Lord Kelvin Part 15

The sounding machine is also well known. At first pianoforte wire was used for deep-sea sounding by Commodore Belknap of the U.S. Navy, and by others, on Sir William Thomson's recommendation. Finally, a form of machine was made by which a sinker could be lowered to the bottom of the sea and brought up again in a few minutes; so that it was possible to take a sounding without the long delay involved in the old method with a reel of hemp-rope, which often tempted shipmasters to run risks of going ash.o.r.e rather than stop the ship for the purpose. The wire offered little resistance to motion through the water, and by a proper winding machine, with brake to prevent the wire from running out too fast and kinking, when it was almost certain to break, one man could quickly sound and heave up again, while another attended to the wire and sinker.

A gauge consisting of a long quill-tube closed at the upper end, and coated inside with chromate of silver, showed by the action of the sea-water on the coating how far the water had pa.s.sed up the tube, compressing the air above it; and from this, by placing the tube along a wooden rule properly graduated, the depth was read off at once. With the improved machine a ship approaching the sh.o.r.e in thick weather could take soundings at short intervals without stopping, and discover at once any beginning of shallowing of the water, and so avoid danger.

The single wire is not now used, as a thin stranded wire is found safer and quite as effective. The gauge also has been improved. The apparatus can be seen in any well-found sea-going vessel; though there are still, or were until not very long ago, steam vessels without this apparatus, though crossing the English Channel with pa.s.sengers. These depended for soundings on the obsolete hemp-rope, wrapped round an iron spindle held vertically on the deck by members of the ship's company, while the cord was unwound by the descent of the sinker.[24]

Sir William Thomson's electrical and other inventions are too numerous to specify here, and they are in constant use wherever precision of measurement is aimed at or required. Long ago he invented electrometers for absolute measurements of electrical potential ("electric pressure"); more recently his current-balances have given the same precision to electrodynamic measurement of currents. All his early instruments were made by Mr. James White, Glasgow. The business founded by Mr. White, and latterly carried on at Cambridge Street, has developed immensely, and is now owned by a limited liability company--Messrs. Kelvin and James White (Limited).

For many years Sir William Thomson was a keen yachtsman, and his schooner yacht, the _Lalla Rookh_, was well known on the Clyde and in the Solent. An expert navigator, he delighted to take deep-sea voyages in his yacht, and went more than once as far as Madeira. Many navigational and hydrodynamical problems were worked out on these expeditions. For a good many years, however, he had given up sea-faring during his times of relaxation, and lived in Glasgow and London and in Largs, Ayrshire, where he built, in 1875, a large and comfortable house, looking out towards the Firth and the Argyleshire lochs he knew and loved so well.

In the course of his deep-sea expeditions in his yacht he became impressed with the utility of Sumner's method of determining the position of a ship. Let us suppose that at a given instant the alt.i.tude of the sun is determined from the ship. The Greenwich meantime, and therefore the longitude at which the sun is vertical, is known by chronometer, and the declination of the sun is known from the Nautical Almanac. The point on the earth vertically under the sun can be marked on the chart, and a circle (or rather, what would be a circle on a terrestrial globe) drawn round it from every point of which the sun would have the observed alt.i.tude. The ship is at a point on this circle.

Some time after the alt.i.tude of the sun is observed again, and a new "circle" is drawn. If the first "circle" be bodily shifted on the chart along the distance run in the interval, it will intersect the second in two points, one of which will be the position of the ship, and it is generally possible to tell which, without danger of mistake.

Sir William Thomson printed tables for facilitating the calculations in the use of Sumner's method, and continually used them in his own voyages. He was well versed in seamanship of all kinds, and used his experience habitually to throw light on abstruse problems of dynamics.

