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DURING the years "1901-1904 Dr. Alexander Macfarlane 
delivered, at Lehigh University, lectures on twenty-five British 
mathematicians of the nineteenth century. The manuscripts of 
twenty of these lectures were discovered in 1916, three years 
after the death of their author, to be almost ready for the printer, 
and ten of them, on ten pure mathematicians, were then pub- 
lished in Monograph No. 17 of this series. Lectures on ten 
mathematicians whose main work was in physics, astronomy, 
and engineering are given in this volume. 

These lectures were given to audiences composed of 
students, instructors and townspeople, and each occupied less 
than an hour in delivery. It should hence not be expected 
that a lecture can fully treat of all the activities of a mathe- 
matician, much less give critical analyses of his work and care- 
ful estimates of his influence. It is felt by the editors, however, 
that the lectures will prove interesting and inspiring to a wide 
circle of readers who have no acquaintance at first hand with the 
works of the men who are discussed, while they cannot fail to be 
of special interest to older readers who have such acquaintance. 

It should be borne in mind that expressions such as " now," 
" recently," " ten years ago," etc., belong to the year when a 
lecture was delivered. On the first page of each lecture will 
be found the date of its delivery. 

For five of the portraits given in the frontispiece the editors 
are indebted to the kindness of Dr. David Eugene Smith, of 
Teachers College, Columbia University. A portrait of Dr. 
Macfarlane will be found on page 4 of Monograph No. 17. 







JAMES CLERK MAXWELL (1831-1879) 7 

A Lecture delivered March 14, 1902. 


A Lecture delivered March 18, 1902. 

PETER GUTHRIE TAIT (1831-1901) 38 

A Lecture delivered March 22, 1902. 


A Lecture delivered March 25, 1902. 

CHARLES BABBAGE (1791-1871) 71 

A Lecture delivered April 21, 1903. 

WILLIAM WHEWELL (1794-1866) 84 

A Lecture delivered April 23, 1903. 


A Lecture delivered April 28, 1903. 

SIR GEORGE BIDDELL AIRY (1801-1892) 106 

A Lecture delivered April 7, 1904. 

JOHN COUCH ADAMS (1819-1892) 119 

A Lecture delivered April 8, 1904. 



A Lecture delivered April n, 1904. 

INDEX 143 






JAMES CLERK MAXWELL was born in Edinburgh, Scotland, 
on the 1 3th of November, 1831. His father, John Clerk, belonged 
to the old family of Clerks of Penicuik near Edinburgh, and 
he added Maxwell to his name, on succeeding as a younger 
son to the estate of Middlebie in Dumfriesshire, which had for 
generations been the home of a Maxwell. Hence it was cus- 
tomary in Scotland to speak of the subject of our lecture as 
Clerk-Maxwell; but by the world at large the " Clerk " has 
been dropped; for instance the magnetic unit recently defined 
in his honor is not denominated a "Clerk " or a " Clerk-Max- 
well," but simply a " Maxwell." His father was by profession 
an advocate, that is, a lawyer entitled to plead before the 
Supreme Court of Scotland; his practice had never been large 
and at the date mentioned he had retired to live on his estate. 
John Clerk-Maxwell was of a family, many members of which 
were talented, and not a few eccentric; to the latter class he 
himself belonged. He took an interest in all useful processes, 
and was successful in extending and improving the stony and 
mossy land which had become his by inheritance. The mother 
of James Clerk Maxwell belonged to an old family of the north 
of England, and was a woman of practical ability. 

Glenlair was the name given to the new mansion and 
improved estate. Here the boy had every opportunity of 
becoming intimate with the ways of nature. He traversed the 

* This Lecture was delivered on March 14, 1902. EDITORS. 



country with the help of a leaping pole, he navigated the duck 
pond in a wash tub, he rode a pony behind his father's phaeton, 
he explored the potholes and grooves in the stony bed of the 
mountain stream which flowed past the house. He studied the 
ways of cats and dogs; he watched the transformation of the 
tadpole into the frog, and he imitated the manner in which a 
frog jumps. But he attracted attention not so much as an 
incipient naturalist as a physicist. He had great work with 
doors, locks and keys, and his constant request was " Show me 
hoo it doos." He investigated the course of the water from the 
duckpond to the river, and the courses of the bell-wires from 
the pulls to the bells in the kitchen, " action at a distance " 
being no explanation to him. When a very small boy he found 
out how to reflect the sun into the room by means of a tin- 
plate. He early acquired manual skill by making baskets, 
knitting elaborate designs and taking part in such other opera- 
tions as went on around him, whether in the parlor, the kitchen, 
or on the farm. 

Being an only child, young Maxwell made playmates of 
the children of the workmen on the farm, which had one bad 
effect; the Scottish dialect became such a native tongue that 
in after life he could not get rid of the brogue. 

His early instruction in the elements of education was 
received from his mother. She taught him to read, stored his 
mind with Scripture knowledge, and trained him to look up 
through Nature to Nature's God. But she died from cancer 
at the early age of 48, and James was left when nine years 
old to the sole charge of his father. Education at home under 
a tutor was first tried, but the result was such that preparations 
were made to send him to the Edinburgh Academy, one of the 
best secondary schools of the Scottish metropolis. He entered 
the Academy in the middle of a term, and his reception by 
the other boys was not auspicious. His manners were not 
only rustic but eccentric; he had a hesitation in his speech, 
and he was clad more for comfort than for fashion. They 
were all dressed in round jacket and collar, the regulation dress 
for boys in the public schools of England; he came in a gray 


tweed tunic and frill; and his shoes were made after a peculiar 
design of his father's with square toes and brass buckles. So 
at the first recess, when they were all outside, they came about 
him like bees, and demanded who made his shoes, to which he 
replied : 

Din ye ken, 'twas a man, 

And he lived in a house 

In whilk was a mouse. 

They tore his tunic .and frill, and gave him the uncom- 
plimentary nickname of " Dafty." Daft is a Scottish word 
meaning deficient in sense, or silly. Such was the first reception 
at public school of the boy who became the greatest mathe- 
matical electrician of the nineteenth century, whose electrical 
work in historical- importance has been judged second only 
to that of Faraday. Had the annoyance to which young 
Maxwell was exposed been confined to the first few days at 
school, it might be set down to that disposition to haze new- 
comers which appears to be part of a boy's nature whether 
in the Old World or the New; but it was too generally per- 
sisted in, with the result that young Maxwell never quite 
amalgamated with the rest of the boys. There were, however, 
some exceptional lads who could appreciate his true worth, 
conspicuous among whom were Peter Guthrie Tait, afterwards 
Professor Tait, and Lewis Campbell, who became his biographer. 

The curriculum at the Academy was largely devoted to 
Latin and Greek; and young Maxwell made a bad start in 
these subjects. A want of readiness, corresponding, I suppose, 
to the hesitation in his speech, kept him down, even in arith- 
metic. But about the middle of his school career he surprised 
his companions by suddenly becoming one of the most brilliant 
among them, gaining high, and sometimes the highest prizes 
for scholarship, mathematics and English verse composition. 
At his home in Edinburgh, his aunt's house, he had a room 
all to himself; it was not a study merely, but a laboratory. 
There before he had entered on the study of Euclid's Elements 
at the Academy he made out of pasteboard models of the five 
regular solids. 


But while still a school boy he achieved a mathematical 
feat which was much more brilliant. His father was a member 
of the Scottish Society of Arts and of the Royal Society of 
Edinburgh, and it was his custom to take his son with him 
to the meetings, and indeed on visits to all places of scientific 
and industrial interest. A prominent member of the Society 
of Arts, Mr. D. R. Hay, a decorative painter, and author of a 
book First Principles of Symmetrical Beauty read a paper before 
that Society on how to draw a perfect oval. His method was 
by means of a string passing round three pegs. Young Maxwell 
had by this time entered on the study of the Conic Sections, 
and he took up the problem in his laboratory. He modified 
the manner of tracing an ellipse by doubling the cord from the 
tracing-point to one of the foci; the curve then described is 
the oval of Descartes. He also found out how to do it when 
twice the distance from one focus plus three times the distance 
from the other focus is to be constant. Maxwell's father wrote 
out an account of his son's method, and gave it to J. D. Forbes, 
then professor of natural philosophy at the University of Edin- 
burgh, and Secretary of the Royal Society of Edinburgh. Both 
Forbes, and Kelland, the professor of mathematics, approved 
the paper as containing something new to science; it was read 
by Forbes at the next meeting of the Society, and is printed 
in the second volume of the Proceedings under the title " On 
the description of oval curves, and those having a plurality of 
foci; By Mr. Clerk-Maxwell, Jr., with remarks by Professor 
Forbes." The author was then 15 years of age. Next year 
(1847) he finished the curriculum at the Academy, first in 
mathematics and in English, and very nearly first in Latin. 

