Incidentally a full and very attractive account of the elastic solid

theory is given in these lectures, accompanied as it is by

characteristic digressions on points of interest which suggest

themselves, and on topics on which the lecturer held strong opinions,

such, for example, as the absurd British system of weights and measures.

The book reads in many places like a report of some of the higher

mathematical lectures which were given every session at Glasgow; and on

that account, if on no other, it will be read by the old students of the

higher class with affectionate interest. But the discussions of the

great fundamental difficulty presented at once by dispersion--the fact,

that is, that light of different wave lengths has different velocities

in ordinary transparent matter--the discussions of the various theories

of dispersion that have been put forward, the construction of the

molecules, gyrostatic and non-gyrostatic, with all their remarkable

properties, which Lord Kelvin invents in order to frame a dynamical

mechanism which will imitate the action of matter as displayed in the

complex manifestations of the optical phenomena, not only of isotropic

matter, but of crystals, will ever afford instruction to every

mathematician who has the courage to attack this subject, and remain as

a monument to the extraordinary genius of their author.

A subject is touched on in these lectures which has not been dealt with

in the present review of Lord Kelvin's work. By four lines of

argument--by the heat of combination of copper and zinc, together with

the difference of electric potential developed when these metals are put

in contact, from the thickness of a capillary film of soap and water

(measured by Rücker and Reinold) just before it gives way, and the work

spent in stretching it, from the kinetic theory of gases and the

estimated length of free path of a particle (given also by Loschmidt

and by Johnstone Stoney), and from the undulatory theory of light--Lord

Kelvin estimated superior and inferior limits to the "size of the atoms"

of bodies, or, more properly speaking, of the molecular structure of the

matter. We cannot discuss these arguments--and they can be read at

leisure by any one who will consult Volume I (Constitution of Matter) of

Lord Kelvin's _Popular Lectures and Addresses_, for his Royal

Institution Lecture on the subject, there given in full--but we may

state his conclusion. Let a drop of water, a rain drop, for example, be

magnified to the size of the earth, that is, from a sphere a quarter of

an inch, or less, in diameter to a sphere 8000 miles in diameter, and

let the dimensions of the molecular structure be magnified in the same

proportion. "The magnified structure would be more coarse-grained than a

heap of small shot, but probably less coarse-grained than a heap of

cricket-balls."

Of course, it is not intended here to convey the idea that the molecules

are spheres like shot or cricket-balls; they undoubtedly have a

structure of their own. And no pronouncement is made as to the

divisibility or non-divisibility of the molecules. All that is alleged

is that if the division be carried to a minuteness near to or beyond

that of the dimensions of the structure, portions of the substance will

be obtained which have not the physical properties of the substance in

bulk.

The recent interesting researches of chemists and physicists into

phenomena which seem to demonstrate the disintegration, not merely of

molecules, but even of the atomic structure of matter, attracted Lord

Kelvin's attention in his last years, and _suo more_ he endeavoured to

frame dynamical explanations of electronic (or, as he preferred to call

it, "electrionic") action. But though keenly interested in all kinds of

research, he turned again and again to the older theories of light, and

his dynamical representations of the ether and of crystals, with renewed

vigour and enthusiasm.

CHAPTER XV

SPEED OF TELEGRAPH SIGNALLING--LAYING OF SUBMARINE CABLES--TELEGRAPH

INSTRUMENTS--NAVIGATIONAL INSTRUMENTS, COMPASS AND SOUNDING MACHINE

THEORY OF SIGNALLING

When the question of laying an Atlantic cable began to be debated in the

middle of the nineteenth century, Professor Thomson undertook the

discussion of the theory of signalling through such a cable. It was not

generally understood by practical telegraphists that the conditions of

working would be very different from those to which they were accustomed

on land lines, and that the instruments employed on such lines would be

useless for a cable. Such a cable consists of a copper conductor

separated from the sea-water by a coating of gutta-percha; it forms an

elongated Leyden jar of very great capacity, which, when a battery is

connected to one end of the conducting core, is gradually charged up,

first at that end, and later and later at greater distances from it, and

then is gradually discharged again when the battery is withdrawn and the

end of the conductor connected to earth. Here, again, an application of

Fourier's analysis solved the problem, which, with certain

modifications, and on the supposition that the working is slow, is

essentially the same problem as the diffusion of heat along a

conducting bar, or the diffusion of a salt solution along a column of

water. The signals are retarded (and this was one of the results of the

investigation) in such a manner "that the time required to reach a

stated fraction of the maximum strength of current at the remote end,"

when a given potential difference is applied at the other, or home end,

is proportional to the product of the capacity and resistance of the

cable, each taken per unit of the length, and also proportional to the

square of the length of cable. In other words, the retardation is

proportional to the product of the resistance of the copper conductor

and the total capacity of the cable. This gave a practical rule of great

importance for guidance in the manufacture of submarine cables. The

conductor should have the highest conductivity obtainable, and should

therefore be of pure copper; the insulating covering should, while

forming a nearly absolutely non-conducting sheath, have as low a

specific inductive capacity as possible. The first of these conditions

ran counter to some views that had been put forward, to the effect that

it was only necessary to have the internal conductor highly conducting

on its surface; and some controversy on the subject ensued. The inverse

square law, as it was called, was vehemently called in question, from a

mistaken interpretation of some experiments that were made to test it.

For if the potential at the home end be regularly altered, according to

the simple harmonic law, so that the number of periods of oscillation in

a second is n, the changes of potential are propagated with velocity

2√(πn⧸cr), where c and r are the capacity and resistance of the cable,

each taken per unit length. In this case, for a long cable, there is a

velocity of propagation independent of the length; and this fact seems

to have misled the experimenters. Thomson's view prevailed, and the

result was the establishment, first by Thomas Bolton & Sons,

Stoke-on-Trent, of mills for the manufacture of high conductivity

copper, which is now a great industry.

The Fourier mathematics of the conduction of heat along a bar suffices

to solve the problem, so long as the signalling is so slow as not to

bring into play electromagnetic induction to any serious extent. For

rapid signalling in which very quick changes of current are concerned

the electromotive forces due to the growth or dying out of the current

would be serious, and the theory of diffusion would not apply. But

ordinary cable working is quite slow enough to enable such electromotive

forces to be disregarded.

LAYING OF FIRST AMERICAN CABLES

The first cable of 1858 was laid by the U.S. frigate Niagara and H.M.S.

Agamemnon, after having been manufactured with all the precautions

suggested by Professor Thomson's researches. It is hard to realise how

difficult such an enterprise was at the time. The manufacture of a huge

cable, the stowage of it in cable tanks on board the vessels, the

invention of laying and controlling and picking-up machinery had to be

faced with but little experience to guide the engineers. Here again

Thomson, by his knowledge of dynamics and true engineering instinct, was

of great assistance. In 1865 he read a very valuable paper on the forces

concerned in the laying and lifting of deep-sea cables, showing how the

strains could be minimised in various practical cases of

importance--for example, in the lifting of a cable for repairs.

