could they encourage new studies, which could never lead those who were following them to any great pecuniary rewards, although they might lead them to the rewards of learning. He thought that was a great problem. This year they had an examination in Oriental languages. There was one candidate for it; they had four examiners, and the cost of that examination, he supposed, was £50 or £60 to the University, which was perfectly right. It was just those studies which could not pay their way, which could never be supported without the help of endowments. He did not think the problem was so serious as it might seem at first. Two years ago, when his predecessor, Dr. Butler, resigned his office, he pointed out some of the needs of the University. Dr. Butler's clear and lucid statement brought forth one magnificent gift and nothing more. He (the speaker) in his turn, in the first year of his office, sent forth "a bitter cry" of the needs of the University. Yet that bitter cry brought forth nothing. Did it seem possible that after all a general cry might not be specially efficacious, while a request for special help might serve for a cry? He was happy to say that this seemed at last to solve the problem of how they could develop the newer studies with the help of those outside who were willing to support them. The engineering school had, by the labours of Prof. Ewing and Mr. Horace Darwin, received money, which he hoped would carry it on sufficiently. He believed so ancient an institution as the Observatory of Cambridge was going to ask for a new telescope to carry on its work. That being so, it seemed that partially at least the problem was solved. The problem concerning agricultural science had been solved by the liberal aid of the County Councils. Those bodies had come to their aid in the most generous manner, and given them enough to carry on their work for at least some years. He hoped, as he said before, they would see their way, not merely to maintain and develop those old institutions which had been from all times the glory of Cambridge, but also to carry on those newer studies and newer developments which would keep them in touch with the nation, and make them remembered for all times, and which, whatever developments might arise elsewhere, would make Cambridge one of our greatest centres of educational life.

In proposing the " Health of the Master and Fellows," the Right Hon. T. H. Huxley, who was enthusiastically received, said he was charged with a very pleasant duty, and one which could be happily performed without either gifts of eloquence or even those of voice, in which unhappily he was at present sadly deficient, and he would not be withdrawn from the simple discharge of that duty by the invitation which had been addressed to him by a previous speaker to enter upon the field of controversy. În proper time and place he imagined that he could hardly be said to have shown any unwillingness for the discussion of controverted questions, but in his judgment they were extremely inappropriate and out of place in a meeting of that kind, and he desired absolutely to abstain from that, and to confine himself to the business in hand, which was of a far more pleasant, and, he ventured to think, more profitable nature: it was to propose to them the health of the Master and Fellows of that College. All those who were present would understand the gratitude which they all felt for the generous and gracious hospitality which they had shown to them on that occasion, but it was a traditional hospitality, and it went back to the time when that important corporation, of which they were the present representatives, extended their hospitality to William Harvey, whose name and fame they were met to celebrate. He did not know whether the Master and Fellows of that time were aware of what they were doing in training and disciplining that young man-boy, indeed, to them to make the best use of the faculties with which