He now became a student of the University of Edinburgh. 
At that time the curriculum in Arts embraced seven subjects: 
Latin, Greek, Mathematics, Physics, Logic and Metaphysics, 
Moral Philosophy, English Literature. Maxwell made a selec- 
tion skipping Latin, Greek, and English Literature. Kelland 
was the professor of mathematics, Forbes of physics, Sir William 
Hamilton of logic and metaphysics; under these he studied for 
two years. To Kelland and Forbes he was already known, 


and the latter gave him the special privilege of working with 
the apparatus used in the lectures on physics. There was 
then no well-appointed physical laboratory; any research 
made was conducted in the lecture room or the room for storing 
the lecture apparatus. But strange as it may seem, Maxwell 
appears to have done most work for the class of logic. Sir 
William Hamilton (that is, the Scottish baronet) was noted for 
his attack on mathematics as an educational discipline, but he 
was learned in scholastic logic and philosophy, and he had the 
power of inspiring his students. It was his custom to print 
on a board the names of the best students for the year in the 
order of merit; I recollect seeing on one board the name of 
James Clerk Maxwell, I think about sixth in the list. About 
this time George Boole published his Mathematical Analysis of 
Logic which found in Maxwell an appreciative reader. In his 
third year at the University, besides continuing his experiments 
in the physical department, he took Moral Philosophy under 
Professor Wilson, who wrote much under the name of Christo- 
pher North but whose lectures on moral science were char- 
acterized by Maxwell as vague harangues; also Chemistry 
in the department of Medicine, and there, as in Physics^ he was 
privileged to make experiments. The academic session at 
Edinburgh is short only six months; the long vacations he 
spent at Glenlair, where he fitted up a small laboratory in the 
garret of the former dwelling house. There he studied and 
experimented on the phenomena of light, electricity and elastic- 
ity. As the outcome of these researches he contributed two 
papers to the Royal Society of Edinburgh, which were printed 
in the Transactions; one on " The Theory of Rolling Curves," 
the other on "The Equilibrium of Elastic Solids." During his 
study at Edinburgh University, Maxwell made great use of the 
high-class works on mathematics and physics which were to 
be found in the University Library, acting unconsciously on the 
advice of his compatriot and subsequent neighbor Thomas 

In sending his son to Edinburgh University it was John 
Maxwell's intention to educate him for the legal profession 


to become an advocate like himself. But the youth's success 
as an investigator in mathematics and physics suggested to 
such friends as Forbes, Kelland, Thomson and Blackburn, a 
scientific career, and it was Maxwell's own conviction that 
he was better fitted to grapple with the laws of nature than 
with the laws of the land. His former school fellow Tait, after 
studying mathematics and physics for one brief session at the 
University of Edinburgh, had taken up the regular course of 
study at the University of Cambridge; and he wished to follow. 
His father was at length persuaded, with the result that Maxwell 
became a member of St. Peter's College, Cambridge, at the 
age of 19. Tait was a member of the same college, now entering 
on the third and last year of his undergraduate course. Thom- 
son was now a fellow of that college. 

The change to Cambridge involved a great discontinuity; 
and Maxwell by nature loved continuity in all his life and 
surroundings. The investigator of rolling curves and the 
compression of solids was now obliged to turn his attention 
again to the Elements of Euclid, and to finding out by the aid 
of lexicon and grammar the meaning of a Greek play. But, 
worse still, he found that his fellow students in Peterhouse had 
no sympathy with physical manipulations. He had brought 
with him from his laboratory a pair of polarizing prisms, the 
gift of the inventor Nicol, pieces of unannealed glass, mag- 
nets, jampots, guttapercha, wax, etc.; why he should fool 
with these things was beyond the comprehension of the young 
gentlemen who lodged and studied in the same college. At 
the end of his first year Maxwell migrated to Trinity College, 
the largest foundation of the University, then governed by 
Whewell who had a broad interest in all the sciences. Physical 
experimenting was not then so fashionable at Cambridge as 
it is now; Newton, indeed, made his experiments on light in 
Trinity College, but very little had been done since his days. 
In the college of Newton, Maxwell found not only congenial 
spirits, but soon came to be looked up to as a leader by a set 
of admiring followers. During his undergraduate years Maxwell 
found time to contribute various papers to the Cambridge and 


Dublin Mathematical Journal; he was also elected into the 
Apostles' Club; so-called from the number of the members; 
their object was the discussion of philosophical questions. 

After passing the Little-go, that is the examination in the 
preliminary studies, he went into training for the mathematical 
tripos, placing himself in the care of the great trainer of the day, 
William Hopkins. Notwithstanding that he turned aside often 
to his favorite pursuits, he succeeded by sheer strength of 
intellect in gaining the place of second wrangler; and in the 
more severe competition for the Smith's prizes he was bracketed 
equal with the senior wrangler. His rival was Routh, who 
subsequently became the leading tutor for the mathematical 
tripos, and in the mathematical world is known as the author 
of a treatise on Rigid Dynamics. Released from a course of 
prescribed study and the tyranny of a mathematical trainer, 
Maxwell rebounded at once to his much-loved researches. The 
spirit in which he now entered upon his independent career 
as an investigator may be gathered from an aphorism which he 
wrote for his own conduct: " He that would enjoy life and 
act with freedom must have the work of the day continually 
before his eyes. Not yesterday's work, lest he fall into despair, 
not to-morrow's, lest he become a visionary not that which 
ends with the day, which is a worldly work, nor yet that only 
which remains to eternity, for by it he cannot shape his action. 
Happy is the man who can recognize in the work of to-day a 
connected portion of the work of life, and an embodiment of 
the work of eternity. The foundations of his confidence are 
unchangeable, for he has been made a partaker of Infinity. 
He strenuously works out his daily enterprises, because the 
present is given him for a possession." 

His activity took two principal directions optical and 
electrical. For the former line of investigation he inquired 
on all sides for color-blind persons, devised an instrument for 
examining the living retina, which he was specially success- 
ful in applying to the dog; read Berkeley's Theory of Vision 
and that part of Mill's Logic which treats of the relation of 
sensation to knowledge; perfected his color top and made an 


extended series of observations with it. Maxwell's color top 
consists of a heavy disk with perpendicular spindle. Sectors 
of different colored papers can be placed on the disk, and made 
to overlap more or less; a smaller colored disk can be attached 
so as to cover the central part only. When the top is made 
to spin, the reflected colors which succeed one another in posi- 
tion are mixed in the eye, and the mind perceives a uniform 
color. The angular lengths are adjusted till, if possible, a 
match is made with the color in the centre; then the color 
equation is read off. 

As regards the electrical line of investigation he had already 
conceived the idea of making the old mathematical theory of 
electrical attraction and repulsion, as elaborated by Coulomb 
and Poisson, harmonize with the method by which Faraday 
was obtaining splendid results, namely, the consideration of 
the lines of force in the medium. With this end in view he 
studied the German and French writers; and in the winter of 
1855-56 he published a paper on Faraday's lines of force. 

At the age of 24 he gained, after competitive examination, 
a fellowship from his college. Soon after, the chair of physics 
(natural philosophy it is there called) in Marischel College, 
one of the teaching colleges of the University of Aberdeen, 
Scotland, fell vacant; and Maxwell was advised by his old 
friend Forbes to become a candidate for the appointment. 
The suggestion agreed with his own aims as to a career, and 
he found that his father also approved of it. He sent in his 
application; and was appointed but not before his father had 
died. So, in the spring of 1856 he became both the master 
of Glenlair and the professor of physics in Marischel College, 
Aberdeen University. 

He entered on his teaching work at Aberdeen with great 
enthusiasm* A professor in the Scottish Universities is free 
to teach his subject according to the most approved method, 
and is not bound to bend all energies towards fitting his students 
for an examination conducted by independent examiners; this 
feature of his duties Maxwell valued highly. At Cambridge 
he had taken a share in lectures to workingmen, and at Aberdeen 


he continued the practice. While he was very skillful as an 
experimenter, he was not so successful as an expositor. He 
had received no training as a teacher; following the example of 
his father he was accustomed to present things after a curiously 
grotesque fashion; his vision was short-sighted; his speech 
was not free from hesitation; his imagination outran his vocab- 
ulary; and he could not easily put himself at the viewpoint of 
the average student attending his lectures. 