A first Atlantic cable had been partly laid in 1857 by the Niagara, when

it broke in 2000 fathoms of water, about 330 miles from Valentia, where

the laying had begun. An additional length of 900 miles was made, and

the enterprise was resumed. This time it was decided that the two

vessels, each with half of the cable on board, should meet and splice

the cable in mid-ocean, and then steam in opposite directions, the

Agamemnon towards Valentia, the Niagara towards Newfoundland. Professor

Thomson was engineer in charge of the electrical testing on board of the

Agamemnon. After various mishaps the cable was at last safely laid on

August 6, 1858, and congratulations were shortly after exchanged between

Great Britain and the United States. On September 6 it was announced

that signals had ceased to pass, and an investigation of the cause of

the stoppage was undertaken by Professor Thomson and the other

engineers. The report stated that the cable had been too hastily made,

that, in fact, it was not good enough, and that the strains in laying it

had been too great and unequal. It was found impossible to repair it, so

that there was no option but to abandon it.

This cable probably suffered seriously from the violent means which seem

to have been employed to force signals through it. Now only a very

moderate difference of potential is applied to a cable at the sending

end, and speed of signalling is obtained by the use of instruments, the

moving parts of which have little inertia, and readily respond to only

an exceedingly feeble current.

A second cable was made and laid in 1865 by the Great Eastern, which

could take on board the whole at once and steam from shore to shore. It

was also well adapted for cable work through having both screw and

paddles. As Thomson points out, "steerage way" could be got on the

vessel by driving the screw ahead, so as to send a stream of water

astern towards the rudder, while the paddles were driven astern to

prevent the ship from going ahead. This was of great advantage in

manœuvring on many occasions.

This cable also broke, but a third was laid successfully in 1866 by the

same vessel, and the second was recovered and repaired, so that two good

cables were secured for commercial working. On both expeditions

Professor Thomson acted as electrical engineer, and received the honour

of knighthood and the thanks of the Anglo-American Telegraph Company on

his return home, when he was also presented with the freedom of the city

of Glasgow.

He afterwards acted as engineer for the French Atlantic Cable, for the

Brazilian and River Plate Company, and for the Commercial Company, whose

two new Atlantic cables were laid in 1882-4.

MIRROR GALVANOMETER AND SIPHON RECORDER

Since whatever the potential applied at the sending end of the cable

might be (and, of course, as has been stated, this potential had to be

kept to as low a value as possible) the current at the receiving end

only rose gradually, it was necessary to have as delicate a receiving

instrument as possible, so that it would quickly respond to the growing

and still feeble current. For unless the cable could be worked at a

rate which would permit of charges per word transmitted which were

within the reach of commercial people, it was obvious that the

enterprise would fail of its object. And as a cable could not cost less

than half a million sterling, the revenue to be aimed at was very

considerable. This problem Thomson also solved by the invention of his

mirror galvanometer. The suspended magnet was made of small pieces of

watch-spring cemented to a small mirror, so that the whole moving part

weighed only a grain or two. Its inertia, or resistance to being set

into motion, was thus very small, and it was hung by a single fibre of

silk within a closed chamber at the centre of the galvanometer coil. A

ray of light from a lamp was reflected to a white paper scale in front

of the mirror, which as it turned caused a spot of illumination to move

along the paper. A motion of this long massless index to the left was

regarded as a dot, a motion to the right as a dash, and the Morse

alphabet could therefore be employed. This instrument was used in the

1858 cable expedition, and a special form of suspension was invented for

it by Thomson, to enable it to be used on board ship. The suspension

thread, instead of being held at one end only, was stretched from top to

bottom of the chamber in which the needle hung, and kept tight by being

secured at both ends. Thus the minimum of disturbance was caused to the

mirror by the rolling or pitching of the ship.

The galvanometer was also enclosed in a thick iron case to guard it

against the magnetic field due to the iron of the ship. The "iron-clad

galvanometer" first used in submarine telegraphy (on the 1858

expedition in the U.S. frigate Niagara) is in the collection of

historical apparatus in the Natural Philosophy Department of the

University of Glasgow.

The mirror galvanometer then invented has become one of the most useful

instruments of the laboratory. Mirror deflection is now used also for

the indicators of many kinds of instruments.

The galvanometer was replaced later by another invention of Professor

Thomson--the siphon recorder. Here a small and delicate pen was formed

by a piece of very fine glass tube (vaccination tubing, in fact) in the

form of a siphon, of which the shorter end dipped into an ink-bottle,

while the other end wrote the message in little zig-zag notches on a

ribbon of paper drawn past it by machinery. The siphon was moved to and

fro by the signalling currents, which flowed in a small coil hung

between the poles of an electromagnet, excited by a local battery, and

the ink was spirted in a succession of fine drops from the pen to the

paper. This was accomplished by electrifying the ink-bottle and ink by a

local electrical machine, and keeping the paper in contact with an

uninsulated metal roller. Electric attraction between the electrified

ink and the unelectrified paper thus drew the ink-drops out, and the

pen, which never touched the paper, was quite unretarded by friction.

Both these instruments had the inestimable advantage that the to and fro

motions of the spot of light or the pen took place independently of

ordinary earth-currents through the cable.

The arrangement of magnet and suspended coil in this instrument has

become widely known as that of the "d'Arsonval galvanometer." This

application was anticipated by Thomson, and is distinctly mentioned in

his recorder patent, long before such galvanometers were ever used. It

was later proposed by several experimenters before M. d'Arsonval.

It is not too much to say that, by his discussion of the speed of

signalling, his services as an electrical engineer, and especially by

his invention of instruments capable of responding to very feeble

currents, Thomson made submarine telegraphy commercially possible. Later

he entered into partnership with Mr. C. F. Varley and Professor Fleeming

Jenkin. A combination of inventions was made by the firm: Varley had

patented a method of signalling by condensers, and Jenkin later

suggested and patented an automatic key for "curb-sending" on a

cable--that is, signalling by placing one pole of the battery for an

interval a little shorter than the usual one to the line, and then

reversing the battery for the remainder. This gave sharper signals, as

the reversal helped to discharge the cable more rapidly than it would

have been by the mere connection to earth between two signals. The firm

of Thomson, Varley & Jenkin took a prominent part in cable work; and

Thomson and Jenkin acted as engineers for many large undertakings. They

employed a staff of young electricians at the cable-works at Millwall

and elsewhere, keeping watch over the cable during manufacture, and sent

them to sea as representatives and assistants to perform similar duties

during the process of cable-laying. On their staff were many men who

have come to eminence in electrical and engineering pursuits in later

life.

MARINERS' COMPASS AND SOUNDING MACHINE

After the earlier Atlantic expeditions Sir William Thomson turned his

attention to the construction of navigational instruments, and invented

the mariner's compass and wire-sounding apparatus which are now so well

known. He had come to the conclusion that the compasses in use had much

too large needles (some of them bar-magnets seven or eight inches long!)

to respond quickly and certainly to changes of course, and, what was

still more serious, to admit of the application of correcting magnets,

and of masses of soft-iron to annul the action of the magnetism of the

ship.

The compass card consists of a paper ring, on which the "points" and

degrees are engraved in the ordinary way, and is kept circular by a

light ring of aluminium. Threads of silk extend radially from the rim to

a central boss of aluminium in which is a cap of aluminium. In the top

of the cap is a sapphire bearing, which rests on an iridium point

projecting upward from the compass bowl. Eight magnets of glass-hard

steel, from 3¼ inches to 2 inches long, and about the thickness of a

knitting-needle, which form the compass needle, are strung like the

steps of a rope ladder, on two silk threads attached to four of the

radial threads.

The weight of the card is extremely small--only 170½ grains; that is

less than ⅖ of an ounce. But the matter is not merely made small in

amount; it is distributed on the whole at a great distance from the

axis; consequently the period of free vibration is long, and the card is

very steady. The great lightness of the card also causes the error due

to friction on the point of support to be very small.