he was endowed, but he thought it lay to their credit that from that time to this, the hospitality which they extended to science to biological science especially, and to that branch of it which was called the science of medicine very particularly-that that had been continued with unbroken openness and readiness. It was for that reason, he thought, that the large proportion of persons present in that room who were devoted to scientific studies would with the greatest possible cordiality drink the toast which he had to propose. For in this matter Gonville and Caius College occupied a position as isolated as it was honourable. He was aware that the studies of biological sciences, and more especially those which had relation to medicine, could not be cleared of the accusation then made against them of utility to mankind. He admitted to the full the charge that was made against those studies, but the present showed, and the future would show more strongly, that quite apart from the bearing of direct utility, it must be regarded as a happy instinct, if not as a purpose of intelligence, which had led that College for these 300 years to cherish and to promote those studies. It was on that ground they who were so deeply interested in its pursuits felt that they owed a debt of gratitude to the College, and he knew of no reason, except the fact that he once took an active part in those biological matters, which had led to his selection as proposer of the health of the College to them on that occasion. Sir James Paget had fully and exhaustively told them, in that admirable language which he had always at command, the great claims of Harvey upon their respect and veneration. He had justly told them that Harvey regarded himself, not merely as a discoverer, but_as a propounder and champion of a new method. Dr. Venn was good enough to tell him before the dinner of a fact of which he (the speaker) was entirely ignorant : that before Harvey's time that College possessed what was called an "anatomer," a gentleman whose duties appeared to have been to dissect bodies, which were given over to him and others, to give the students of the College a practical contact with the nature of things. It was in that respect that modern science differed from ancient science; it was in that respect that Harvey was essentially modern. It was therefore to the wise provision of the founders of that College that they owed the beginning of that movement commenced in this country by Gilbert, followed up in Italy by Galileo, followed up conscientiously here by Harvey himself, which had led to the great modern development of scientific culture. They trusted that the hospitality which had hitherto been extended by that College to purely scientific investigations would be continued upon the lines laid down by Harvey. It might be that Harveys existed among them now, and the only thing they had to hope for, and to wish for was, that those Harveys of the future might not be compelled, as the Harvey of the past, to obtain a higher scientific training by going to the University at Padua. They hoped that in this University men would have the opportunity of obtaining the highest scientific culture which was to be given. That he understood was the object and purpose and desire of the Master and Fellows of that College, in inviting persons like himself to take part in that great celebration; he presumed they wished them to understand that they recognised Science as a fundamental branch of human culture, and that they would do what in them lay to promote that happy commemoration to which he ventured to allude.

The toast was drunk with enthusiasm.

The Master briefly returned thanks, and stated that it had given them very sincere pleasure to entertain so illustrious an assembly, and expressed his deep regret that Sir George Paget was not with them.

The Rev. B. H. Drury proposed the health of the younger members of the College, saying that they were

the life-blood of their College to-day, the source of their vitality, without whom they would have really little cause for existence.

Mr. Keeble, Natural Science Scholar of the College, made a short and graceful reply.

At the conclusion of dinner a move was made to the Combination Room, where friendly and animated intercourse was kept up for some time, and it was late before the last of those engaged in the celebration separated for the night.

Breakfast was provided the following morning from eight to ten for those resident in College overnight, and by midday the guests had departed, leaving the courts once more to solitude, and to their hosts a keen feeling of satisfaction at the honour done to the memory of William Harvey and to the College by the recent presence of so representative and distinguished a gathering of visitors.

SOME POINTS IN THE PHYSICS OF GOLFA III.

IN N Part II of this paper (NATURE, Sept. 24, 1891) the following statements were made :"The only way of reconciling the results of calculation with the observed data is to assume that, for some reason, the effects of gravity are at least partially counteracted. This, in still air, can only be a rotation due to undercutting."

66

And, as a practical deduction from these principles, it would appear that, to secure the longest possible carry, the ball should be struck so as to take on considerable spin ———."

As these statements, and some of their consequences, have been strenuously denied, I must once more show at least the nature of the evidence for them

It depends, in one of its most telling forms, upon the contrast between the length of time a well-driven ball remains in the air (as if in defiance of gravity) and the comparatively paltry distance traversed. Every one who thinks at all on the subject must see that, without some species of support, the ball could not pursue for six seconds and a half a course of a mere 180 yards, nowhere more than 100 feet above the ground.

In fact, if we assume the initial slope of the path to be I in 4, as determined for the average of fine drives by Mr. Hodge with his clinometer (NATURE, Aug. 28, 1890) the carry of a non-rotating ball will be approximately (in feet)

AgT3,

where g is the acceleration due to gravity, T the time of flight in seconds, and A a numerical quantity depending on the resistance. The value of A varies continuously between the limits, 2 for no resistance, and I for infinitely great resistance. [It is assumed that the resistance is as the of the speed.] square

This formula gives, with the average observed value of T (65, see Part II.) carries varying from about 900 down to 450 yards! The initial speed required varies from 416 foot-seconds upwards. The longest actually measured carry on record, when there was no wind, is only 250 yards. Unfortunately, in that case T was not observed, but analogy shows that it was probably much more than 7. Even if we take it as 75 only, the carry" ought to have been, by the formula (which is based on the absence of rotation), 522 yards at the very least!

