of this lamp would have to be very carefully considered, and, in any case, it will certainly hold an important place in all investigations into the subject. The lamp of M. Werdermann appears to be identical in principle with, and only slightly different in detail from, that of M. Reynier, and we may fully expect that these inventors will have to come to terms with each other-so much alike are their inventions. Of the details of Mr. Edison's invention-if there are any, nothing is known beyond the fact stated in the Scientific American, that it is a light produced from a spiral of incandescent platinum; while the reports in the Anerican daily press show such an effervescent ignorance of the

fundamental principles both of electricity and of dynamics, that no reliance whatever can be placed upon them.

Experience, then, has shown that a light by incandescence comes before us in a very questionable shape, and it is essentially a light which discourages the notion of its practical application. The question indeed may be very properly asked: How is it that light by incandescence has always proved such an utter failure? It has had a period of thirty-three years in which to develop; it has been divided into various lesser lights, numbering from two to two hundred and it has arrested the attention and taxed the skill of the greatest electricians in the world. How is it that it is obliged to give way to light by the voltaic arc? The answer is at hand. The light by incandescence can only be obtained and divided by a great sacrifice of light and power. This is imperative from the fundamental principles of electrical science. The diminution according to the "square," and not according to simple proportion, applies to electricity just as it applies to light, heat, sound, gravitation, and other physical phenomena. Thus if a circuit be divided into two branches whose resistances are equal, a current of half the strength passes through each branch, producing at the point of resistance, not half the light, but only a quarter, because the effect follows the square of the current strength. If the current had been divided into three equal branches, in each branch only one-ninth part of the original light would be obtained, and so on; so that if an electric light of 1,000 candles were divided into ten equal lights, the result would be ten lights of ten candles each, instead of one of 1,000 candles. When this law is borne in mind, and when it is also remembered that to produce the electric light by incandescence at least one-half of the current is lost, it will easily be imagined what a wasteful light it is. Recent experiments prove this. It was recently stated, in reference to M. Werdermann's incandescent light, that he produced two lights of 320 candles each (total, 640 candles), with a prime mover of 2 horse-power; and this was considered a great result—as indeed it was for an incandescent light. But how this sinks into insignificance when compared with the results of lighting by the voltaic arc. A few days ago M. Rapieff, with two of his regulators and a small Gramme machine known as the M machine, and which M. Gramme says requires only 1 horse-power, produced two lights, which, when carefully measured by the photometer, were found to be each equal to 1,150 candles, or a total of 2,300 candles, while with one of M. Gramme's A machines, requiring 24 horse-power, a light of 6,000 candles can be obtained from one of M. Rapiefi's regulators. Some experiments detailed in M. Fontaine's book on "Electric Lighting" gave a similar result. M. Fontaine's experiments with an incandescent light show that, under the most favourable circumstances, with a Bunsen battery of forty-eight cells, eight inches high, the diminution of the sub-divided light was so great that, where he put five lights in one circuit, he only obtained a total illuminating power of a quarter of a burner, with four lamps only three-quarters of a burner, with two lamps six-and-a-half burners, and with one lamp fifty-four burners. These numbers give the following ratio: 1, 3, 8, 26, 216, thus showing how rapidly the light diminishes when divided. With the voltaic arc, however, and with the same battery, he was able, by a Serrin lamp, to obtain a light of 105 burners.

It will be seen, then, from what has been above stated, that the production and the divisibility of the light by incandescence practical application impossible for general lighting. If, thereis a very wasteful process-so wasteful, indeed, as to render its fore, all Mr. Edison has to announce to the world is that he has succeeded in dividing an incandescent light-and the announcement that such is so is made on authority-his discovery amounts to very little. Both the light and its divisibility were discovered long ago. It will easily be seen that it is not in that direction that any great practical results can be obtained. The voltaic and it is in its development that any real progress must be looked arc supplies the only divisible light of any utility and economy,

for.

WILLIAM TRANT

you will in fairness allow me to take advantage, to prove that your article does scant justice to Mr. Stearns' predecessors in the application of the duplex system to long submarine cables, and that their success has been something more than only partial" in the opinion of those who have employed their system.

Mr. Stearns' first success on a long cable dates from a few days ago. In February, 1876, Dr. Muirhead and myself obtained experimentally a perfect balance on the Suez-Aden cable, which, though shorter in miles, is electrically longer than either of the Anglo Company's cables from Valentia on which Mr. Stearns has worked.

In March of the same year Mr. J. Muirhead and myself duplexed the Marseilles-Malta cable, which, though only 825 miles in length, is worked by Sir W. Thomson's syphon recorder, and our system has been in commercial operation on the line ever since.

Early in 1877 Dr. Muirhead applied the system to the AdenBombay Cable, which is longer in miles and far longer electrically than either of the cables from Valentia, and since that time this line, as well as that from Suez to Aden, has been worked duplex" whenever the traffic required it, to the entire satisfaction of the company.

Next, as to your remark that "Mr. Muirhead has been at work duplexing the Direct United States Cable with some prospect of success," the facts of the case are these :

The cable, in its linear measurement, exceeds the longest Valentia cable by 543 miles; electrically it is twice as long.

It is worked with the mirror galvanometer, and not with the recorder, and these circumstances render the difficulty of obtaining a duplex balance upon it immensely greater than upon any of the other lines referred to.