During the next year he was married to Katherine Dewar, 
daughter of the principal of the college and a Presbyterian 
divine, sister I believe of James Dewar who in recent years 
has become famous for his investigation of the properties of 
bodies at temperatures bordering on the absolute zero. 

St. John's College, Cambridge, had founded an Adams 
prize in honor of the discoverer of Neptune, to be awarded to 
the writer of the best essay on a prescribed subject, and to be 
open to all graduates of the University. In 1857 the examiners 
chose for the subject "The motion of Saturn's rings." Max- 
well made an elaborate investigation, and his essay carried off 
the prize. 

Galileo in 1610 by means of his small telescope discovered 
a pair of satellites attached to the planet, one on either side. 
Huyghens in 1659 resolved the pair of satellites into a con- 
tinuous ring. Cassini in 1679 resolved the continuous ring 
into an outer and inner ring. Herschel in 1789 determined 
the period of rotation of the outer ring. In 1850 a dusky ring 
within the inner bright ring was discovered by Bond at Cam- 
bridge, Mass. Maxwell opens his essay as follows: "When 
we contemplate the rings of Saturn from a purely scientific 
point of view, they become the most remarkable bodies in 
the heavens, except, perhaps those still less useful bodies the 
spiral nebulae. When we have actually seen that great arch 
swung over the equator of the planet without any visible con- 
nection, we cannot bring our minds to rest. We cannot simply 
admit that such is the case, and describe it as one of the observed 
facts in nature not admitting or requiring explanation. We 
must either explain its motion on the principles of mechanics 


or admit that, in the Saturnian realms, there can be motion 
regulated by laws which we are unable to explain." Maxwell 
then showed that the rings, if either solid or liquid, would break 
into pieces, and concluded as follows: "The final result of the 
mechanical theory is, that, the only system of rings which can 
exist is one composed of an indefinite number of unconnected 
particles, revolving round the planet with different velocities 
according to their respective distances. These particles may 
be arranged in series of narrow rings, or they may move through 
each other irregularly. In the former case the destruction 
of the system will be very slow; in the second case it will be 
more rapid, but there may be a tendency towards an arrange- 
ment in narrow rings, which may retard the process." It 
follows from Maxwell's theory that the inner ring must have 
a greater angular velocity than the outer ring; and that this 
is the fact was later shown by Keeler at the Allegheny 
Observatory. ,- 

Aberdeen was the meeting place of the British Association 
in 1859. William Rowan Hamilton was there, full of his new 
method of quaternions; also Tait, now professor of mathe- 
matics at Belfast, and a disciple of Hamilton's. Maxwell was 
introduced to Hamilton by Tait. He had doubtless already 
studied the new method, from which he assimilated many ideas 
which figure largely in his Treatise on Electricity and Magnetism. 
At Aberdeen there are two colleges, Marischel College and 
King's College, each of which had then a Faculty of Arts. An 
agitation for a change had been in progress for some years; 
in 1860 it ended in a fusion of the two faculties of arts. The 
Kings College professor of physics was David Thomson, of 
whom you doubtless have never heard, yet Thomson was 
retained, and the gifted Clerk Maxwell was left out. However 
the Crown gave him compensation in the form of a pension. 
Just then Forbes resigned the chair of physics at Edinburgh; 
the two friends Maxwell and Tait were rival candidates, and 
Tait was successful. The contest did not change their friend- 
ship. Maxwell was immediately appointed to the correspond- 
ing chair in King's College, London. 


In London his duties were not so congenial as they had 
been in Aberdeen. The session was much longer, and he was 
not so free to adopt his own methods, for the college was affil- 
iated to the University of London, which alone had the power 
of granting degrees. After five years in this office he retired 
to his own estate. While in London he carried out three 
important investigations. He had already investigated the 
mixing of colors reflected from colored papers; he now took 
up the mixing of pure colors of the spectrum. For this pur- 
pose he made a wooden box 8 feet long, painted it black both 
inside and outside, fitted it with the necessary slits, prisms, 
and lenses; and, in order to get the necessary sunlight, placed 
it in the window of the garret of his house. Here he observed 
the effect of mixing the spectral tints, and his neighbors thought 
him mad to spend so many hours staring into a coffin. 

His investigation of the stability of Saturn's rings intro- 
duced to his attention the flight of a countless horde of small 
solid bodies; from this to the kinetic theory of gases the tran- 
sition is natural. 

The third task was the construction for the British Asso- 
ciation of a material ohm, defined as the resistance of a circuit 
when an electromotive force of one volt sends a current of one 
weber through it. Maxwell, more than any other man, was 
the founder of the C.G.S. system of units, which became the 
basis of that practical system of electrical units which is now 
legalized in all civilized countries. " Weber " was originally 
the name for a unit of current. In the last verse of his " Valen- 
tine from a male telegraphist to a female telegraphist," Maxwell 
introduces the newly defined units: 

Through many an ohm the weber flew, 
And clicked the answer back to me, 
I am thy farad, staunch and true 
Charged to a volt with love for thee. 

It was eminently appropriate that in 1900 the International 
Electrical Congress should give Maxwell's own name to the unit 
of magnetic flux. 


For five years (1865-1870) he lived a retired life at Glenlair, 
broken by visits to London, Cambridge, Edinburgh, and the 
Continent. But it was then that he found leisure to complete 
the great work of his life the Treatise on Electricity and Magnet- 
ism, published in two volumes in 1873. The aim of the work 
is to give a connected and thorough mathematical theory of 
all the phenomena of electricity and magnetism. He started 
from the facts observed in Faraday's experiments, and in their 
light he read the old theory of electnc action. This work 
has served as the starting point of many of the advances made 
in recent years. Maxwell is the scientific ancestor of Hertz, 
Hertz of Marconi and all other workers at wireless telegraphy. 
In the introductory chapter Maxwell remarks that the Earth 
(which was made the basis of the metric system) is not sufficiently 
constant either in form or in period of rotation; and advises 
physicists who may judge their papers worthy of a greater 
endurance to base their units upon the wave-length and period 
of some specified molecule. Humor or not, Michelson in this 
country has actually compared the meter of the archives with 
the wave-length of a certain ray of light. 

Professor Tait gave Maxwell much assistance in the prep- 
aration of his great Treatise. He urged him to introduce 
the Quaternion method; but Maxwell found serious practical 
difficulties. For one thing Hamilton makes use of the Greek 
alphabet, and Maxwell found that all the Greek letters had 
already been appropriated to denote physical quantities. But 
Maxwell was an intuitionalist, and he never trusted to analysis 
beyond what he could picture clearly. So he adopted the 
rather curious middle course. "I am convinced that the 
introduction of the ideas, as distinguished from the operations 
and methods of Quaternions, will be of great use to us in all 
parts of our subject." In this departure we have the origin 
of the school of vector-analysts as opposed to the pure quater- 

In 1870 the Duke of Devonshire, who was Chancellor of the 
University of Cambridge, signified his desire to build and 
equip a physical laboratory. The Senate accepted the gift, 


and founded in connection a chair of experimental physics. Sir 
William Thomson was invited to become a candidate, but 
declined; Maxwell was invited, and after some hesitation 
acceded. He was elected without opposition. For some time 
after his appointment Maxwell's principal work was that of 
designing and superintending the erection of the Cavendish 
Laboratory, so-called after the family name of the donor. It 
was opened in 1874. In the following vacation I visited it, 
but Maxwell as was his wont, had gone to his country home. 
His assistant mentioned that the equipment was far from 
complete, and that they were afraid that the Duke of Devon- 
shire might die before his promise of a complete equipment 
had been availed of. It was not till 1877 that the equipment 
was completed. 

Soon after (1873) ne became Cavendish professor he delivered 
the famous " Discourse on Molecules " in an evening lecture 
before the British Association, then assembled in Bradford. 
Maxwell viewed the doctrine of evolution, or at any rate the 
extreme consequences deducible from that doctrine, with 
marked disfavor. This dislike originated in part from his bias 
as a Christian and a theist, but it rested also on philosophical 
convictions which he set forth in this address. The conclusion 
is as follows: "In the heavens we discover by their light, 
and by their light alone, stars so distant from each other that 
no material thing can ever have passed from one to another; 
and yet this light, which is to us the sole evidence of the exist- 
ence of these distant worlds, tells us also that each of them is 
built up of molecules of the same kinds as those which we find 
on earth. A molecule of hydrogen, for example, whether in 
Sirius or in Arcturus, executes its vibrations in precisely the same 
time. Each molecule therefore throughout the universe bears 
impressed upon it the stamp of a metric system as distinctly 
as does the meter of the Archives at Paris, or the double royal 
cubit of the temple of Karnac. No theory of evolution can 
be formed to account for the similarity of molecules, for evolu- 
tion necessarily implies continuous change, and the molecule 
is incapable of growth or decay, of generation or destruction. 