Some of these will be found in "Thomson and Tait"; for instance, in Part I, -- 325, where a number of nautical phenomena are cited in ill.u.s.tration of an important principle of hydrodynamics. The fifth example stated is as follows: "In a smooth sea, with moderate wind blowing parallel to the sh.o.r.e, a sailing ship heading towards the sh.o.r.e, with not enough of sail set, can only be saved from creeping ash.o.r.e by setting more sail, and sailing rapidly towards the sh.o.r.e, or the danger that is to be avoided, so as to allow her to be steered away from it. The risk of going ash.o.r.e in fulfilment of Lagrange's equations is a frequent incident of 'getting under way' while lifting anchor or even after slipping from moorings."

His seamanship was well known to shipmasters, with whom he had much intercourse, and whose intelligence and practical skill he held in very high regard.

CHAPTER XVI

LORD KELVIN IN HIS CLa.s.s-ROOM AND LABORATORY

It is impossible to convey to those who never studied at Glasgow any clear conception of Thomson as he appeared to students whom he met daily during the session. His appearance at meetings of the British a.s.sociation, and his vivacious questionings of the various authors of papers, his absorption in his subject and oblivion to the flight of time when he read a paper himself, will long be remembered by scientific men: but though they suffice to suggest what he was like in his own lecture-room, the picture lacks the setting of furniture, apparatus, a.s.sistants, and students, which all contributed to the unique impression made by his personality on his pupils. The lecture-table--with long straight front and ends refracted inward, flanked by higher small round tables supported on cylindrical pillars--laden with instruments; the painted diagrams of the solar spectrum and of the paths of coloured rays through a prism, hung round the walls; the long wire with the cylindrical vibrator attached, for experiments on torsion, and the triple spiral spring vibrator, which hung at the two ends of the long blackboard; the pendulum thirty feet long, consisting of a steel wire and a twelve-pound cannon-ball as bob, suspended from the apex of the dome-roof above the lecture-table; the large iron wheel in the beautiful oriel window on the right of the lecturer, and the collection of optical instruments on the table in front of the central window s.p.a.ces, from which the small iron-framed panes--dear to the heart of the architect--had been removed; the clock on either side of the room, one motionless, the other indicating the time, and having attached to it the alarm which showed when the "angry bell" outside had ceased to toll; the ten benches of eager and merry students, which filled the auditorium; all these combined to form a scene which every student fondly recalls, and which cannot be adequately described. A similar scene, with some differences of arrangement and having its own particular a.s.sociations, will occur to every student who attended in the Old College.

The writer will never forget the lecture-room when he first beheld it, from his place on Bench VIII, a few days after the beginning of session 1874-5. Sir William Thomson, with activity emphasised rather than otherwise by his lameness, came in with the students, pa.s.sed behind the table, and, putting up his eye-gla.s.s, surveyed the apparatus set out.

Then, as the students poured in, an increasing stream, the alarm weight was released by the bell-ringer, and fell slowly some four or five feet, from the top of the clock to a platform below. By the time the weight had descended the students were in their places, and then, as Thomson advanced to the table, all rose to their feet, and he recited the third Collect from the Morning Service of the Church of England. It was the custom then, and it is still one better honoured in the observance than in the breach (which has become rather common) to open all the first and second cla.s.ses of the day with prayer; and the selection of the prayers was left to the discretion of the professors. Next came the roll-call by the a.s.sistant; each name was called in its English, or Scottish (for the clans were always well represented) form, and the answer "adsum" was returned.

Then the Professor began his lecture, generally with the examination of one of the students, who rose in his place when his name was called.

Thomson, as the quotation in Chapter VI from the Bangor Address shows, was fond of oral examination, and after the second hour had begun to decline as one of regular attendance, habitually devoted ten or fifteen minutes to asking questions and criticising the answers. The names of the students to be questioned were selected at random from the cla.s.s register, or by a kind of lottery, carried out by placing a small card for each student in a box on the table, and drawing a name whenever a member of the cla.s.s was to be examined. The interest in the drawing each day was intense, for there was a glorious uncertainty as to what might be the line of examination adopted. Sometimes, in the midst of a criticism of an answer, an idea would suddenly occur to the Professor, and he would enlarge upon it, until the forgotten examinee slipped quietly back into his seat, to be no more disturbed at least for that day! And how great the relief if the ordeal was well pa.s.sed and the card was placed in that receptacle of the blessed, the compartment reserved for those who had been called and duly pa.s.sed the a.s.size! But there was a third compartment reserved for the cards of those unfortunates who failed to satisfy the judge! The reader may have antic.i.p.ated the fact that the three divisions of this fateful box were commonly known to students by the names of the three great habitations of spirits described in the _Divina Commedia_ of Dante.