The errors of the compass in an iron ship are mainly the semicircular

error and the quadrantal error. We can only briefly indicate how these

arise and how they are corrected. The ship's magnetism may be considered

as partly permanent, and partly inductive. The former changes only very

slowly, the latter alters as the ship changes course and position. For

the ship is a combination of longitudinal, transverse, and vertical

girders and beams. As a whole it is a great iron or steel girder, but

its structure gives it longitudinal, transverse, and vertical

magnetisation. This disturbs the compass, which is also affected by the

magnetisation of the iron or steel masts and spars, or of iron or steel

carried as cargo.

The semicircular error is due to a great extent to permanent magnetism,

but also in part to induced magnetism. It is so called because when the

ship's head is turned through 360°, the error attains a maximum on two

courses 180° apart. It may amount to over 20° in an ordinary iron

vessel, and to 30° or 40° in an armour-clad. It is corrected by two sets

of steel magnets placed with their centres under the needle in the

binnacle. One set have their lengths fore and aft, the others in the

thwart-ship direction. These magnets annul the error on the north and

south and on the east and west courses, due to the two horizontal

components of magnetic force produced mainly by the permanent magnetism

of the ship. A regular routine of swinging the ship when marks on the

shore (the true bearings of which from the ship are known) are

available, is followed for the adjustment.

The quadrantal error is so called because its maxima are found on four

compass courses successively a quadrant, or 90°, from one another. It

amounts in general to from 5° to 10° at most. It is due to induced

magnetism, and is corrected by a pair of soft-iron spheres, placed on

the two sides of the compass with their centres in a line transverse to

the ship, through the centre of the compass needle. There are, however,

exceptional cases in which they are placed in the fore and aft line one

afore, the other abaft, the needle. When the quadrantal error has once

been annulled it is always zero, for as the induced magnetism changes,

so does that of the spheres, and the adjustment remains good. In a new

ship the permanent magnetism slowly alters, and so the semicircular

correction has to be improved from time to time by changing the magnets.

These adjustments are not quite all that have to be made; but enough has

been stated to show how the process of compensation can be carried out

with the Thomson compass. The immensely-too-large magnets used formerly

as compass needles, through a mistaken notion, apparently, that more

directive force would be got by their means, rendered the quadrantal

adjustment an impossibility. The card swinging round brought the large

needles into different positions relatively to the iron balls, when

these were used, and exerted an inductive action on them which reacted

on the needles, producing more error, perhaps, than was corrected.

Thomson invented also an instrument called a "deflector," by which it is

possible to adjust a compass when sights of sun or stars, or bearings of

terrestrial objects, cannot be obtained. By means of it the directive

forces on the needles on different courses can be compared. Then the

adjustment is made by placing the correctors so that the directive force

is as nearly as may be the same on all courses. The compass is then

quite correct.

The theory of deviations of the compass, it is right to say, was

discussed first partially by Poisson, but afterwards very completely and

elegantly by the late Mr. Archibald Smith of Jordanhill, whose memoirs,

now incorporated in the _Admiralty Manual of Deviations of the Compass_,

led to Lord Kelvin's inventions.

Lord Kelvin's compass is now almost universally in use in the merchant

service of this country, and in most of the navies of the world. It has

added greatly to the certainty and safety of navigation.

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

ashore 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 passed 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 shore 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 passengers. 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 altitude

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 altitude. The ship is at a point on this circle.

Some time after the altitude 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 illustration

of an important principle of hydrodynamics. The fifth example stated is

as follows: "In a smooth sea, with moderate wind blowing parallel to the

shore, a sailing ship heading towards the shore, with not enough of sail

set, can only be saved from creeping ashore by setting more sail, and

sailing rapidly towards the shore, or the danger that is to be avoided,

so as to allow her to be steered away from it. The risk of going ashore

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 CLASS-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

Association, 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,

assistants, 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

spaces, 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 associations,

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, passed behind the

table, and, putting up his eye-glass, 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 classes 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 assistant; 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 class

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 class 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 passed and the card

was placed in that receptacle of the blessed, the compartment reserved

for those who had been called and duly passed the assize! But there was

a third compartment reserved for the cards of those unfortunates who

failed to satisfy the judge! The reader may have anticipated 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 circumstances. 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 illustrated 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-illustrations for next day, a student came into the class-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 Hell! 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 illustrated 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 mass of the planet was comparable with that of the

sun. Sometimes Thomson would read the remarkable passage 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 gods," 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 glass 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 retarding 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 illustration by a model of a terrestrial globe, arranged

so that the centre should be a fixed point, while its axis--a material

spike of brass--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

glasses 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 illustration of the two different forms

of solution of the differential equation, [:θ] + μθ = 0, according as μ

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 class, 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 title--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 assistant 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

assistant, 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 class next morning was delighted, and

very appreciative of McFarlane's diligence. Thomson came in, put up his

eye-glass, 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 class 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 massive 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 mass 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-glass, 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

27⅓ grains. Thus so many drams of powder required to charge a rifle

is a very much larger quantity 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 assistants.

Another experiment which caused a great sensation was that known as the

"dewdrop"! A funnel of brass, 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 accumulate--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 anticipated 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 space 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

class, as the mass quivered, remark, "The trembling of the dewdrop,

gentlemen!"

Vibrations of elastic solids were illustrated 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, homogeneous, 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

class, 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 classes." 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

assistants for data of all kinds. In the busiest time of his life--the

fifteen years from 1870 to 1885--he trusted to his assistants for the

preparation of his class illustrations, and it was sometimes a little

difficult to anticipate 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 class

which had not been anticipated, and all kinds of things were kept in

readiness, lest they should be wanted suddenly.

It has often been asserted that Thomson appealed to his assistant 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 class, 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 analysis 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 illustrate 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-analysis,

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 class 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 nobody 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 embarrassing 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 analytical

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

analysis, 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.

Thomson's concentration on the work in hand, and his power of simply

taking possession of men, even mere spectators, and converting them into

assistants, was often shown in the laboratory. Several men who have

since become eminent were among the assistants enrolled from the

laboratory students. Professor W. E. Ayrton and, later, Professor John

Perry, were students at Glasgow for a time, and rendered the most able

and willing help in the researches which were then proceeding. This

power was, no doubt, the secret of his success in gathering round him an

enthusiastic corps of laboratory workers in the early years of his

professorship, and it was shown also by the ease with which he annexed

the Blackstone examination-room and, later, various spaces in the new

University buildings. There, after a time, the Natural Philosophy rooms

were found by the senatus to include not only the original class-room,

laboratory, etc., but also all the spare attics and corridors in the

neighbourhood, and even the University tower itself! One of his

colleagues, who venerated him highly, remarked recently, "He had a great

faculty for annexation!"