None of the processes of Nature, since the time when Nature 
began, have produced the slightest difference in the properties 
of any molecule. We are therefore unable to ascribe either 
the existence of the molecules or the identity of their properties 
to any of the causes which we call natural. On the other hand, 
the exact quality of each molecule to all others of the same 
kind gives it, as Sir John Herschel has well said, the essential 
character of a manufactured article, and precludes the idea 
of its being eternal and self existent." 

The next year, 1874, a counterblast was delivered by Prof. 
Tyndall in his address at Belfast, as president of the Association. 
In it occurs the following passage: " Believing as I do, in the 
continuity of Nature, I cannot stop abruptly where our micro- 
scopes cease to be of use. Here the vision of the mind authorita- 
tively supplements the vision of the eye. By an intellectual 
necessity I cross the boundary of the experimental evidence, 
and discern in that Matter which we, in our ignorance of its 
latent powers, and notwithstanding our professed reverence 
for its Creator, have hitherto covered with opprobrium, the 
promise and potency of all terrestrial life." Maxwell was 
present, and he sent to Blackwood's Magazine verses entitled 
"Notes of the president's address " in which the different points 
of the address are hit off very nicely. 

After accepting the Cavendish professorship he unfortu- 
nately took on hand the work of editing the unpublished electrical 
researches, made 100 years before, by the Hon. Henry Cavendish, 
a member of the Devonshire family. The task cost him 
much time and labor which could have been better spent on 
his 'own unfinished projects, one of which was an Experimental 
Treatise on Electricity and Magnetism. 

Mrs. Maxwell was now an invalid, and depended much 
on his care. In the spring of 1879 he himself began to be 
troubled with dyspeptic symptoms, especially with a painful 
choking sensation after eating meat; in the fall he sent for an 
Edinburgh physician to come to Glenlair, and was then informed 
that he had only a month to live. To get the best medical 
attention, he and his wife set out for Cambridge; the worst 


features of his suffering were alleviated, and his intellect 
remained unclouded to the last. He died on the 5th of I^ovem- 
ber, 1879, having nearly completed the 48th year of his age. 
It is supposed that he inherited the same disease which had 
caused the untimely death of his mother. He was buried in 
Parton churchyard among the Maxwells of Middlebie. He 
left no descendants. Mrs. Maxwell lingered a few years longer, 
and she bequeathed the residue of her estate to founding a 
scholarship for experimental work in the Cavendish Laboratory. 
In the laboratory there is a bust of its first professor, and 
what is of greater interest, the collection of the models and 
apparatus which he made with his own hands. Maxwell's 
portrait hangs in the dining hall of Trinity College, alongside 
that of Cayley. He was the founder and benefactor of a Pres- 
byterian Church near his home; there he used to officiate as an 
elder, and in that church there is now a window in his memory. 
Since the time of his death his fame has grown immensely, 
especially in consequence of the wonderful applications made 
of his electro-magnetic theory. That theory led to the con- 
clusion that the velocity of propagation of electrical disturbances 
is the same as the velocity of light, that light itself is an electro- 
magnetic phenomenon, and that the ratio of the units of the 
electro-magnetic and electro-static units is the same as the 
velocity of light in a vacuum. In 1873 he predicted that in the 
discharge of a Leyden jar electric waves would be produced 
in the ether, and in 1879 such waves were detected experimentally 
by Hertz. As a consequence wireless telegraphy is now possible 
across the Atlantic Ocean. 



burgh, Scotland, on the 5th of July, 1820, He was by descent 
a Scot of Scots. His father, David Rankine, descended from 
the Rankines of Carrick, could trace his descent back to Robert 
the Bruce. Carrick is a hill district of Ayrshire in the south- 
west of Scotland, famous for its breed of dairy cattle. Before 
his accession to the Crown of Scotland, Robert the Bruce was 
Earl of Carrick. In youth Rankine's father was a lieutenant 
in the regular army, but later in life he became a railroad 
engineer and eventually Secretary of the Caledonian Railway 
Company. His mother was Barbara Graham, daughter of a 
Glasgow banker, and second cousin of Thomas Graham who 
is celebrated for his investigation of the diffusion of gases and 

Rankine spent his first years in Ayrshire among the Carrick 
Hills, which he afterwards celebrated in verse, for Rankine, 
like Maxwell, was an amateur poet: 

Come busk ye braw, my bonnie bride, 
And hap ye in my guid gray plaid, 
And ower the Brig o' Boon we'll ride 

Awa' to Carrick Hills, love. 

For there's flowery braes in Carrick land, 
There's wimplin' burns in Carrick land, 
And beauty beams on ilka hand 
Amang the Carrick Hills, love. 

*This Lecture was delivered on March 18, 1902. EDITORS. 


There dwalt my auld forefathers lang, 
Their hearts were leal, their arms were strang, 
To thee my heart and arm belang 
Amang the Carrick Hills, love. 

I'll bear thee to our auld gray tower, 
And there we'll busk a blythesome bower, 
Where thou shalt bloom, the fairest flower, 
Amang the Carrick Hills, love. 

In spring we'll watch the lammies play, 
In summer ted the new-mown hay, 
In harvest we'll sport the lee-lang day 
Amang the Carrick Hills, love. 

When winter comes wi' frost and snaw, 
We'll beet the bleeze, and light the ha', 
While dance and song drive care awa' 
Amang the Carrick Hills, love. 

In these verses we have a description by Rankine of the 
scenes and pastimes in which he spent his earliest years. Car- 
rick borders on Galloway, and there, ten years later, Clerk- 
Maxwell grew up in a similar environment. After some pre- 
liminary education at home he was sent when eight years of 
age, to the public school; first to the Academy of the neighbor- 
ing town of Ayr, afterward to the High School of the City of 
Glasgow. But his health broke .down, and he was restricted 
for some years to private instruction at his home now in Edin- 
burgh. To his father he was indebted for superior instruction 
in arithmetic, elementary mathematics, mechanics and physics. 
When 14 years of age he received from his mother's brother 
a present, which had a powerful effect on his subsequent career 
a copy of Newton's Principia. To his private study of that 
book and of other books of the like order, he was indebted 
for his skill in the higher mathematics. While his education 
proceeded at home, he received instruction in the composition 
and playing of music, which enabled him in after years to com- 
pose the tunes for his own songs. 


At the age of 16 he entered the University of Edinburgh. 
Instead of taking a regular course, he selected chemistry, physics, 
zoology and botany. Forbes was then the professor of physics; 
Rankine attended his class twice; the first year he received 
the gold medal for an -essay on "3"he Undulatory Theory of 
Light," and the subsequent year an extra prize for one on 
" Methods of Physical Manipulation." It appears that he 
did not enter any class of pure mathematics at the University, 
having already advanced beyond the parts then taught. At 
this time he was attracted, like many other mathematicians 
at the beginning of their independent career, by the theory of 
numbers. In his leisure time he studied extensively the works 
of Aristotle, Locke, Hume, Stewart, and other philosophers. 

Before finishing his studies at the University of Edinburgh, 
he had gained some practical experience by assisting his father 
in his work as a railroad engineer. There was then no professor 
of engineering at the University of Edinburgh; some 20 years 
later Fleeming Jenkin was appointed, and given that whole 
province which is now divided at this University into four great 
departments. Hence, at the age of 18, Rankine was made 
a pupil of Sir John Macneill, civil engineer, and as a pupil he 
was employed for four years on various surveys and schemes 
for river improvements, waterworks, and harbors in Ireland. 
It was then that he became personally acquainted with the 
"gorgeous city of Mullingar," which he has described minutely 
and gracefully in an ode to its praise. He was likewise employed 
on the construction of the Dublin and Drogheda railway and 
it was while so engaged that he contrived the method of setting 
out curves which is known as Rankine's method. 

Having finished his term of pupilage, he returned to his 
father's home in Edinburgh, and commenced the practice of 
his profession. One of the first projects entrusted to his care 
was rather singular. In 1842 Queen Victoria visited Scotland 
for the first time, and resided for several days in the home of 
her Stuart ancestors Holyrood Palace in Edinburgh. Royal 
visits to Scotland were not so frequent then as they afterwards 
became. One manifestation of rejoicing took the form .of a 


large bonfire on the top of Arthui's Seat, a precipitous rock 
which rises 700 feet above the level of the park surrounding 
the palace. To Rankine was entrusted the engineering of this 
bonfire. Applying his knowledge of chemistry he constructed 
the pile of fuel with radiating air passages underneath. 