As has been stated, the oral examination with which the lectures opened was the cause of a good deal of excitement, which was added to by the element of chance introduced by drawing the names from the purgatorial compartment of the box. The ordeal was dreaded by backward students, whom Thomson found, as he said, aphasic, when called on to answer in examination, but who certainly were anything but aphasic in more congenial circ.u.mstances. Occasionally they abstained from responding to their names, modestly seeking the seclusion of the crowd, and some little time would be spent in ascertaining whether the examinee-designate was present. When at last he was discovered, he generally rose with a fervent appeal to his fellows on either side to help him in his need.

McFarlane used to tell of an incident which ill.u.s.trated the ingenuity with which it was sometimes attempted to evade the ordeal of the _viva voce_ examination. One afternoon, when he was busily preparing the lecture-ill.u.s.trations for next day, a student came into the cla.s.s-room, and engaging him in conversation on some point of dynamics, regarding which he professed to have a difficulty, hovered round the box which contained the three compartments popularly known as Purgatory, Heaven, and h.e.l.l! Always when McFarlane left the room to bring something from the adjoining cabinet of apparatus, he found, when he returned, his inquiring friend hurriedly quitting the immediate vicinity of the box.

At last the student took leave, with many apologies for giving so much trouble. As McFarlane suspected would be the case, the ticket bearing the name of that student was no longer to be found! He used to conclude the story as follows: "I just made a new ticket for him, and placed it on the top of the other tickets, and next day Sir William called him, the very first time." What were his feelings, who had fondly thought himself safe for the session, and now found himself subjected to a "heckling" which he probably expected would be repeated indefinitely, may be imagined.

The subject of the first lecture which the writer attended was simple harmonic motion, and was ill.u.s.trated by means of pendulums, spiral springs with weights, a long vertical rod of steel tipped with an ivory ball and fastened to a heavy base, tuning-forks, etc.

The motion was defined as that of a particle moving along the diameter of a circle--the "auxiliary circle," Thomson called it--so as always to keep pace, as regards displacement in the direction along that diameter, with a particle moving with uniform speed in the circle. Then the velocity and acceleration were found, and it was shown that the particle was continually accelerated towards the centre in proportion to the distance of the particle from that point. The constant ratio of acceleration to displacement was proved to be equal to the square of the angular velocity in the auxiliary circle, and from this fact, and the particular value of the acceleration when the particle was at either end of its range of motion, an expression for the period in terms of the speed and radius of the auxiliary circle was deduced. Then the ordinary simple pendulum formula was obtained.

This mode of treatment of an elementary matter, so entirely different from anything in the ordinary text-books, arrested the attention at once, and conveyed, to some at least of those present, an idea of simple harmonic motion which was directly applicable to all kinds of cases, such as the motion of the air in a sound wave, or of the medium which conveys the waves of light.

The subject of Kepler's laws was dealt with in the early lectures of every course, and Newton's deductions were insisted on as containing the philosophy of the whole question, leading, as they did, to the single principle from which the laws could be deduced, and the third law corrected when the ma.s.s of the planet was comparable with that of the sun. Sometimes Thomson would read the remarkable pa.s.sage in Hegel's Logik, in which he refers to the Newtonian theory of gravitation and says, "The planets are not pulled this way and that, they move along in their orbits like the blessed G.o.ds," and remark upon it. On one occasion his remark was, "Well, gentlemen, if these be his physics, what must his metaphysics be?" And certainly that a philosopher should deny, as Hegel seemed to do, all merit to the philosophical setting in which Newton placed the empirical results of Kepler, is a very remarkable phenomenon.