The incident referred to occurred while he was preparing the article on

Heat for the ninth edition of the _Encyclopædia Britannica_. It seemed

at first a pity that Thomson should undertake to write such articles;

but in the course of their preparation he came upon so many points on

which experimental information was wanting, and instituted so many

researches to answer his questions, that the essays took very much the

character of original papers. In the article on Heat (he also wrote

Elasticity), will be found a long account of "Steam Thermometry," that

is, of thermometers in which the indicating substance was to be the

saturated vapours of different substances, water, sulphurous acid, etc.,

etc., for he did not limit the term "steam" to water-vapour. For some

time every one in the laboratory was employed in making sulphurous acid,

by heating copper in sulphuric acid in the usual way, and condensing the

gas in tubes immersed in freezing mixtures; and the atmosphere of the

room was of a sort which, however noxious to germs of different kinds,

it was a little difficult to breathe. One morning, when all were thus

occupied, an eminent chemist, who had just come home from the south for

a vacation, called to pay his respects. After a word or two of inquiry

as to how his young friend was prospering in his new post, Thomson said,

"We are all very busy brewing liquid sulphurous acid, for use in

sulphurous acid steam thermometers; we want a large quantity of the

liquid; would you mind helping us?" So, desiring an assistant to find a

flask and materials, he enrolled this new and excellent recruit on the

spot; and what was intended to be a mere call, was prolonged into a long

day of ungrudging work at an elementary chemical exercise!

CHAPTER XVII

PRACTICAL ACTIVITIES--HONOURS AND DISTINCTIONS--LAST ILLNESS AND DEATH

It remains to say something of Lord Kelvin's public and practical

activities. All over the world he came ultimately to be recognised as

the greatest living scientific authority in almost all branches of

physics. Every existing learned society sought to make him a Fellow,

honorary degrees were showered on him from all quarters. A list of some

of the most important of these distinctions is given in the Royal

Society Year-Book for 1907; it is doubtful if a complete list could be

compiled. He was awarded the Keith Medal and the Victoria Jubilee Medal

by the Royal Society of Edinburgh, and received in succession the Copley

and Royal Medals of the Royal Society of London, of which he was elected

a Fellow in 1851, and was President from 1890 to 1895. For several

periods of years he was President of the Royal Society of Edinburgh, to

which he communicated his papers on heat, dissipation of energy, vortex

motion, and many other memoirs.

He was President of the British Association at the Edinburgh meeting in

1871, when he delivered a presidential address, noteworthy in many

respects, but chiefly remarkable in the popular mind on account of his

suggestion that life was conveyed to the earth by a seed, a germ

enclosed in a crevice of a meteorite. This was understood at the time by

many people as an attempt to explain the origin of life itself, instead

of what it was intended to be, an explanation of the beginning of the

existence of living things on a planet which was originally, on the

completion of its formation by the condensation of nebular matter, red

hot even at its surface. On several occasions he was president of

Section A, and he was constant in attendance at the Association

meetings, and an eager listener and participator in the discussions and

debates. His scientific curiosity was never at rest, and he dearly liked

to meet and converse with scientific workers.

Lady Thomson, who had been long an invalid, died in 1870, and in 1874

Sir William Thomson was married to Miss Frances Anna Blandy (daughter of

Mr. Charles R. Blandy of Madeira) who survives him as Lady Kelvin. To

her tender solicitude he owed much of his constant and long-continued

activity in all kinds of work. She accompanied him on all public

occasions, and he relied greatly on her helpfulness and ever watchful

care.

In 1892 Sir William Thomson, while President of the Royal Society, was

raised to the Peerage, with the title of Baron Kelvin of Netherhall,

Largs; and more lately he was created a member of the Order of Merit and

a G.C.V.O. His foreign distinctions were very numerous. He was a Knight

of the Order _Pour le Mèrite_ of Prussia, a Foreign Associate of the

Institute of France, and a Grand Officer of the Legion of Honour. But no

public honour or mark of royal favour could raise him in the estimation

of all who know anything of science or of the labours of the scientific

men to whom we owe the necessities and luxuries of our present

civilisation.

In 1896 the City and University of Glasgow celebrated the jubilee of his

Professorship of Natural Philosophy. The rejoicings on that occasion

will never be forgotten by those whose privilege it was to take part in

them. Delegates came from every country in the world, and kings and

princes, universities and learned societies, colleges and scholastic

institutions of every kind, vied with each other in doing honour to the

veteran who had fought for truth and light for so many years, and won so

many victories. A memorial volume of the proceedings was published,

including a review of Lord Kelvin's work by the late Professor

FitzGerald, and a full report appeared in Nature and other journals at

the time, so that it is unnecessary to give particulars here. And indeed

it is impossible by any verbal description to convey an idea of the

enthusiasm with which the scientific world acclaimed its leader, and of

the dignity and state of the ceremonies.

In 1899, at the age of seventy-five, Lord Kelvin resigned the Chair of

Natural Philosophy, and retired, not to rest, but to investigate more

vigorously than ever the properties of matter. One remarkable fruit of

his leisure we have in his great book, the _Baltimore Lectures_, in

which theories of light are discussed with a power which excites the

reverence of all engaged in the new researches and which recent

discoveries have called into existence. And it is not too much to say

that the means of discussing and extending these discoveries are in

great measure due to Lord Kelvin.

During the year 1907 Lord Kelvin performed many University duties and

seemed to be in unusually good health. He presided as Chancellor at the

installation of Mr. Asquith as Lord Rector on January 11, and in the

same capacity attended a few days later the funeral of Principal Story,

the Vice-Chancellor, who died on January 13. On April 23 he presided at

the long and arduous ceremonies of honorary graduation, and the public

opening of the new Natural Philosophy Institute and the new Medical

Buildings, by the Prince of Wales. As Chancellor he conferred the degree

of Doctor of Laws on the Prince and Princess, and took the chair at the

luncheon which followed the proceedings, when he proposed in a short and

graceful speech the health of the Princess.

He was able to take part also in various political and social meetings,

and to give attention to the work in progress at the factories of his

firm in Cambridge Street. Lady Kelvin and he left Netherhall, Largs, for

Aix les Bains, at the end of July, but visited the British Association

at Leicester in passing. There he heard the presidential address of his

old friend, Sir David Gill, to whom he moved a vote of thanks in his

usual vivacious manner.

Lord Kelvin had been accustomed for a good many years to spend a month

or six weeks in summer or early autumn at the famous French

watering-place, from which he seemed always to receive much benefit. For

a long time he had suffered from an intermittent and painful form of

facial neuralgia, which, except during its attacks, which came and

passed suddenly, did not incapacitate him from work. With the exception

of a rather serious illness in 1906, this was the only ailment from

which he had suffered for many years, and his general health was

otherwise uniformly good.

Lord and Lady Kelvin returned to Netherhall on September 14, with the

intention of going in a day or two to Belfast, to open the new

scientific buildings of Queen's College. But, unfortunately, on the day

of their arrival Lady Kelvin became very seriously ill, and the visit to

Ireland had to be abandoned. His address was, however, read by his

nephew, James Thomson, son of his elder brother, and was a tribute to

the city of his birth, and the memory of his father.

The illness of Lady Kelvin caused much anxiety for many weeks, and this,

and perhaps some incautious exposure, led to the impairment of Lord

Kelvin's health. A chill caught on November 23 caused him to be confined

to bed; and though he managed for a week or two still to do some work on

a paper with which he had been occupied for a considerable time, he

became worse, and gradually sank, until his death at a quarter-past ten

o'clock on the evening of December 18.

The keen sorrow which was universally felt for Lord Kelvin's death was

manifested by all classes of the community. In Glasgow every one mourned

as for the greatest of the land, and the testimony to the affection in

which he was held, and the reverence for his character and scientific

achievements, was extraordinary. And this feeling was universal; from

all parts of the world poured in telegrams of respectful sympathy with

Lady Kelvin and with the University of Glasgow in their bereavement.