I have purposely, in this example, kept to the case of an initial slope of 1 in 4; because those (and they are many, some of them excellent golfers) who altogether reject the notion that undercutting lengthens the carry, would of course in consistency refuse to believe that a 1 Part of the substance of a paper on the Path of a Rotating Spherica! Projectile, read to the Royal Society of Edinburgh on June 5.

long ball may sometimes start horizontally. But, to those who allow this statement, the fact that the action of gravity is occasionally largely interfered with, or even counteracted, is obvious without any numerical calculations. In fact, from my present point of view, initial slope is of little importance:-except, of course, in avoiding hazards. The want of it is easily made up for by a slightly increased rate of spin.

Another way of looking at the matter is to assume, from Mr. Hodge's data, 180 yards as a really fine carry, and thence to calculate by the formula the requisite time of flight. It varies from 451 to 259 according as the resistance, and therefore the necessary initial speed, are gradually increased; the former from nil to infinity, thẻ latter from 132 foot-seconds upwards. Thus the observed time exceeds that which is really required when there is no spin, by 60 per cent. at the very least!

The necessity for underspin being thus demonstrated, we have next to consider how its effect is to be introduced in our equations. On this question I expressed a somewhat too despondent opinion in the previous part of this | paper. A rather perilous mode of argument (which i have since been able to make much more conclusive first suggested to me that the deflecting force, which is perrotation, must be at least approximately proportional to pendicular at once to the line of flight and to the axis of the speed and the angular velocity conjointly. But i tried (with some success) to verify this assumption by various experimental processes. These, as will be seen. deflecting force. [And I was greatly encouraged in this led also to a numerical estimate of the magnitude of the work by the opinion of Sir G. G. Stokes, who wrote:-"1 think your suggestion of the law of resistance a reasonable one, and likely to be approximately true." This is quite as much as I could have hoped for.]

:

First by the well-known phenomena called heeling, toeing, and slicing, which are due to the ball's rotation about a vertical axis. I have often seen a well-sliced ball, after steadily skewing to the right through a carry of 150 yards or even less, finally move at right angles to its initial direction, and retain very considerable spin when it reached the ground. Neglecting the effects of gravity, the equations of the path should be, in such a case,

Thus it is clear that we may easily produce rotation enough in a golf-ball to make the value of ko as great as 03 or even o 4. And this can, of course, be greatly increased when desired. This datum will be utilised later. The fact (noticed above) that the time of flight, and the carry, are both reduced by slicing, gives another illustration of the necessity for underspin when the time of flight is to be long, and the carry far.

Secondly by a laboratory experiment which, I have only recently learned, is due in principle to Robins. (An Account of Experiments relating to the Resistance of the Air. R.S. 1747.) I suspended a wooden shell, turned very thin, by a fine iron wire rigidly fixed in it, the other end of the wire being similarly attached to the lower end of a vertical spindle which could be made to rotate at any desired rate by means of multiplying gear. Thin as was the wire, it was but slightly twisted in any of the experiments, so small was the moment of inertia of the wooden shell. The wire acted as a universal flexure joint; and, by lengthening or shortening it I could make the ball's mean speed, in small pendulum-oscillations, vary within considerably wide limits. I verified this result by substituting for the shell a leaden pellet of equal mass but of far smaller radius, as I feared that some part of the result might be due to stiffness of the wire, produced by torsion. But with the pellet the rotation of the orbit was exceedingly slow. Thus w, and the average value of 3, could have any assigned values; and from the elli tic form and the rate of rotation of the orbit of the ball, the transverse force was found to be proportional to either of them while the other was kept constant. An exceedingly interesting class-illustration can be given by making the ball revolve as a conical pendulum, and while it is doing so giving it spin alternately with, and opposite to, the direction of revolution. The effects on the dimensions of the orbit and on the periodic time are beautifully shown. This form of experiment could be easily applied to considerable speeds, both of the translation and of rotation, if the use of a proper hall could be secured. But it cannot be made strictly comparable with the case of a golf-ball; as the speed of translation can never much exceed that for which the resistance is as its first power only. [Robins' suspension was bifilar, and the rotation he gave depended more on the twisting of the two strings together than on the torsion of either. In this mode of arrangement it is difficult to measure the rate of spinning of the bob, and almost impossible to vary it at pleasure.]