The vivacity and enthusiasm of the Professor at that time were very great. The animation of his countenance as he looked at a gyrostat spinning, standing on a knife-edge on the gla.s.s plate in front of him, and leaning over so that its centre of gravity was on one side of the point of support; the delight with which he showed that hurrying of the precessional motion caused the gyrostat to rise, and r.e.t.a.r.ding the precessional motion caused the gyrostat to fall, so that the freedom to "precess" was the secret of its not falling; the immediate application of the study of the gyrostat to the explanation of the precession of the equinoxes, and ill.u.s.tration by a model of a terrestrial globe, arranged so that the centre should be a fixed point, while its axis--a material spike of bra.s.s--rolled round a horizontal circle, the centre of which represented the pole of the ecliptic, and the diameter of which subtended an angle at the centre of the globe of twice the obliquity of the ecliptic; the pleasure with which he pointed to the motion of the equinoctial points along a circle surrounding the globe on a level with its centre, and representing the plane of the ecliptic, and the smile with which he announced, when the axis had rolled once round the circle, that 26,000 years had elapsed--all these delighted his hearers, and made the lecture memorable.

Then the gyrostat, mounted with its axis vertical on trunnions on a level with the fly-wheel, and resting on a wooden frame carried about by the professor! The delight of the students with the quiescence of the gyrostat when the frame, gyrostat and all, was carried round in the direction of the spin of the fly-wheel, and its sudden turning upside down when the frame was carried round the other way, was extreme, and when he suggested that a gyrostat might be concealed on a tray of gla.s.ses carried by a waiter, their appreciation of what would happen was shown by laughter and a tumult of applause.

Some would have liked to follow the motions of spinning bodies a little more closely, and to have made out clearly why they behaved as they did.

Apparently Thomson imagined the whole affair was self-evident, for he never gave more than the simple parallelogram diagram showing the composition, with the already existing angular momentum about the axis of the top, of that generated about another axis, in any short time, by the action of gravity.

As a matter of fact, the stability and instability of the gyrostat on the tray give the best possible ill.u.s.tration of the two different forms of solution of the differential equation, [:?] + ? = 0, according as is positive or negative; though it is also possible to explain the inversion very simply from first principles. All this was no doubt regarded by Thomson as obvious; but it was far from being self-evident to even good students of the ordinary cla.s.s, who, without exception, were beginning the study of dynamics.

Thomson's absorption in the work of the moment was often very great, and on these occasions he much disliked to be brought down to sublunary things by any slight mischance or inconvenience. Examples will occur to every old pupil of the great emphasis with which he commanded that precautions should be taken to prevent the like from happening again.

Copies of Thomson and Tait's _Natural Philosophy_--"T and T'" was its familiar t.i.tle--and of other books, including Barlow's Tables and other collections of numerical data, were always kept on the lecture-table.

But occasionally a laboratory student would stray in after everything had been prepared for the morning lecture, and carry off Barlow to make some calculation, and of course forget to return it. Next morning some number would be wanted from Barlow in a hurry, and the book would be missing. Then Thomson would order that Barlow should be chained to the lecture-table, and enjoin his a.s.sistant to see that that was done without an hour's delay!

On one occasion, after working out part of a calculation on the long fixed blackboard on the wall behind the table, his chalk gave out, and he dropped his hand down to the long ledge which projected from the bottom of the board to find another piece. None was just there; and he had to walk a step or two to obtain one. So he enjoined McFarlane, his a.s.sistant, who was always in attendance, to have a sufficient number of pieces on the ledge in future, to enable him to find one handy wherever he might need it. McFarlane forgot the injunction, or could not obtain more chalk at the time, and the same thing happened next day. So the command was issued, "McFarlane, I told you to get plenty of chalk, and you haven't done it. Now have a hundred pieces of chalk on this ledge to-morrow; remember, a hundred pieces; I will count them!" McFarlane, afraid to be caught napping again, sent that afternoon for several boxes of chalk, and carefully laid the new shining white sticks on the shelf, all neatly parallel at an angle to the edge. The shelf was about sixteen feet long, so that there was one piece of chalk for every two inches, and the effect was very fine. The cla.s.s next morning was delighted, and very appreciative of McFarlane's diligence. Thomson came in, put up his eye-gla.s.s, looked at the display, smiled sweetly, and, turning to the applauding students, began his lecture.