It was now, when he was 22 years of age, that he pub- 
lished his first scientific pamphlet " An experimental inquiry 
into the advantage of cylindrical wheels on railways." The 
course of experiments was suggested by his father, and was 
carried out by father and son working together. It was fol- 
lowed by a series of papers on subjects suggested by his father's 
railroad experience; of which one was on the "Fracture of 
axles." He showed that such fractures arose from gradual 
deterioration or fatigue, involving the gradual extension inwards 
of a crack originating at a square-cut shoulder. In this paper 
the importance of continuity of form and fiber was first shown, 
and the hypothesis of spontaneous crystallization was disproved. 
His father was connected with the Caledonian Railway Com- 
pany, and by that Company young Rankine was professionally 
employed on various schemes. The work in Ireland had 
impressed on him the great importance of an abundant supply 
of pure water to the health of a city. He brought forward a 
scheme for supplying the city of Edinburgh with water from 
a lake in the hilly region to the south; a scheme which was 
thorough and would have solved the problem once and for all. 
It was defeated by the existing Water Company, with the result 
that to this day the water supply of the city of Edinburgh is 

While engaged in engineering work in Ireland, he had thought 
much on the mechanical nature of heat, a doctrine which was 
then engaging the attention of the scientific world. In reading 
the Principia of Newton, Rankine must have observed how the 
action of heat was a difficulty in the theory of Dynamics. In 
France, Carnot had in 1820 given a theory of the heat-engine 
which assumed that heat was a material substance. Mayer 
had advanced the theory that heat is a mode of motion. 
Rankine to explain the pressure and expansion of gaseous 


substances due to heat, conceived the hypothesis of molecular 
vortices. He worked out his theory, but owing to the want 
of experimental data, did not publish immediately. In 1845 
Joule brought to a successful result a series of experimental 
investigations designed to measure t&e exact mechanical equiva- 
lent of a given amount of heat. In 1849 William Thomson, 
professor of physics at Glasgow, gave an account to the Royal 
Society of Edinburgh of Carnot's theory, and the problem 
then was, " How must the theory of the heat-engine be modi- 
fied, supposing that heat is not a substance, but a mode of 
motion?" Rankine reduced his results to order, and contributed 
them to the Royal Society of Edinburgh in two papers entitled 
"On the mechanical action of heat, especially in gases and 
vapors" and "The centrifugal theory of elasticity as applied 
to gases and vapors." He was elected a fellow, and read his 
papers early in 1850. That same year the British Association 
met in Edinburgh. Rankine was Secretary of Section A, 
and he had ready an elaborate paper " On the laws of the 
elasticity of solid bodies," in which the same hypothesis of 
molecular vortices is the guiding idea. 

Rankine was not content to suppose the heat of a body 
to be the energy of the molecules due to some kind of motion. 
.He supposed, like the other pioneers in thermodynamics, that 
the invisibly small parts of bodies apparently at rest are in a 
state of motion, the velocity of which, whether linear or angular, 
is very high. But he went further; he imagined the motion 
to be like that of very small vortices each whirling about its own 
axis; from which it would follow that the elasticity of a gas is 
due to the centrifugal force of this motion; an increase of angular 
velocity would mean an increase of centrifugal force. His own 
statement of the hypothesis is as follows: " The hypothesis 
of molecular vortices may be defined to be that which assumes 
that each atom of matter consists of a nucleus or central point 
enveloped by an elastic atmosphere, which is retained in its 
position by attractive forces, and that the elasticity due to heat 
arises from the centrifugal force of those atmospheres, revolving 
or oscillating about their under or central points." Rankine's 


molecular vortex is the attracting point of Boscovich surrounded 
by an elastic atmosphere. 

Maxwell wrote in Nature in 1878: "Of the three founders 
of theoretical thermodynamics (Rankine, Thomson, Clausius) 
Rankine availed himself to the greatest extent of the scientific 
use of the imagination. His imagination, however, though 
amply luxuriant, was strictly scientific. Whatever he imagined 
about the molecular vortices with their nuclei and atmospheres 
was so clearly imaged in his mind's eye, that he, as a practical 
engineer, could see how it would work. However intricate, 
therefore, the machinery might be which he imagined to exist 
in the minute parts of bodies, there was no danger of his going 
on to explain natural phenomena by any mode of action of 
this machinery which was not consistent with the general laws 
of mechanism. Hence, though the construction and distribu- 
tion of his vortices may seem to us as complicated and arbitrary 
as the Cartesian system, his final deductions are simple, neces- 
sary, and consistent with facts. Certain phenomena were to 
be explained. Rankine set himself to imagine the mechanism 
by which they might be produced. Being an accomplished 
engineer, he succeeded in specifying a particular arrangement 
of mechanism competent to do the work, and also in predicting 
other properties of the mechanism which were afterwards 
found to be consistent with observed facts." 

In his paper on the " Mechanical Action of Heat," Rankine 
applied the dynamical theory of heat and his hypothesis of 
molecular vortices, to discuss new relations among the physical 
properties of bodies, and especially to a relation between the 
true specific heat of air, the mechanical equivalent of heat, 
and certain other known constants. He found, using the value 
for the mechanical equivalent which had just been published 
by Joule, that the true specific heat of air relative to that of 
water has the value 0.2378. The best value for that quantity 
which had been obtained by direct experiment was that of 
De la Roche and Berard, 0.2669. Rankine concluded, not that 
his theory was wrong, but that Joule's result was too small. 
On further examination of Joule's investigation, just printed in 


the Philosophical Transactions, he concluded that De la Roche 
and Berard's value was too large; and predicted that the true 
specific heat of air would be found to be 0.2378. Three years 
later Regnault obtained by direct experiment the value 0.2377. 
Soon after this he moved to Glasgow, and founded there 
the firm of Rankine and Thomson \ civil engineers. They took 
up a scheme for supplying the City of Glasgow with water 
from Loch Katrine. They were not the originators of the 
scheme, but they were successful in carrying it out. The City 
of Glasgow solved effectively the problem of an abundant supply 
of pure water; and in so doing commenced a career which has 
made it the model municipality of the British Islands. As a 
resident of Glasgow he became an active member of the Philo- 
sophical Society of Glasgow; and to that Society he contrib- 
uted in 1853 one of his most important memoirs " The general 
law of the transformation of energy." Two years later he 
contributed " Outlines of the science of energetics," on the 
abstract theory of physical phenomena in general, which has 
now become the logical foundation for any treatise on physics. 
In it he introduces and defines exactly a number of terms 
which were then strange or altogether new, but are now familiar 
concepts in physical science, such as " actual energy " and 
" potential energy." 

To the doctrines of the Conservation and Transformation 
of Energy, Prof. William Thomson added the doctrine of the 
dissipation of energy. This doctrine asserts that there exists 
in nature a tendency to the dissipation or uniform diffusion of 
mechanical energy originally collected in stored up form; in 
consequence of which the solar system (and the whole visible 
universe) tends towards a state of uniformly diffused heat; 
in which state according to the laws of thermodynamics no 
further transformation of energy is possible; in other words, 
nature tends towards a state of universal death. Rankine 
speculated as to how this dire result may be provided against 
in nature, and contributed to the meeting of the British Asso- 
ciation, held at Belfast in 1852 a paper " On the reconcentration 
of the mechanical energy of the universe." " My object," 


he said, " is to point out how it is conceivable that, at some 
indefinitely distant period, an opposite condition of the world 
may take place, in which the energy which is now being diffused 
may be reconcentrated into foci, and stores of chemical power 
again produced from the inert compounds which are now being 
continually formed. There must exist between the atmospheres 
of the heavenly bodies a material medium capable of trans- 
mitting light and heat; and it may be regarded as almost cer- 
tain that this interstellar medium is perfectly transparent 
and diathermanous; that is to say, that it is incapable of con- 
verting heat or light from the radiant into the fixed or conductible 
form. If this be the case, the interstellar medium must be 
incapable of acquiring any temperature whatever, and all 
heat which arrives in the conductible form at the limits of the 
atmosphere of a star or planet, will there be totally converted, 
partly into ordinary motion by the expansion of the atmosphere, 
and partly into the radiant form. The ordinary motion will 
again be converted into heat, so that radiant heat is the ultimate 
form to which all physical energy tends; and in this form it is, 
in the present condition of the world, diffusing itself from the 
heavenly bodies through the interstellar medium. Let it now 
be supposed, that, in all directions round the visible world, the 
interstallar medium has bounds beyond which there is empty 
space. If this conjecture be true, then on reaching those 
bounds, the radiant heat of the world will be totally reflected, 
and will ultimately be reconcentrated into foci. At each of 
these foci the intensity of heat may be expected to be such, 
that should a star (being at that period an extinct mass of 
inert compounds) in the course of its motions arrive at that 
point of space, it will be vaporized and resolved into its elements; 
a store of chemical power being thus reproduced at the expense 
of a corresponding amount of radiant heat. Thus it appears, 
that although, from what we can see of the known world, its 
condition seems to tend continually towards the equable dif- 
fusion in the form of radiant heat, of all physical energy, the 
extinction of the stars, and the cessation of all phenomena; 
yet the world, as now created, may possibly be provided within 


itself with the means of reconcentrating its physical energies, 
and renewing its activity and life. For aught we know, these 
opposite processes may go on together, and some of the luminous 
objects which we see in distant regions of space may be, not 
stars, but foci in the interstellar ether." 