We must next say a few words as to the manner in which the spin, thus proved to have so much influence on the length of the carry, is usually given. I pointed out, in the earliest article I wrote on the subject, "The Unwritten Chapter on Golf" (Scotsman, Aug 31, or NATURE, Sept. 22, 1887), that spin is necessarily produced when the direction of motion of the club head, as it strikes the ball, is not precisely perpendicular to the face. Now, even when the head is not purposely laid a ittle back in addressing the ball, (many of the longest drivers do this without asking Why) it must always become 50 in the act of striking if the player stand ever so little behind the ball --especially if, as Mr. Hutchinson so strongly urges upon him, he makes the path of the head at striking as nearly straight as possible. Mr. Hutchinson gives a highly specious, but altogether fanciful, reason

for this advice. We now see why the suggestion is a really valuable one. A "grassed" club, and especially a spoon, gives this result more directly. As soon as I recognised this, I saw that it furnished an explanation of a fact which had long puzzled me :-viz. that one of my friends used invariably to call for his short spoon when he had to carry a bunker, so distant that it appeared impossible of negotiation by anything but a play-club. And, if the ball be hit ever so little under the level of its centre, with the upper edge of the face, very rapid underspin may be produced. This was probably at least one of the objects aimed at (however unwittingly) by the best club makers of last generation, for they made the faces of drivers exception lly narrow. Some time ago I proposed, with the same object in view, to bevel the face by deeply rasping off both its upper and lower edges: -thus in addition saving the necessity for the "bone."

I have neither leisure nor inclination to attempt (for the present at least) more than a first approximation to the form of the path under the conditions just pointed out. Anything further would involve a laborious process of quadratures, mechanical or numerical, only to be justified by the command of really accurate data as to the values of a and V. I shall therefore at once assume that neither gravity nor the spin affects the translatory speed of the ball. (If the spin have such an effect, it will be taken account of sufficiently by a slight change in the constant of resistance; and the effect of gravity on a low trajectory is mainly to produce curvature which, in this case, is to a great extent counteracted by the spin. It is easy to see that the effects of this ignoration of gravity, in the tangential equation of motion, are to make the path rise a little too slowly at first, then too fast; to make it rise too high, and descend at too small a slope.) Hence we may keep the first equation of motion above, and write the second as

fault. I regret this for the additional reason that I should have liked to add an illustration of an extremely exaggerated path in which e is (say) zero, and k unity at the least. Under conditions of this kind there might be kinks in the path! For a similar reason I cannot attempt to work out the effect of wind with any attempt at precision, at least in the case when the drive is against the wind and the upward concavity of the path becomes in consequence much more prominent. It is easy in every case to form the more exact equations, but the labour of treating them even to a rough approximation would be considerable.

Next, with each pair of these numbers, and with the successive values,, and o for e, I found k from the condition that yo for x = 540. These values of k are of course greater as e is less, and also as a is less. But all are found to lie between the limits derived, above, from the data for a sliced ball. All the constants being thus found, the curves were easily traced by a few points--and the position of the maximum ordinate was found as above. For contrast, I have put in (dotted) the paths of drives corresponding in all respects with the others, except the absence of rotation. Poorly as these show, they are probably unduly favoured at the expense of the others, as I have taken a the same for each of the group; though it is probably reduced by the spin, so that rotation increases the direct resistance. The comparison of these with those in which rotation has a share shows that, though strength and agility are undoubtedly of importance in long-driving, even a store of these qualities equalling in amount that of a full-sized tiger is comparatively inefficient as against the skill which imparts a sound undercut. For here, as elsewhere, the race is not to the swift, nor the battle to the strong. Craft beats Kraft all the world over! La Puissance! ce n'est pas frapper fort, mais frapper juste !