From time to time there were special experiments, which excited the interest of the cla.s.s to an extraordinary degree. One was the determination of the velocity of a bullet fired from a rifle into a Robins ballistic pendulum. The pendulum, consisting of a ma.s.sive bob of lead attached to a rigid frame of iron bars turning about knife-edges, was set up behind the lecture-table, and the bullet was fired by Thomson from a Jacob rifle into the bob of the pendulum. The velocity was deduced from the deflection of the pendulum, its known moment of inertia about the line of the knife-edges, the distance of the line of fire from that line, and the ma.s.s of the bullet.

In some of the notices of Lord Kelvin that have appeared in the newspapers, the imagination of the writers has converted the Jacob rifle into one which Professor Thomson carried in the early years of the volunteer movement, as a member of a Glasgow corps. It is still used in the Natural Philosophy Department for the same experiment, and is a muzzle-loading rifle of large calibre, which throws an ounce bullet. It was invented by the well-known Indian sportsman, Colonel Jacob, for big-game shooting in India. Thomson held a commission as captain in the K (or University) Company of rifle volunteers, and so did not shoulder a rifle, except when he may have indulged in target practice.

The front bench students were always in a state of excitement, mingled in some cases perhaps with a little trepidation. For the target was very near them, and though danger was averted by placing a large wooden screen in front of the bob, to prevent splinters of the bullet from flying about in the event of its missing the target and striking the iron casing of the bob, there was a slight amount of nervousness as to what might happen. The rifle, loaded by McFarlane, who had weighed out the charge of powder (so many drams) from a prescription kept in a cavity of the stock, was placed on the table, and two rests, provided with V notches to receive the rifle, were placed in the proper position to enable a bull's eye to be obtained. Thomson generally produced a small box of cotton wool, and inserted a little in each of his ears to prevent injury to the tympanum from the report, and advised the spectators to do the same. Then, adjusting his eye-gla.s.s, he bent down, placed the rifle in position, and fired, and the solemn stillness with which the aiming and adjustments had been witnessed was succeeded by vociferous applause. The length of tape drawn out under a light spring was read off by McFarlane, who had already placed on the blackboard the formula for calculation of the velocity, with the factor by which the length of tape had to be multiplied to give the velocity in feet per second. Then, with the intimation that a question involving numerical calculation would be set on the subject, in the ensuing Monday morning examination paper, the lecture generally closed, or was rounded off with some further observations on angular (or, as Thomson always preferred to call it, moment of) momentum.

Long after in the course of a debate in the House of Lords on a proposal to make the use of the metric system of weights and measures compulsory, Lord Kelvin told their lordships how he had weighed out the powder to charge this rifle, and, mistaking the weights, had loaded the rifle with an amount of powder which would have been almost certain to burst the piece, but had happily paused before firing it off.

He often interrupted the course of a lecture with a denunciation of the British "no-system of weights and measures"--"insane," "brain-wasting,"

"dangerous," were among the mildest epithets he applied to it, and he would deeply sympathise with the student whose recollection of avoirdupois weight, troy weight, apothecaries' weight, etc., was somewhat hazy. The danger of the system consisted mainly in the fact that the apothecaries' dram is 60 grains, while the avoirdupois dram is 27? grains. Thus so many drams of powder required to charge a rifle is a very much larger quant.i.ty when reckoned in apothecaries' drams than when reckoned in avoirdupois. As a rule he left the loading of the rifle, like all the other lecture-room experiments, to his a.s.sistants.