In 1853 Rankine was elected a Fellow of the Royal Society 
of London; and in the following year he sent to that Society 
one of his important memoirs " The geometric representation 
of the expansive action of heat." 

Glasgow University was in advance of the Edinburgh Uni- 
versity in having a chair of civil engineering and mechanics. 
At the beginning of 1855 the incumbent of the chair was inca- 
pacitated by ill health, and Rankine acted as substitute for 
the remainder of the session. That same year at the age of 35 
he was appointed to the chair. 

Professor Rankine has been described by an intimate friend, 
Professor Tait: " His appearance was striking and prepos- 
sessing in the extreme, and his courtesy resembled almost that 
of a gentleman of the old school. His musical tastes had been 
highly cultivated, and it was always exceedingly pleasant to 
see him take his seat at the piano to accompany himself as he 
sang some humorous or grotesquely plaintive song words and 
music alike being generally of his own composition. His con- 
versation was always interesting, and embraced with equal 
seeming ease all topics, however various. He had the still rarer 
qualification of being a good listener also. The evident interest 
which he took in all that was said to him had a most reassuring 
effect on the speaker, and he could turn without apparent 
mental effort from the prattle of young children to the most 
formidable statement of new results in mathematical or physical 
science, when his note-book was at once produced, and in a 
few lines he jotted down the essence of the statement, to be 
pondered over at leisure, provided it did not at once appear 
to him how it was to be modified. The questions which he 
asked on such occasions were always almost startlingly to the 
point, and showed a rapidity of thought not often met with 
in minds of such caliber as his, where the mental inertia which 


enables them to overcome obstacles, often prevents their being 
quickly set in motion. His kindness, shown in the readiness 
with which he undertook to read proof sheets for a friend, or 
even to contribute a portion of a chapter (when the subject 
was one to which he had paid special attention) was, for a man 
so constantly at work, absolutely astonishing." 

It is customary in the Scottish Universities for a new pro- 
fessor to deliver an inaugural lecture on some subject of general 
interest connected with his chair; and at that time the discourse 
was in tiie Latin language. Professor Rankine chose for his 
subject u De concordia inter scientiarum machinalium con- 
templationem et usum "; or the concord in the mechanical 
sciences between theory and practice; it is printed as a pre- 
liminary dissertation in his Manual of Applied Mechanics. 
In it he traces from ancient down to medieval times the course 
of the fallacy that there is a double system of natural laws, one 
theoretical, geometrical, rational, discoverable by contemplation, 
applicable to celestial ethereal indestructible bodies, and a fit 
object for the noble and liberal arts; the other system practical, 
mechanical, empirical, discoverable by experience, applicable 
to terrestrial gross destructible bodies, and fit only for what 
were once called the vulgar and sordid arts. And he showed 
that this fallacy, although no longer formally maintained, 
still exerted an influence. In reference to this, Professor Green- 
hill has observed " Although the double system of natural 
laws mentioned by Rankine is now exploded, we still have a 
double system of instruction in mechanical textbooks, one 
theoretical, general, rational; the other practical, empirical, 
discoverable by experience. It should be the object of modern 
science to break down the barriers between these two systems, 
and to treat the subject of mechanics from one point of view." 

Appointed to the chair of engineering, Rankine was soon 
the recipient of many honors. He was made president of the 
section of engineering, when the British Association met in 
Glasgow; and the following year, on the occasion of their meet- 
ing in Dublin, he received from the University of Dublin the 
honorary degree of LL.D. The following year he was chosen 


the first president of the Institution of Engineers in Scotland, 
an organization of which he had been a principal promoter. 
Professor Rankine had by this time abundantly proved himself 
as a pathfinder in the undiscovered regions of science; he 
was now to prove himself as a roadmaker. His practice as an 
engineer had made him fully aliffe to the important difference 
between the crude results of theoretical reasoning from prin- 
ciples and the reduced formulas adapted to the data obtainable 
from observation or specification. No sooner was he settled 
in his chair, than he began the preparation of his celebrated 
series of engineering manuals. In 1857 appeared Applied 
Mechanics; in 1859 Steam-engine; in 1861 Civil Engineering; 
in 1869 Machinery and Mill Work; supplemented in 1866 by 
Useful Rules and Tables. These manuals have gone through 
many editions, and there is still a demand for them. Why 
this phenomenal success? Professor Tait answered, " Rankine 
was peculiarly happy in discriminating between those branches 
of engineering knowledge which grow from daily experience, 
and those which depend on unchangeable scientific principles. 
In his books he dealt almost exclusively with the latter, which 
may, and certainly will, be greatly extended, but so far as they 
have been established can never change. . . . Really 
original papers and monographs rapidly lose their interest and 
importance, except as historical landmarks, but Rankine 's 
works will retain their value after this generation has passed 

In 1859 tne volunteer movement spread over Great Britain. 
In view of possible invasion of the country it was thought that 
the regular army and the militia ought to be supplemented by 
bodies of trained citizens; the motto was for defence, not defiance. 
The movement spread to the University of Glasgow, and Ran- 
kine, true to transmitted instincts, gave in his name. He 
was made captain, and rose to be senior major; but after 
serving for five years he was obliged to resign on account of 
the pressure of his professional duties and of the labor involved 
in the preparation of the manuals. In 1861 he was made 
president of the Philosophical Society of Glasgow, and from the 


chair he delivered an address " On the use of mechanical hy- 
pothesis in science, especially in the theory of heat." The address 
shows a clear appreciation of the logical bearing of scientific 
hypothesis. He had been criticised for holding the hypothesis 
of molecular vortices. " In order to establish," he said, " that 
degree of probability which warrants the reception of a hypoth- 
esis into science, it is not sufficient that there should be a mere 
loose and general agreement between its results and those of 
experiment. Any ingenious and imaginative person can frame 
such hypotheses by the dozen. The agreement should be 
mathematically exact to that degree of precision which the 
uncertainty of experimental data renders possible, and should 
be tested in particular cases by numerical calculation. The 
highest degree of probability is attained when a hypothesis 
leads to the prediction of laws, phenomena and numerical 
results, which are afterwards verified by experiment, as when the 
wave-theory of light led to the prediction of the true velocity 
of light in refracting media, of the circular polarization of light 
by reflection, and of the previously unknown phenomena of 
conical and cylindrical refraction; and as when the hypothesis 
of atoms in chemistry led to the prediction of the exact pro- 
portions of the constituents of innumerable compounds. . . . 
I think I am justified in claiming for the hypothesis of molec- 
nlar vortices, as a means of advancing the theory of the mechan- 
ical action of heat, the merit of having fulfilled the proper pur- 
poses of a mechanical hypothesis in physical science, which 
are to connect the laws of molecular phenomena by analogy 
with the laws of motion; and to suggest principles such as the 
second law of thermodynamics and the laws of the elastic- 
ity of perfect gases, whose conformity to fact may afterwards 
be tested by direct experiment. And I make that claim the 
more confidently that I conceive the hypothesis in question 
to be in a great measure the development and the reduction 
to a precise form of ideas concerning the molecular condition 
which constitutes heat, that have been entertained from a 
remote period by the leading minds in physical science. . . . 
I wish it, however, to be clearly understood, that although I 


attach great value and importance to sound mechanical hy- 
potheses as means of advancing physical science, I firmly hold 
that they can never attain the certainty of observed facts; and, 
accordingly, I have labored assiduously to show that the two 
laws of thermodynamics are demonstrable as facts, independent 
of any hypothesis; and in treating of the practical application 
of those laws, I have avoided all reference to hypothesis 

The pressure of a gas is now explained by the impacts and 
collisions of the molecules. But a sound hypothesis, although 
displaced, may afterwards turn out to be very valuable. When 
Crookes started on a search for Newton's corpuscles by con- 
structing a radiometer, he was generally laughed at and his 
motives explained away by the received hypotheses, but in 
passing electric discharges through glass tubes exhausted more 
perfectly than had been done before, he hit on the phenomena 
of radiant matter, which are now explained by corpuscles much 
smaller than the atoms. 