The view was immediately and strongly expressed, both privately and by

the press, that the most illustrious natural philosopher since Newton

should rest beside the great founder of physical science in Westminster

Abbey, and a requisition was immediately prepared and forwarded by the

Royal Society of London to the Dean of Westminster. The wish of the

whole scientific world was at once acceded to, and on December 23, at

noon, the interment took place, with a state and yet a simplicity which

will never be forgotten by those who were present.

Nearly all the scientific notabilities of the country were present, and

the coffin, preceded by the choristers and the clergy, while the hymn,

"Brief life is here our portion," was sung, was followed round the

cloistered aisles from St. Faith's chapel to the choir, by the

relatives, representatives of His Majesty the King and the Prince of

Wales, by the Royal Society, by delegates from the Institute of France,

representatives of the Universities of Cambridge, Oxford, Glasgow, and

other universities, of the Royal Society of Edinburgh (of which Lord

Kelvin was president when he died), and of most of the learned societies

of the kingdom. Then, after a short service, the body was followed to

the grave in the cloisters by the same company of mourners, and to the

solemn words of the Burial Service was laid close by where rests all

that was mortal of Isaac Newton. There he sleeps well who toiled during

a long life for the cause of natural knowledge, and served nobly, as a

hero of peace, his country and the world.

CONCLUSION

The imperfect sketch of Lord Kelvin's scientific life and work which

this book contains can only give a faint notion of the great

achievements of the long life that has now ended. Beyond the researches

which he carried out and the discoveries he made, there is the

inspiration which his work and example gave to others. Inspired himself

by Lagrange, Laplace, Ampère, and Fourier, and led to experimental

research by the necessity for answers to the questions which his

mathematical expression of the discoveries of the twenty-five years

which preceded the establishment of his laboratory had suggested--the

theories of electricity and magnetism, of heat, of elasticity, his

discoveries in general dynamics and in fluid motion, the publication of

"Thomson and Tait," all made him the inspirer of others; and there was

no one, however eminent, who was not proud to acknowledge his

obligations to his genius. Clerk Maxwell, before he wrote the most

original treatise on electricity that has ever appeared, gave himself to

the study of Faraday's Experimental Researches and to the papers of

Thomson. And if some, like FitzGerald and others, have regretted that

the electromagnetic theory of light to which Maxwell was led by Faraday,

and, indeed, by Thomson himself, did not meet with a more sympathetic

reception at his hands, they have not been unmindful of the source from

which much of their illumination has come.

He has founded a school of thought in mathematical physics, of men in

whose minds the symbol is always the servant of the ideas, whose motto

is interpretation by dynamical processes and models as far as that is

possible, who shirk no mathematical difficulties when they have to be

encountered, but are never led away from the straight road to the goal

which they seek to reach--the systematic and clear formulation of the

course of physical action.

And in Lord Kelvin's mind there was blended with a clear physical

instinct which put aside all that was extraneous and unessential to the

main issue an extraordinary power of concentration on the problem in

hand, and a determination that was never daunted by failure, which

consented to postponement but never to relinquishment, and which led

often after long intervals of time to success in the end. He believed

that light would come at last on the most baffling of problems, if only

it were looked at from every point of view and its conditions were

completely formulated; but he could put what was for the time impossible

aside, and devote himself to the immediately possible and realisable.

And as often happens with every thinker, his mind, released from the

task, returned to it of itself, and what before appeared shrouded in

impenetrable mist stood out suddenly sharp and distinct like a

mountain-top before a climber who has at last risen above the clouds.

With the great mathematical power and sure instinct which led him to

success in physical research was combined a keen perception of the

importance of practical applications. Sometimes the practical question

suggested the theoretical and experimental research, as when the needs

of submarine telegraphy led to the discussion of the speed of signalling

and the evolution of the reflecting galvanometer and the siphon

recorder. On the other hand, the mathematical theory of electricity and

magnetism had led to quantitative measurement and absolute units at an

earlier time, when the need for these was beginning to be felt clearly

by scientific workers and dimly by those far-sighted practical men who

dreamed--for a dream it was thought at the time--of linking the Old

World with the New by a submarine cable. But the quantitative study of

electricity in the laboratory threw light on economic conditions, and

the mass of data already obtained, mainly as a mere matter of

experimental investigation of the properties of matter, became at once a

valuable asset of the race of submarine cable engineers which suddenly

sprang into existence.

And so it has been with the more recent applications of electricity. The

induction of currents discovered by Faraday could not become of

practical importance until its laws had been quantitatively discussed, a

much longer process than that of discovery; and we have seen how the

British Association Committee, led by Thomson and Maxwell, brought the

ideas and quantities of this new branch of science into numerical

relation with the units of already existing practical enterprise. The

electrical measuring instruments--first the electrometers, and more

recently the electric current balances and other beautiful instruments

for the dynamo-room and the workshop--which Lord Kelvin invented have

brought the precision of the laboratory into the everyday duties of the

secondary battery attendant and the wireman.

And as to methods of measurement, those who remember the haziness of

even telegraph engineers as to the measurement of the efficiency of

electrical currents and electromotive forces in the circuits of lamps

and dynamos, in the early days of electric lighting, know how much the

world is indebted to Thomson.[26] He it was who showed at first how

cables were to be tested, as well as how they were to be worked; it was

his task, again, to show how instruments were to be calibrated for

practical measurement of current and energy supplied by the early

contractors to consumers. He had in the quiet of his laboratory long

before elaborated methods of comparing resistances, and given the

Wheatstone balance its secondary conductors for the comparison of low

resistances; he now showed how the same principles could be applied to

measure the efficiencies of dynamos and to make up the account of charge

and discharge for a secondary battery.

And if the siphon-recorder and the mariners' compass and the sounding

machine proved pecuniarily profitable, the reward was that of the

inventor, who has an indefeasible right to the fruit of his brain and

his hand. But Lord Kelvin's activity was not confined merely to those

practical things which have, to use the ordinary phrase, "money in

them"; he gave his time and energies freely to the perfecting of the

harmonic analysis of the tides, undertook again, for a Committee of the

British Association, the investigation of the tides for different parts

of the world, superintended the analysis of tidal records, and invented

tide-predicting machines and improved tide-gauges.

Lord Kelvin's work in the theory of heat and in the science of energy

generally would have given him a title to immortality even if it had

stood alone; and there can be no doubt, even in the mind of the most

determined practical contemner of the Carnot cycle, of the enormous

importance of these achievements. Here he was a pioneer, and yet his

papers, theoretical and yet practical, written one after another in

pencil and despatched, rough as they were, to be printed by the Royal

Society of Edinburgh, form, as they are collected in volume i of his

_Mathematical and Physical Papers_, in some respects the best treatise

on thermodynamics at the present time! There are treatises written from

a more general standpoint, which deal with complex problems of chemical

and physical change of means of thermodynamic potentials, and processes

which are not to be found set forth in this volume of papers; but even

these are to a great extent an outcome of his "Thermoelastic,

Thermomagnetic and Thermoelectric Properties of Matter."

In hydrodynamics also Lord Kelvin never lost sight of practical

applications, even while pursuing the most intensely theoretical

researches into the action of vortices or the propagation of waves. In

his later years he worked out the theory of ship-waves with a power

which has made more than one skilful and successful cultivator of this

branch of science say that he was no mere mathematician, but a man who,

like the prophets of old, could divine what is hid from the eyes of

ordinary mortals. Of the ultimate importance of these for practical

questions of the construction of ships, and the economy of fuel in their

propulsion, there can be little doubt. Unhappily, the applications will

have now to be made by others.