Another experiment which caused a great sensation was that known as the "dewdrop"! A funnel of bra.s.s, composed of a tube about 30 inches long and an inch wide, and a conical mouth about ten inches wide, had a piece of stout sheet India-rubber stretched, as tightly as it could be by hand, across its mouth, and made water-tight by a serving of twine and cement round the edge. A wire soldered round the outside of the lip gave a good hold for this serving and made all perfectly secure. On the plane surface of the sheet geometrical figures were drawn in ink, so that their distortion could be afterwards studied. The funnel was then hung by a strong support in an inverted position behind the table, and water poured gently into it from a rubber supply pipe connected with the water-main. As the water was allowed to acc.u.mulate--very slowly at first--the sheet of rubber gradually stretched and bulged out, at first to a flat lens-shape, and gradually more and more, till an immense water-drop had been formed, 15 or 18 inches in horizontal diameter, and of still greater vertical dimensions. The rubber film was now, at the place of greatest tension, quite thin and transparent, and its giving way was antic.i.p.ated by the students with keen enjoyment. A large tub had been placed below to receive the water, but the deluge always extended over the whole floor s.p.a.ce behind the table, and was greeted with rapturous applause.

Before the drop burst, and while it was forming, Thomson discoursed on surface tension, emphasising the essential difference between the tension in the rubber-film and the surface-film of a dewdrop, and pointing out how the geometrical figures had changed in shape. Then he would poke it with the pointer he held in his hand, and, turning to the cla.s.s, as the ma.s.s quivered, remark, "The trembling of the dewdrop, gentlemen!"

Vibrations of elastic solids were ill.u.s.trated in various ways, frequently by means of a symmetrical shape of calves'-foot jelly, at the top of which a coloured marble had been imbedded as a molecule, the motions of which could be followed. And then he would discourse on the Poisson-Navier theory of isotropic solids, and the impossibility of the fixed relation which that theory imposed between the modulus of rigidity and the modulus of compression; and refer with approval to the series of examples of "perfectly uniform, h.o.m.ogeneous, isotropic solids," which Stokes had shown could be obtained by making jellies of different degrees of stiffness. Another example, frequently adduced as indicating the falsity of the theory, was the entirely different behaviour of blocks of India-rubber and cork, under compression applied by a Bramah press. The cork diminished in thickness without spreading out laterally; the rubber, being very little compressible, bulged out all round as its thickness was diminished.

The lectures on acoustics, which came late in the course, were also exceedingly popular. Two French horns, with all their crooks and accessories, were displayed, and sometimes, to the great delight of the cla.s.s, Thomson would essay to show how the pitch of a note could be modified by means of the keys, or by the hand inserted in the bell. The determination by the siren of the pitch of the notes of tuning-forks excited by a 'cello bow, and the tuning of a major third by sounding at the same time the perfect fifth of the lower note, were often exhibited, and commented on with acute remarks, of which it is a pity no statement was ever published.[25]

The closing lecture of the ordinary course was usually on light, and the subject which was generally the last to be taken up--for as the days lengthened in spring, it was possible sometimes to obtain sunlight for the experiments--was often relegated to the last day or two of the session. So after an hour's lecture Thomson would say, "As this is the last day of the session, I will go on for a little longer, after those who have to leave have gone to their cla.s.ses." Then he would resume after ten o'clock, and go on to eleven, when another opportunity would be given for students to leave, and the lecture would be again resumed.

Messengers would be sent from his house, where he was wanted for business of different sorts, to find out what had become of him, and the answer brought would be, hour after hour, "He is still lecturing." At last he would conclude about one o'clock, and gently thank the small and devoted band who had remained to the end, for their kind and prolonged attention.

In the course of his lectures Thomson continually called on his a.s.sistants for data of all kinds. In the busiest time of his life--the fifteen years from 1870 to 1885--he trusted to his a.s.sistants for the preparation of his cla.s.s ill.u.s.trations, and it was sometimes a little difficult to antic.i.p.ate his wishes, for without careful rehearsal it is almost impossible to make sure that in an experimental lecture everything will go without a hitch. The digressions, generally most interesting and instructive, in which he frequently indulged, almost always rendered it necessary to bring some experiment before the cla.s.s which had not been antic.i.p.ated, and all kinds of things were kept in readiness, lest they should be wanted suddenly.