Rankine was a frequent attendant at the meetings of the 
British Association, where his social gifts, added to his scientific 
eminence, made him a conspicuous figure. He was president 
of the section of engineering, and also of the section of mathe- 
matics and physics; and rose to be " King " of the social section 
known as Red Lions. At the meeting held at Bath in 1864 
he produced " The Three-foot Rule," a song about standards 
of measure, and sang it, to his own accompaniment and in the 
capacity of a British workman. 

When I was bound apprentice, and learned to use my hands, 
Folk never talked of measures that came from foreign lands; 
Now I'm a British Workman, too old to go to school, 
So whether the chisel or file I hold, I'll stick to my three-foot rule. 

Some talk of millimeters, and some of kilograms, 
And some of deciliters, to measure beer and drams; 
But I'm a British Workman, too old to go to school, 
So by pounds I'll eat, and by quarts I'll drink, and I'll work by my 
three-foot rule. 


A party of astronomers went measuring of the Earth, 

And forty million meters they took to be its girth; 

Five hundred million inches, tho', go through from pole to pole; 

So let's stick to inches, feet and yards, and the good old three-foot rule. 

The great Egyptian pyramid's a thousand yards about ; 
And when the masons finished it, they raised a joyful shout; 
The chap that planned that building, I'm bound he was no fool, 
And now 'tis proved beyond a doubt he used a three-foot rule. 

Here's a health to every learned man, that goes by common sense, 

And would not plague the workman by any vain pretence; 

But as for those philanthropists who'd send us back to school, 

Oh! bless their eyes, if ever they tries to put down the three-foot rule. 

This song indicates the great inconvenience and expense 
which would for a short time follow the change to the metric 
system; but it says nothing of the enormous inconvenience 
and expense which must always accompany the continued 
use of that muddle of units which prevails in Great Britain, 
and to a lesser degree in the United States. The want of sys- 
tem in the units obscures and clouds the whole subject of 
arithmetic; the school boy's time is spent on artificial reduc- 
tions instead of the real relations existing between quantities. 
Consider the great convenience of the American decimal system 
of coinage, compared with the pounds, shillings, pence and 
farthings still inflicted on commerce in the old country. It 
was learned men of the three-foot rule type who prevented 
the decimal reform of the coinage advocated by De Morgan. 
" Too old to go to school " is a sentiment worthy of the Chinese, 
and its prevalence in Great Britain for generations is a cause 
which at the present moment threatens her industrial supremacy. 
The argument drawn from the length of the polar axis of the 
Earth, is said to be due to Sir John Herschel. At one time 
it was possible to choose the yard and the pound, but that time 
has been allowed to slip away. The system of electric units, 
universally adopted, calls for a change to the meter and the 
kilogram. Had Rankine received any part of his education 
abroad, he would probably have opposed this insular idea; his 


colleague, Sir William Thomson was so educated, and has all 
his life been an enthusiastic advocate of the metric system. 

When one sails up the river Clyde towards Glasgow, he 
sees on either bank a long succession of shipbuilding yards. 
Glasgow was in Rankine 's time faiiious for its naval architects 
and shipbuilders, and they were Rankine's special friends. 
Hence, he was led into a number of investigations which are of 
importance in navigation. One of his papers is on the exact 
form of waves near the surface of deep water, and another 
investigates the lines of motion of water flowing past a ship. 
M. Napier, a naval architect, asked him to estimate the horse- 
power necessary to propel at a given rate a vessel which he was 
about to construct; and supplied him in confidence with the 
results of a great number of experiments on the horsepower 
required to propel steamships of various sizes and figures at 
various speeds. Rankine deduced a general formula, which he 
communicated to Napier directly and to the world at large in 
the form of an anagram: 2oA. 46. 6C. gD. 33E. 8F. 4G. i6H. 
id. sL. 3M. i5N. 146. 4?. 3Q. ^R. 138. 251. 4!!. 2V. 2W. iX. 
4 Y. " 

The meaning of this anagram was afterwards explained as 
follows: " The resistance of a sharp-ended ship exceeds the 
resistance of a current of water of the same velocity in a chan- 
nel of the same length and mean girth, by a quantity propor- 
tional to the square of the greatest breadth, divided by the 
square of the length of the bow and stein." Rankine and his 
naval friends prepared an elaborate Treatise on Shipbuilding 
which was published in 1866. 

Rankine's only brother had died while yet young, and 
it seems that in later life his father and mother lived with him. 
In 1870 his father died, and in the following year his mother. 
Rankine never married; when he composed the song about 
a bridal tour to the Carrick Hills, his eyesight had failed so 
that- he could not read. He had undertaken to write the 
memoir of John Elder, a shipbuilder, and this he was able to 
finish in 1872. Mrs. Elder endowed his chair so that it is now 
called the John Elder Chair of Engineering; it was however too 


late to benefit Rankine. A substitute had to be appointed to 
take charge of his classwork; and at the close of the year he 
died suddenly; not of any special disease, but as the result of 
overwork. His death occurred on the 24th of December, 1872, 
in the 53d year of his age. 

When I first came to this country and. attended a meeting 
of the American Association for the Advancement of Science, 
I was eagerly sought out by a professor of the Stevens Institute 
who was a great admirer of Rankine and desired to learn about 
his personality. I had to say that I had never met Rankine 
but that he could learn something of the man from the Collection 
of his Songs and Fables. The fables are founded on the curious 
signs which distinguish inns in England, such as the "Swan 
with two necks," the " Cat and Fiddle," etc.; they are illustrated 
by a lady who was a cousin of Maxwell and who also depicted 
scenes in Maxwell's country life. From my conversation with 
this professor I learned how widely the engineering manuals 
of Rankine were used in the United States, that his thermo- 
dynamic researches were well known, and that his name was 
everywhere held in high honor, 



PETER GUTHRIE TAIT was born at Dalkeith, near Edin- 
burgh, Scotland, on the 28th of April, 1831. His father was 
then private secretary to the Duke of Buccleuch, afterwards, 
I believe, a bookseller and the publisher of a monthly called 
Tail's Magazine. Peter Guthrie was educated at the Grammar 
School of Dalkeith, then at the Circus Place School in Edin- 
burgh, and eventually at the Edinburgh Academy, where he 
had Maxwell for a classmate. Of equal age and similar genius 
they were drawn into close friendship. They left the Academy 
together, and took up the same classes of mathematics and 
physics at the University of Edinburgh. But 1 while Maxwell 
continued in his studies there for three years, and drank deeply 
of philosophy and natural science as well as of mathematics 
and physics, Tait left after one brief session for the University 
of Cambridge. I dare say had Tait studied philosophy and 
natural science as Maxwell did ; his writings would have been 
more logical, and his mental makeup less eccentric. 

When he entered Peterhouse College, Cambridge, he was 
1 8 years of age. His private tutor was William Hopkins the 
most successful coach of his time. He graduated as senior 
wrangler in 1852, and was also first Smith's prizeman. He 
was immediately made a mathematical tutor to his college, 
and very soon a Fellow. The second wrangler and second 
Smith's prizeman of the same year was W. J. Steele, an intimate 
friend of Tait. The two friends proceeded forthwith to pre- 
pare in conjunction a treatise called Dynamics of a Particle; 
but Steele lived to write only a few chapters. The book was 

* This Lecture was delivered on March 22, 1902. EDITORS. 



first published in 1856, and has gone through a number of 
editions, Steele's name remaining on the title page. Two 
years after graduation he was appointed professor of mathe- 
matics in the Queen's College, Belfast. Then, if not before, 
he became acquainted with Andrews, the professor of chemistry 
and vice-president of the college; a skillful experimenter, fa- 
mous for his researches on the nature of ozone and on the com- 
pression of gases. It is doubtful whether Tait did any experi- 
menting under Forbes at Edinburgh; Andiews appears to have 
been his guide and master in physical manipulation. 