Notwithstanding the difficulties mentioned, Dr. Muirhead and myself, in April last, obtained a perfectly satisfactory balance, enabling us to transmit sixteen words a minute in both direc tions at the same time, between Ireland and Nova Scotia, a cable distance of 2,420 nautical miles. HERBERT TAYLOR 7, Pope's Head Alley, Lombard Street

P.S.-Since writing the above my attention has been called to NATURE, vol. xv. p. 180, containing an article on this subject, in which the applications of Muirhead's system to some of the cables referred to in my letter are spoken of as being the first practical successes in submarine duplex telegraphy.

Remarkable Colour-Variation in Lizards

MR. WALLACE's observations in NATURE, vol. xix. p. 4, on a black variety of the common lizard of Capri, as met with on the neighbouring islet of Faraglioni, induces me to refer to a similar appearance in the lizards frequenting the islet of Filfla, on the southern coast of Malta. As recorded in my book, "Notes of a Naturalist in the Nile Valley and Malta," p. 80, I have stated that during a visit to Filfla I was surprised to find that all the lizards on the rock were a beautiful bronze black and so much tamer than their timider brethren on the mainland. Many individuals were so tame that they scrambled about our feet and fed on the refuse of our luncheon. I subsequently sent specimens of this variety, or rather race, to Dr. Günther, F.R.S., who pronounced them identical with the Podarcis muralis, so extremely plentiful in Malta and Gozo. Now although the denizens of the two latter islands present divers shades of colouring, I never observed (and I looked carefully during several years) a black or dark-coloured individual. Filfia is about 600 yards in circumference and three miles distant from Malta. It is formed of the upper miocene limestone, and marks an important fault or down-throw which runs along the coast of Malta opposite, by which, as seen in the sketches Figs. 1 and 2 of the work referred to, it appears clear that the severance took place long subse. quent to the days of the pigmy elephants, hippos, giant dormice and tortoises, whose remains have been found in such abundance in the crevices of the rocks opposite Filfla. There is no verdure on this bare rock-islet, the surface of which is darkcoloured, whilst its crevices shelter the lizards and furnish abodes for the nests of Manx and cenereous shearwaters, whose docility at the breeding season is equally remarkable, both reptile and birds being like their compeers of Enoch Arden's island, "so wild that they were tame."

Probably the dark colouring is protective, and thus consorting well with the surrounding surfaces, would tend to preserve them

from the harriers, buzzards, and hawks which tarry in the
Maltese Islands during the spring and autumn migrations
November II
A. LEITH ADAMS

THE remarkable case of local colour-variation in lizards communicated by Mr. A. R. Wallace to NATURE (vol. xix. p. 4), had already been investigated by Dr. Theodor Eimer, an abstract muralis cærulea, a Contribution to the Darwinian Theory," is or translation of whose memoir on the subject, entitled "Lacerta to be found in Ann. and Mag. Nat. Hist., 1875, 4th ser., vol. xvi. p. 234. J. WOOD-MASON 54, Claverton Street, S.W., November 16

The Drought

AT the present time, when more attention is paid to the influence of meteorological phenomena upon society, it would be useful to give some information as to the bearing of the local droughts and famines on our trade and the prospect of its revival. The China and Indian trades have not yet recovered. The droughts have also affected Egypt and Morocco. In the West Indies, Guiana, Venezuela, Colombia, and Brazil they are still operative.

They act to prevent the growth of produce, and in many countries, by reducing the water-ways, they impede its shipment. The people cannot consume our imports, the transit of which is in some cases impeded. The whole of these difficulties affects the exchanges and interferes with the money market and remittances.

The severity of the crisis is abating, but we can hardly feel assured of the revival of trade in Europe and the United States till there is a complete recovery over the vast areas of producing and consuming countries.

Thus the study of meteorological phenomena and facts acquires a new value for practical men and society at large, as stated by Prof. Jevons in your last number. HYDE CLARKE

Sewerage and Drainage

IN NATURE, vol. xix. p. 1, you touch upon a most important point in sanitary engineering which I have for ten years been striving by every means in my power to press upon the public, and I therefore venture to trouble you with a few lines on the subject.

The most important argument in favour of the exclusion of storm water from sewers consists, as you say, in the liability of road detritus to form deposits on the wide flat surface of any channels large enough to convey to one point an exceptionally heavy fall of rain over the area covered by a town, and the inevitably slow course of the infinitely smaller volume of sewage flowing or stagnating in dry weather along the same channels.

When separate sewers are provided for sewage they can be made of such smaller capacity as to keep up a constant flow from the houses in which the sewage is produced, to the land upon which it is to be purified, because the volume of liquid will very nearly correspond with the water supply, and the engineer has safe data upon which to adjust his means to the desired end.

In every town there are, or were, lines of natural watercourses, and if the scavengers' work is properly done the rain-water from roofs and streets may safely be discharged into any of these by short lengths of drains, less liable to be encumbered with deposits of road detritus, and with the certainty that if such ac cumulations should occur, they will be perfectly harmless from the absence of sewage.

The experiments of Mr. Way with London street water have been seized upon by Mr. Baldwin Latham in order to cover his retreat from the false position unfortunately taken up by himself and most of our senior engineers in the earlier days of sanitary science, and as he knows as well as any one else that it was a grand mistake to confuse and combine sewerage and drainage in one system, I agree with you in thinking it a pity that he has not acknowledged the facts more distinctly in the recent edition of his well-known work.

The greater proportion of the impurities detected by Prof. Way in the few samples of London street water which he tested are mineral ones which would be comparatively harmless, and, in the opinion of Dr. Voelcker, the experiments must have been vitiated by some mistake. Now as the latter authority has