From the very nature of the process I used in approximating, none of these curves can be quite trustworthy, those giving the greater elevations being most at

I am engaged at present in endeavours to find something like a proper value of a, or of V, above; so as to have reasonable confidence in my data before I engage in what promises to be a heavy task. Of course, if I can obtain a satisfactory value of one of them, that of the other would follow. But independent determinations of both would enable me to subject the theory to the most complete test imaginable. I am inclined to think that the value of a (280 feet), which I calculated from Bashforth's data, is too large (i.e. it makes the resistance too small) for a golf-ball:-and thus that the true path is intermediate in form between those of the first and of the second series in the cut. For the initial speeds required, even with a = 270, to give a carry of 540 feet without spin, are 462 and 653 foot-seconds for slopes of I in and 1 in 8 respectively :-the corresponding times of flight being only 357 and 256.

NOTES.

P. G. TAIT.

WE are glad to record that the Council of the Imperial University of Kasan has elected Prof. J. J. Sylvester honorary member of the University.

THE Albert Medal of the Society of Arts for the present year has been awarded to Sir John Bennet Lawes and a like medal

to Mr. John Henry Gilbert "for their joint services to scientific agriculture, and notably for the researches which throughout a period of fifty years have been carried on by them at the experimental farm, Rothamsted.”

PROF. W. H. PICKERING, the Director of the Harvard College Mountain Observatory at Arequipa, is expected to be in London in the course of a few days.

THE distribution of prizes to the students of Charing Cross Hospital Medical School will take place at the School on July 4, at three o'clock precisely. The Right Hon. the Baron de Worms, M.P., F.R.S., will occupy the chair.

THE Dental Hospital of London will hold a conversazione at the Royal Institute Galleries, Piccadilly, on July 14. There will be a distribution of prizes at 8.30 p.m. by Prof. Sir W. H. Flower, K.C.B., F.R.S.

ACCORDING to Dalziel's agency, a cyclone passed over Williamstown and its immediate vicinity on June 21. Its path was six miles long by half a mile wide, and in this track not a house, barn, or tree was left standing. The wind rush was followed by a terrific downpour of rain. About twenty persons lost their lives.

DR. NANSEN and the members of his expedition to the North Pole sailed from Christiania on Saturday, and arrived at Laurvig on the following day. After taking on board two covered boats, to be used in case the members of the expedition are compelled to leave the Fram in the ice, the vessel proceeded on her voyage. Reuter says that intelligence has been received from Siberia that twenty-six dogs, for service with the expedition, have been brought down to the mouth of the River Olensk. Parties have been sent out to leave stores of provi. sions for twelve men at two places on the islands of Kotelnoi and Liakow. These depots will be inspected in 1894 and 1895. Sealers report that the sea around these islands was quite open in 1888, 1889, and 1890, while in 1891 and 1892 there was little ice in the vicinity.

INFORMATION with regard to the social, physical, and mental condition of children is being accumulated by the committee appointed by the International Congress of Hygiene and Demography. Nearly 30,000 children, chiefly in London Board Schools, have been inspected, and important facts have been obtained as to the variation of educational requirements of boys and girls, and the causes of low mental development. It is desired to extend the inquiry among 100,000 children before submitting the statistics to a complete investigation. For this purpose Sir Douglas Galton, writing from the Parkes Museum, has made an appeal for financial help. The deep importance of the work is fully understood by educationalists, hence there should be no difficulty in obtaining sufficient funds to render the investigation as comprehensive as possible.