It is interesting to note that the investigation of waves in canals with

which Lord Kelvin recently enriched the _Proceedings of the Royal

Society of Edinburgh_ have been carried out by a strikingly ingenious

adaptation of the Fourier solution of the differential equation of the

diffusion of heat along a bar, or of electricity along a slowly worked

cable. Thus, beginning with Fourier mathematics in his earliest

researches, he has in some of his last work applied the special

exponential form of Fourier solution of the diffusion equation to a

case, that of wave propagation, essentially different in physical

nature, and distinct in mathematical signification, from that for which

it was originally given.

Lord Kelvin's written work consists of the _Electrostatics and

Magnetism_, three volumes of _Collected Mathematical and Physical

Papers_, three of _Popular Lectures and Addresses_, the _Baltimore

Lectures_, a very considerable number of papers as yet uncollected, and

the _Natural Philosophy_. But this, great as it was, represented only a

relatively small part of his activities. He advised public companies on

special engineering and electrical questions, served on Royal

Commissions, acted as consulting engineer to cable companies and other

corporations, was employed as arbiter in disputes when scientific

questions were involved, advocated distinctive signalling for

lighthouses and devised apparatus for this purpose, and he was, above

all, a great inventor. His patents are many and important. One of them

was for a water-tap warranted not to drip, another, for electrical

generating machines, meters, etc., was perhaps the patent of largest

extent ever granted.

To Lord Kelvin's class teaching reference has been made in an earlier

chapter. He was certainly inspiring to the best students. At meetings of

the British Association his luminous remarks in discussion helped and

encouraged younger workers, and his enthusiasm was infectious. But with

the ordinary student who cannot receive or retain his mental nutriment

except by a carefully studied mode of presentation, he was not so

successful. He saw too much while he spoke; new ideas or novel modes of

viewing old ones presented themselves unexpectedly, associations crowded

upon his mind, and he was apt to be discursive, to the perplexity of all

except those whose minds were endued also with something of the same

kind of physical instinct or perception. Then he was so busy with many

things that he did not find time to ponder over and arrange the matter

of his elementary lectures, from the point of view of the presentment

most suitable to the capacity of his hearers. To the suggestion which

has lately been made, that he should not have been obliged to lecture to

elementary students, he would have been the first to object. As a matter

of fact, in his later years he lectured to the ordinary class only twice

a week, and to the higher class once. The remainder of the lectures were

given by his nephew, Dr. J. T. Bottomley, who for nearly thirty years

acted as his deputy as regards a great part of the routine work of the

chair.

It is hardly worth while to refute the statement often made that Lord

Kelvin could not perform the operations of simple arithmetic. The truth

is, that in the class-room he was too eager in the anticipation of the

results of a calculation, or too busy with thoughts of what lay beyond,

to be troubled with the multiplication table, and so he often appealed

to his assistants for elementary information which at the moment his

rapidly working mind could not be made to supply for itself.

To sum up, Lord Kelvin's scientific activity had lasted for nearly

seventy years. He was born four years after Oersted made his famous

discovery of the action of an electric current on a magnet, and two

years before Ampère, founding on this experiment, brought forth the

first great memoir on electromagnetism. Thus his life had seen the

growth of modern electrical science from its real infancy to its now

vigorous youth. The discoveries of Faraday in electrical induction were

given to the world when Lord Kelvin was a boy, and one of the great

tasks which he accomplished was to weave these discoveries together in a

uniform web of mathematical theory. This theory suggested, as we have

seen, new problems to be solved by experiment, which he attacked with

the aid of his students in the small and meagrely equipped laboratory

established sixty years ago in the Old College in the High Street. It

was his lot to live to see his presentations of theory lead to new

developments in his own hands and the hands of other men of

genius--Helmholtz and Clerk Maxwell, for example--and to survive until

these developments had led to practical applications throughout our

industries, and in all the affairs of present-day life and work. His

true monument will be his work and its results, and to only a few men

in the world's history has such a massive and majestic memorial been

reared.

He was a tireless worker. In every day of his life he was occupied with

many things, but he was never cumbered. The problems of nature were ever

in his mind, but he could put them aside in the press of affairs, and

take them up again immediately to push them forward another stage

towards solution. His "green book" was at hand on his table or in his

pocket; and whenever a moment's leisure occurred he had pencil in hand,

and was deep in triple integrals and applications of Green's Theorem,

that unfailing resource of physical mathematicians.

Saepe stilum vertas quae digna legi sint

Scripturus,

the motto which Horace recommends, was his, and he would playfully quote

it, pointing to the eraser-pad in the top of his gold pencil-case. He

erased, corrected, amended, and rewrote with unceasing diligence, to the

dismay of his shorthand-writing secretary.

The theories and facts of electricity and magnetism, the production and

propagation of waves in water or in the luminiferous ether, the

structure and density of the ether itself, the relations of heat and

work, the motions of the heavenly bodies, the constitution of crystals,

the theory of music, the practical problems of navigation, of

telegraphing under the sea, and of the electric lighting of cities--all

these and more came before his mind in turn, and sometimes most of them

in the course of a single day. He could turn from one thing to another,

and find mental rest in diversity of mental occupation.

He would lecture from nine to ten o'clock in the morning to his ordinary

class, though generally this was by no means the first scientific work

of the day. At ten o'clock he passed through his laboratory and spoke to

his laboratory students or to any one who might be waiting to consult

him, answered some urgent letter, or gave directions to his secretary;

then he walked or drove to White's workshop to immerse himself in the

details of instrument construction until he was again due at the

university for luncheon, or to lecture to his higher mathematical class

on some such subject as the theory of the tides or the Fourier analysis.

As scientific adviser to submarine telegraph companies and other public

bodies, and more recently as President of the Royal Society of London,

he made frequent journeys to London. These were arranged so as to

involve the minimum expenditure of time. He travelled by night when

alone, and could do so with comfort, for he possessed the gift of being

able to sleep well in almost any circumstances. Thus he would go to

London one night, spend a busy day in all kinds of business--scientific,

practical, or political--and return the next night to Glasgow, fresh and

eager for work on his arrival. Here may be noticed his power of

detaching himself from his environment, and of putting aside things

which might well have been anxieties, and of becoming again absorbed in

the problem which circumstances had made him temporarily abandon.

Genius has been said to be the power of taking infinite pains: it is

that indeed, but it is also far more. Genius means ideas, intuition, a

faculty of seizing by thought the hidden relations of things, and

withal the power of proceeding step by step to their clear and full

expression, whether in the language of mathematical analysis or in the

diction of daily life. Such was the genius of Lord Kelvin; it was lofty

and it was practical. He understood--for he had felt--the fascination of

knowledge apart from its application to mechanical devices; he did not

disdain to devote his great powers to the service of mankind. His

objects of daily contemplation were the play of forces, the actions of

bodies in all their varied manifestations, or, as he preferred to sum up

the realm of physics, the observation and discussion of properties of

matter. But his eyes were ever open to the bearing of all that he saw or

discovered on the improvement of industrial appliances, to the

possibility of using it to increase the comfort and safety of men, and

so to augment the sum total of human happiness.