It has often been a.s.serted that Thomson appealed to his a.s.sistant for information contained in the multiplication-table, and could not perform the ordinary operations of arithmetic. His active mind, working on ahead of the statements he was making at the moment, often could not be brought back to the consideration of the value of 9 times 6, and the like; but it was quite untrue that he was incapable of making calculations. His memory was good, and though he never could be, for example, sure whether the aqueous humour was before or behind the crystalline in the eye, he was generally able at once to tell when a misstatement had been made as to any numerical question regarding the subject under discussion.

In the higher mathematical cla.s.s, to which he lectured on Wednesdays, at noon, Thomson was exceedingly interesting. There he seemed to work at the subject as he lectured; new points to be investigated continually presented themselves, and the students were encouraged to work them out in the week-long intervals between his lectures. Always the physical interpretation of results was aimed at, even intermediate steps were discussed. Thus the meaning of the mathematical processes was ever kept in view, and the men who could follow were made to think while they worked, and to regard the mathematical a.n.a.lysis as merely an aid, not an end in itself. "A little expenditure of chalk is a saving of brains;"

"the art of reading mathematical books is judicious skipping," were remarks he sometimes made, and ill.u.s.trate his view of the relative importance of mathematical work when he regarded it as the handmaid of the physical thinker. Yet he valued mathematics for its own sake, and was keenly alive to elegance of form and method, as readers of such great mathematical discussions as the "Appendix on Spherical Harmonics,"

in Thomson and Tait, will observe. He spoke with unqualified admiration of the work of Green and Stokes, of Cauchy's great memoir on Waves, and of Hamilton's papers on Dynamics. But no form of vector-a.n.a.lysis, neither the Quaternions of Hamilton nor the Vectors of Willard Gibbs and Heaviside, appealed to him, and the example of his friend and co-worker, Tait, had no effect in modifying his adverse verdict regarding this department of mathematics, a verdict which in later years became only more emphatic.

One session he began the first lecture of the higher cla.s.s by writing dx?dt in the middle of the blackboard, and demanding of each of the ten or a dozen students present, some of them distinguished graduates, what it meant! One student described it as the limiting value of the ratio of the increment of the dependent variable x to the increment of the independent variable t, when the latter increment is made indefinitely small. He retorted, "That's what Todhunter would say!" The others gave various slightly different versions of the same definition. At last he impatiently remarked, "Does n.o.body know that dx?dt means velocity?" Here the physical idea as a whole was before his mind; and he did not reflect that if t denoted time and x distance in any direction, the explanation given by the student did describe velocity with fair accuracy.

An embarra.s.sing peculiarity of his mathematical discussions was his tendency, when a difficulty of symbolisation occurred, to completely change the notation. Also he was not uniformly accurate in a.n.a.lytical work; but he more than made up for this by the faculty he had of devising a test of the accuracy of the result and of divining the error which had crept in, if the test was not satisfied.

The subjects he treated were always such great branches of mathematics as the theory of the tides--he discussed the tidal phenomena of the English Channel in one course--the general theory of vibrations, Fourier a.n.a.lysis, the theory of waves in water, etc., etc. A very good idea of the manner and matter of his mathematical prelections can be obtained from a perusal of the _Baltimore Lectures_.

In the physical laboratory he was both inspiring and distracting. He continually thought of new things to be tried, and interrupted the course of the work with interpolated experiments which often robbed the preceding sequence of operations of their final result. His ideas were on the whole better worked out by a really good corps of students when he was from home, and could only communicate by letter his views on the work set forth in the daily reports which were forwarded to him.

He insisted with emphasis that a student who found that a quadrant electrometer would not work well should take it to pieces to ascertain what was the matter. This of course generally resulted in the return of the instrument to White's shop to be put together again and adjusted.

But, as he said, there was a cause for every trouble of that kind, and the great thing was to find out at once what it was.