A SPECIAL general meeting of the Royal Geographical Society will be held on July 3 in the hall of the University of London, Burlington Gardens, to consider the proposal that ladies should be admitted as ordinary Fellows. On the evening of the same day the Earl of Dunmore will give a paper on his "Journeys in the Pamirs and Central Asia."

DR. M. MOBIUS, of Heidelberg, has been appointed Director of the Botanic Gardens at Frankfort-a-M., and Dr. F. Pax, Director of the Botanic Garden at Breslau.

THE French Academy has awarded the Prix Desmazières to M. P. Viala, for his researches on viticulture; the Prix Montagne to M. l'Abbé Hue, for his work in lichenology; and

the Prix de la Fons Mélicocq to M. Maseleff, for his work on the Botanical Geography of the north of France.

SOME interesting scientific documents changed hands at the sale this week of the library of the late Lord Brabourne. Among the lots was a quantity of the correspondence of Sir Joseph Banks, to whom Sir Edward Knatchbull, Lord Brabourne's father, was executor. An interesting autograph letter from John Hunter, dated 1792, appears to be one covering the despatch to the Royal Society of his paper on the natural history of the common bee. He hopes Sir Joseph and his worthy council will think the results of twenty years of observation and experiment suitable for publication in the transactions, and details some of the obstacles which had prevented an earlier forwarding of the paper. About 1830 the Royal Society claimed and received from Sir Edward Knatchbull the letters and papers of Sir Joseph Banks, referring to the society over which he so long presided, but evidently this particular letter was overlooked. A document, apparently in the handwriting of Duhamel du Monceau, is an appeal to Sir Joseph on behalf of Dolomieu, the French mineralogist, imprisoned at Messina, by order of the Neapolitan Court, as he was returning to Europe from serving on the scientific staff which accompanied Bonaparte's expedition to Egypt. It is signed by thirty-nine famous men of science of the time, including Cuvier, Lamarck, Laplace and Lalande.

THE weather during the past week has been of a decidedly unsettled type. On Thursday, the 22nd inst., a depression advanced over Scotland and moved slowly to the North Sea and Norway, causing some rain over most parts of these islands; in the north-east of Scotland the fall amounted to 2:2 inches in forty-eight hours, and a moderate gale blew from the northwest on our northern coasts. During the early part of the present week important depressions advanced over the western parts of the country from off the Atlantic, causing exceptionally heavy rain in the south of Ireland, the fall at Roche's Point on Tuesday morning registering II inch, while the amount was very considerable in many other parts of the kingdom. During the first part of the period the temperature was from 25° to 30° lower than in the previous week; the maxima rarely reached 70° in any part of the country, while in the north the highest daily readings were frequently below 60°, but on Tuesday the temperature rose considerably in most parts, and reached 80° at Cambridge. The Weekly Weather Report of the 24th inst. showed that the rainfall exceeded the mean in the east of Scotland only. Bright sunshine was above the average in Ireland and the greater part of England; the percentage of possible duration amounted to 77 in the Channel Islands.

MR. W. H. PREECE, F. R. S., in giving evidence before the joint committee of Lords and Commons on Electric Powers Protective Clauses, is reported to have shown a series of diagrams illustrating the effect upon the earth of the City and South London Electric Railway. That railway did not designedly use the earth, but the return circuit was made by means of the rails, and also by the tubes or tunnels. Currents were produced which had disturbed the observing instruments at Greenwich, and which had been traced as far as North Walsham, in Norfolk. Last year the disturbances began to increase, and his attention was called to the fact that in Clapham Road there was a chemist who had in his shop window an instrument for recording the passing movement of every train on the electric railway, the instrument being connected on one side with gas-pipes, and on the other with water-pipes in the house. He had caused the currents to be measured, and they were found to be sufficient to light a lamp or, as he had proved, to ring one of the division bells of the House of Commons. Another difficulty had occurred n connection with the railway block system. Some years ago

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