His statement, which has been so often quoted, that after fifty-five

years of constant study he knew little more of electricity and magnetism

than he did at the beginning of his career, is not to be taken as a

confession of failure. It was, like Newton's famous declaration, an

indication of his sense of the vastness of the ocean of truth and the

manifoldness of the treasures which still lie within its "deep

unfathomed caves." Like Newton, he had merely wandered along the shore

of that great ocean, and here and there sounded its accessible depths,

while its infinite expanse lay unexplored. And also like Newton--indeed

like all great men--he stood with deep reverence before the great

problems of the soul and destiny of man. He believed that Nature, which

he had sought all his life to know and understand, showed everywhere

the handiwork of an infinite and beneficent intelligence, and he had

faith that in the end all that appeared dark and perplexing would stand

forth in fulness of light.

FOOTNOTES:

[1] Lord Kelvin's address on his installation as Chancellor of

the University of Glasgow, November 29, 1904.

[2] Successor of Dr. Dick, the Professor of Natural Philosophy

who induced the Faculty to grant a workshop to James Watt when

the Corporation of Hammermen prevented him from starting

business in Glasgow, and for whom Watt was repairing the

Newcomen engine when he invented the separate condenser.

[3] A model steam-engine which he made in his youth was

carefully preserved by his brother in the Natural Philosophy

Department. It was homely but accurate in construction: the

beam was of wood, and the piston was an old thick copper penny!

[4] Proceedings on the occasion of the Presentation to the

University of Glasgow of the Portrait of Emeritus Professor G.

G. Ramsay. November 6, 1907.

[5] Apparently for a short time in 1841, when Dr. Meikleham was

laid aside by illness.

[6] The C.U.M.S. began as a Peterhouse society in 1843, and

after a first concert, which was followed by a supper, and that

by "certain operations on the chapel roof," the Master would

only give permission to hold a second concert in the Red Lion

at Cambridge, there being no room in College, on condition that

the society called itself the University Musical Society. The

new society was formed in May 1844; the first president was G.

E. Smith, of Peterhouse, the second was Blow, also of

Peterhouse, a violin player and 'cellist, and the third was

Thomson. [See _Cambridge Chronicle_, July 10, 1903, and _The

Cambridge Review_, Feb. 20, 1908.]

[7] It is rather strange that the ninth edition of the

_Encyclopædia Britannica_ contains no biography of Green. Born

in the year 1793 at Nottingham, the son of a baker, he assisted

his father, who latterly acquired a miller's business at the

neighbouring village of Sneinton. In 1829 his father died, and

he disposed of the business in order that he might have leisure

to give to mathematics, in which, though entirely self-taught,

he had begun to make original researches. His famous 'Essay'

was published by subscription in 1828, and attracted but little

attention. In 1833, at forty years of age, Green entered at

Gonville and Caius College, and obtained the fourth place in

the mathematical tripos of 1837, the year of Griffin,

Sylvester, and Gregory. His university career, whatever else it

may have done, apparently did not tend to make his earlier work

much better known to the general scientific public, and he died

in 1841 without the scientific recognition which was his due.

That came later when, as stated below, Thomson discovered him

to the French mathematicians and republished his 'Essay.'

[8] January 1869, Reprint, etc., Article XV.

[9] Reprint, Article V.

[10] The geometrical idea was, however, given and applied at

least as early as 1836 by Bellavitis, for a paper entitled

"Teoria delle figure inversa" appears in the _Annali delle

Scienze del Regno Lombardo-Veneto_ for that year. It was also

described as an independent discovery by Mr. John Wm. Stubbs,

in a paper in the _Philosophical Magazine_ for November 1843.

In a note on the history of the transformation in Taylor's

_Geometry of Conics_ the date (without reference) of Bellavitis

is given, and it is stated that the method of inversion was

given afresh by Messrs. Ingram and Stubbs (Dublin, _Phil. Soc.

Trans._ I). The note also mentions that inversion was "applied

by Dr. Hirst to attractions," but contains no reference to

Thomson's papers!

[11] "_De Caloris distributione per Terræ Corpus_" in the

Faculty minute, as stated above.

[12] _Sic._ Without doubt a mistake of the scribe for

"Liouville."

[13] _North Wales Chronicle_, Report, Feb. 7, 1885.

[14] Published: _Treatise on Natural Philosophy_, vol. i in

1867; _Elements of Natural Philosophy_ in 1873.

[15] The exact date at which this was done cannot be determined

from the Minutes of the Faculty, as they contain no reference

to the appropriation of space for the purpose. In his _Oration

on James Watt_, delivered at the Ninth Jubilee of the

University of Glasgow, in 1901, Lord Kelvin referred to the

Glasgow Physical Laboratory as having grown up between 1846 and

1856; and elsewhere he has referred to it as having been

"incipient" in 1851.

[16] There are now in Glasgow in the winter session alone about

360 elementary students and 80 advanced students, and about 250

taking practical laboratory work.

[17] Before his death (in 1832) Carnot had obtained a clear

perception of the true state of the case, and of the complete

doctrine of the conservatism of energy. [See extracts from

Carnot's unpublished writings appended, with a biography, to

the reprinted Memoir, by his younger brother, Hippolyte

Carnot.]

[18] This equation for the porous plug experiment may be

established in the following manner, which forms a good example

of Thomson's second definition of absolute temperature. Take

pressure and volume of the gas on the supply side of the plug

as p + dp and v, and on the delivery side as p and v + dv, so

that dp and dv are positive. The net work done in forcing the

gas through the plug = (p + dp)v － p(v + dv) = － pdv + vdp.

Let a heating effect result so that temperature is changed from

T to T + ∂T. Let this be annulled by abstraction of heat

Cp∂T at constant pressure. (Cp = sp. heat press. const.)

[It is to be understood that dv is the total expansion

existing, after this abstraction of heat.] The energy e of the

fluid has been increased by de = － pdv + vdp － Cp∂T.

Now, since the original temperature has been restored, the

same expansion dv if imposed isothermally would involve the

same energy change de; but in that case heat dH (dynamical)

would be absorbed, and work pdv would be done by the gas.

Hence de = dH － pdv. This, with the former value of de, gives

dH = vdp － Cp∂T. Thomson's work-ratio is thus pdv⧸(vdp － Cp∂T).

Now suppose dp imposed without change of volume, and dT to be the

resulting temperature change. The temperature and pressure ratios

are dT⧸T, dp⧸p. Thus dT⧸T = dp dv⧸(vdp － Cp∂T), or

(v⧸T)(dT⧸dv) = 1⧸[1 － (Cp⧸v)(∂T⧸dp)]

which is Thomson's equation. The minus sign on the right arises

from a heating effect having been taken here as the normal

case.

If the temperature T is restored by removing the heat at

constant volume, a similar process gives the equation

(v⧸T)(dT⧸dv) = [1 + (∂T⧸∂p)(∂T⧸dp)]⧸[1 － (Cv⧸v)(∂T⧸dp)]

where dp is the change of pressure before the restoration of

the temperature T, and ∂T⧸∂p is the rate of variation of T

with p, volume constant.

[19] "On a Universal Tendency in Nature to Dissipation of

Energy," _Proc. R.S.E._, 1852, and _Phil. Mag._, Oct., 1852.

[20] To this may be added the extremely useful theorem for such

problems, that if any directed quantity L, say, characteristic

of the motion of a body, be associated with a line or axis Ol,

which is changing in direction, it causes a rate of production

of the same quantity for a line or axis instantaneously at

right angles to Ol, towards which Ol is turning with angular

velocity ω, of amount ωL. If M be the amount of the

quantity already existing for this latter line or axis, the

total rate of growth of the quantity is there M + ωL. For

example, a particle moving with uniform speed v in a circle of

radius r, has momentum mv along the tangent. But the tangent is

turning round as the particle moves with angular speed v⧸r,

towards the radius. The rate of growth of momentum towards the

centre is therefore

mv × v⧸r = mv²⧸r.

[21] See Gray's _Lehrbuch der Physik_, s. 278. Vieweg u. Sohn,

1904.

[22] Gray, Royal Institution, Friday Evening Discourse,

February 1898.

[23] See the _Reports of the Committee on Electrical Standards_,

edited by Prof. Fleeming Jenkin, F.R.S., Maxwell's _Electricity

and Magnetism_, and Gray's _Theory and Practice of Absolute

Measurements in Electricity and Magnetism_, Vol. II, Part II.

[24] The writer once, on a thick night, in a passenger steamer

in the Race of Alderney, when the engines were stopped and

soundings were being taken, saw the reel and cord go overboard,

nearly taking one of the men with it. A new hank of cord had to

be got and bent on a new reel; an operation that took a long

time, during which the exact locality of the ship was a matter

of uncertainty. Comment is needless!

[25] The tuning of a major third, in this way, is described in

the paper entitled "Beats on Imperfect Harmonies," published in

_Popular Lectures and Addresses_, vol. ii.

[26] The writer well remembers meeting a man of some experience

in cable work who was on his way to measure the alternating

currents in a Jablochkoff candle installation by the aid of an

Ayrton and Perry galvanometer with steel needle!

INDEX

Atlantic cables, 267, 268

Atmospheric electricity, 226

Atoms, size of, 261

Ayrton, W. E., 296

Baltimore lectures, 254-263

Bertrand's theorem of maximum kinetic energy, 158

Bottomley, James Thomson, 311

Bottomley, William, 7

British Association, electrical standards, 244-253

Cambridge University Musical Society, 24

_Cambridge and Dublin Mathematical Journal_, 25, 31, 78

Carnot, Sadi, 77, 101

Carnot's _Théorie Motrice du Feu_, 87, 101, 108 _et seq._

Cauchy, 294

Chasles, 28, 43

Clapeyron, 101, 112

Clausius, 114 _et seq._

College, the old, of Glasgow, 10

Compass, errors of, 273

"Dew-drop," artificial, 290

Dynamical theorems, Thomson's and Bertrand's, 158 _et seq._

Earth, the age of, 196, 229-243

Earth, tidal retardation of, 230

Elasticity, Poisson-Navier theory of, 291;

encyclopædia article on, 297

Electrical oscillations, 181 _et seq._

Electricity, mathematical theory of, 33

Electrolysis, mechanical theory of, 176

Electrometers, 223 _et seq._

Electromotive forces, estimation of, by heats of combination, 178

Electromotive forces, measurement of, 179

_Electrostatics and Magnetism_, 222 _et seq._

Ellis, Robert Leslie, 26

Energy, dissipation of, 139

Faculty, the, of the University of Glasgow, 4, 63-67

Faraday, 61

Faure, M., 81

FitzGerald, G. F., 301, 305

Fourier, _Théorie Analytique de la Chaleur_, 16 _et seq._

Gauss, 28

Gauss and Weber, 245

Green, George, of Nottingham, 21, 30, 294

Gregory, J. W., 241

Goodwin, Harvey, 26

Gyrostats and gyrostatic action, 214, 284-286

Hamilton, Sir William Rowan, 196, 294

Heat, encyclopædia article on, 297

Heaviside, Oliver, 294

Helmholtz, von, 113

Hertz, 191, 256

Hopkins, William, 23

Huxley, 77, 196, 242

Hydrodynamics, 153-175

Images, electric, 31, 38-59

Inversion, electrical, 49 _et seq._

Inversion, geometrical, 59, 60

Joule, James Prescott, 77, 86 _et seq._, 101 _et seq._

Larmor, Joseph, 256

Lectures on Natural Philosophy at Glasgow, 279 _et seq._

Liouville, 31

Liouville's _Journal de Mathématiques_, 25, 26, 31

Loschmidt, 262

Lubbock, Sir John (Lord Avebury), 85

Luminiferous ether, motion of planets through, 256

Magnetism, theory of, 227

Mariners' compass, 272 _et seq._

Maxwell, 117, 193, 305

Mayer, of Heilbronn, 105

McFarlane, Donald, 96, 287, 289

McKichan, Dugald, 193

_Mécanique Analytique_ of Lagrange, 199, 205

_Mécanique Céleste_ of Laplace, 199, 205

Meikleham, William, 61

Mirror galvanometer, 268

Motivity, thermodynamic, 138

Natural Philosophy, Chair of, at Glasgow, 63

_Natural Philosophy_, Thomson and Tait's, 196 _et seq._

Navigational sounding machine, 272

Newton, 195, 202

Nichol, John, Professor of English Language and Literature, 5

Nichol, John Pringle, Professor of Astronomy, 5, 20, 61, 63

Oersted, 61

Oscillations, electrical, 181 _et seq._

Parkinson, Stephen, 27

Peltier, 148

Pendulum, ballistic, 288

Perry, John, 240, 296

Phosphorescence, dynamical theory of, 259

Physical laboratory, first, 70

Pickering, 217

Polarised light, rotation of plane of, 220

Principia, Newton's, 195, 202

Ramsay, George Gilbert, Professor of Humanity, 11

Regnault, 29

Royal Society of Edinburgh, presidency of, 299

Royal Society of London, presidency of, 299

Rumford, Count, 103

Seebeck, 148

Signalling, theory of telegraphic, 264

Siphon recorder, 268, 270

Smith, Archibald, 275

Spectrum analysis, dynamical theory of, 84

Stokes, Sir George Gabriel, 24, 79, 80, 81, 85, 291, 294

Stoney, Dr. Johnstone, 262

Sun's heat, age of, 232

Tait, Peter Guthrie, 194 _et seq._

Temperature, absolute, 125 _et seq._;

comparison of, with scale of air thermometer, 135

Thermodynamics, 99-152

Thermoelasticity, 142 _et seq._

Thermoelectricity, 147 _et seq._

Thermometry, absolute, 114-152

Thomson, David, 61

Thomson, James, Professor of Mathematics, 1-4, 7

Thomson, James, Professor of Engineering, 113, 209;

integrating machine, 209, 303

Thomson and Tait's Natural Philosophy, 68, 196 _et seq._, 218

Thomson's theorem of minimum kinetic energy, 158

Thomson, Thomas, Professor of Chemistry, 6

Thomson, prevalence of name at Glasgow College, 5

Thomson, William, Lord Kelvin:--

Parentage and early education, 1-12

Career at Universities of Glasgow and Cambridge, 13-32

Early researches, 16, 18, 31

Election to Chair of Natural Philosophy at Glasgow, 64

Scientific researches, passim;

Jubilee of, 301;

Chancellor of University of Glasgow, 302

In class-room and laboratory, 279-298

Practical activities, honours and distinctions, last illness and

death, 299-304;

funeral in Westminster Abbey, 304

Tidal Analyser, 211

Tide Predicter, 208

Vortex-Motion, 161-175

Waldstein sonata, 24

Weber, W., 193

Weights and measures, British, 289, 290

White, James, 276

Willard Gibbs, 294

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