In 1853, one year after Tait's appointment at Belfast, 
Hamilton published his Lectures on Quaternions. The young 
professor had a great power of doing work; in the day time 
he taught mathematics and experimented with Andrews; and 
at night he studied the new method of Quaternions. He soon 
mastered it sufficiently to be able to write papers on it, which, 
lie published in the Messenger of Mathematics and the Quarterly 
Journal of Mathematics and eventually he planned a volume of 
examples on Quaternions. There were, however, to Tait's 
mind numerous obscure points in the theory, and to elucidate 
them he wished to correspond with Hamilton directly. His 
friend Andrews wrote to Hamilton asking the favor; in this 
way a correspondence originated which was kept up till the 
death of Hamilton. In 1859 Hamilton met Tait at the British 
Association meeting at Aberdeen, and Tait introduced another 
disciple, Clerk Maxwell, then professor of physics at Aberdeen. 
The year following Professor Forbes resigned the chair of 
physics in Edinburgh University; the former schoolmates, 
Tait and Maxwell, were both candidates; the choice of the 
electors fell on the energetic professor of mathematics at Belfast. 
This contest, it is pleasant to say, did not diminish the friend- 
ship between the two mathematicians. In his letter Tait 

used the symbol for Maxwell, because in thermodynamics 

there is the equation = J.C.M. Maxwell addressed one of his 
odes to Tait as " The chief musician upon Nabla." 


Tail's Quaternion project had now developed into a formal 
introduction to Quaternions; an announcement of the forth- 
coming book appeared soon after Tait removed to Edinburgh. 
He had now ceased to teach pure mathematics; he and Prof. 
William Thomson had sketched oujt an elaborate treatise on 
natural philosophy in four volumes'; for which reasons he was 
anxious to have the Quaternion volume off his hands. Sir 
William Hamilton was then engaged in the preparation of his 
" Elements of Quaternions" and he did not like the idea of 
Tait's book appearing before his own. He did not object to 
examples, but he wished to have the priority in all matters 
of principle. Tait, hearing of the situation, offered of his own 
accord to delay the publication of his volume until the Hamil- 
ton's Elements should have appeared. To arrange the matter 
more definitely Tait made a visit to Dunsink Observatory, 
Dublin, in the summer of 1861. Hamilton expected to publish 
before the end of the year, and asked Tait to wait till the year 
following. But the printing of Hamilton's book went on for 
four years longer, and was stopped only by Hamilton's death 
in 1865. It was published, incomplete, in 1866; and true to 
his promise Tait did not publish till 1867. The work then 
given to the public was entitled an Elementary Treatise on 
Quaternions. The articles which deal with the theory of Qua- 
ternions have always presented numerous difficulties to the 
reader; this phenomenon is explained partly by the history 
of the volume, and especially by Hamilton's desire that Tait 
should confine the work to applications. I think it unfortunate 
that Hamilton adopted such an attitude. It was a mistake 
to present the method in such tremendous volumes as the 
Lectures and the Elements] it was a mistake to retard the publica- 
tion of Tait's volume; it was a mistake to reserve the discussion 
of principles and of notation. Unfortunately, Tait, in his turn, 
advised inquirers to leave principles and notation alone and go on 
to applications, from which it has come about that the method of 
quaternions, presenting as it does, many points of novelty to the 
mathematician, has never been adequately discussed; only a few 
have looked upon it as a very important subject for discussion. 


When Tait became professor of physics at Edinburgh Uni- 
versity, laboratory teaching of physics was unknown in Scot- 
land. It had been Forbes' custom to allow now and then a 
promising pupil such as Maxwell the use of the lecture apparatus, 
and in this as in many other customs he was followed by Tait. 
About ten years later Prof. Tait, following the example of 
Prof. Sir William Thomson of Glasgow, instituted a practical 
class. It was his idea that each student, taking that class, 
should be instructed how to make a series of measurements, 
and then should try some real experimental problem. Prior 
to the founding of the Cavendish Laboratory at Cambridge, 
the facilities at Edinburgh and Glasgow for gaining an experi- 
mental knowledge of physics were the best in Great Britain 
and this was due to the circumstance that in these twin cities 
of the North, the chairs of physics were occupied by twin giants 
in physical science. At the Scottish Universities the academic 
classes meet only in the winter for six months; the medical 
and other professional classes have a summer session in addi- 
tion. In the winter session Tait lectured five times a week to 
the academic students, about 200 in number, and endeavored 
to traverse the whole range of elementary physics. Every other 
Saturday there was a one-hour examination; at which, follow- 
ing a custom of his predecessor, he did not give out printed 
questions, nor write them on a board, but dictated them at 
uniform intervals of five minutes. Having propounded his 
problem Tait grinned with satisfaction; if a member of the class 
asked a question about it Tait reminded him that he had 
changed for the time being from a benevolent teacher into a 
relentless inquisitor. The papers were afterwards returned 

marked with i or o or , the length of the dash indicating 

the degree of imperfection. 

To help those who wished to make a more thorough study 
of physics he instituted an advanced class; at this work he 
appeared to the greatest advantage. Before entering the 
lecture-room he glanced for a short time at his notes; thereafter 
he would write out mathematical equations for an hour without 
referring to any notes whatever. It was astonishing to see 


the way in which he could " sling " the symbols. Tait was 
not only an intellectual, but likewise a physical, giant. I am 
nearly six feet high, but standing beside Tait, I used to feel 
diminutive. He was well-built, and muscular. He wore a long 
beard, the hair on the top of his -head had disappeared at an 
early date, and left exposed a massive forehead. To protect 
his head while lecturing it was his custom to wear a skull cap. 
On the street he wore a sack-coat and a soft felt hat, and with 
cane in hand, was always walking rapidly. About the time 
of his moving to Edinburgh he married a lady who proved 
a genuine helpmate. She took full charge of all the affairs 
of the household, so that her distinguished husband might 
have perfect leisure for his scientific labors; and her influence 
was also such as to steady his attachment to religion. 

Before the year 1860, when Tait became a professor of 
physics, Joule had made his determination of the mechanical 
equivalent of heat, thus establishing the first law of thermo- 
dynamics; Thomson, Rankine and Clausius had established 
the second law; and Rankine had drawn the outlines of the 
science of " energetics." In the first edition of Dynamics of a 
Particle there is no mention of the doctrines of energy; it is 
probable that Tait's experimental work with Andrews led him 
to study the papers of Thomson, Joule and Rankine. Anyhow 
the main object of Thomson and Tait's Treatise on Natural 
Philosophy was to fill up Rankine's outlines, expound all the 
branches of physics from the standpoint of the doctrine of 
energy. The plan contemplated four volumes; the printing 
of the first volume began in 1862 and was completed in 1867. 
The other three volumes never appeared. When a second 
edition was called for, the matter of the first volume was increased 
by a number of appendices and appeared as two separately 
bound parts. The volume which did appear, although judged 
rather difficult reading even by accomplished mathematicians, 
has achieved a great success. It has been translated in French 
and German; it has educated the new generation of mathe- 
matical physicists; and it has been styled the " Principia" of 
the nineteenth century. Such was his admiration of Newton 


that Tait I am sure could not conceive of any higher compli- 
ment. Maxwell had facetiously referred to Thomson as T 
and to Tait as T 1 . Hence the Treatise on Natural Philosophy 
came to be commonly referred to as T and T 1 in the conversa- 
tion of mathematicians. 

It appears that the introduction of the quaternion method 
was a serious point of difference between the joint authors. 
Prof. Thomson, as you know, subsequently became Lord 
Kelvin and recently he wrote to Prof. Chrystal as follows 
with respect to the joint authorship of the Treatise. " I first 
became personally acquainted with Tait a short time before 
he was elected professor in Edinburgh; but, I believe, not 
before he became a candidate for the chair. It must have been 
either before his election or very soon after it that we entered 
on the project of a joint treatise of natural philosophy. He 
was then strongly impressed with the fundamental importance 
of Joule's work, and was full of vivid interest in all that he had 
learned from and worked at, with Andrews. We incessantly 
talked over the mode of dealing with energy which we adopted 
in the book, and we went most cordially together in the whole 
affair. He gave me a free hand in respect to names, and warmly 
welcomed nearly all of them. We have had a thirty-eight 
years' war over quaternions. He had been captivated by the 
originality and extraordinary beauty of Hamilton's genius 
in this respect, and had accepted, I believe, definitely, from 
Hamilton to take charge of quaternions after his death, which 
he has most loyally executed. Times without number I offered 
to let quaternions into Thomson and Tait, if he could only 
show that in any case our work would be helped by their use. 
You will see that from beginning to end they were never 

In 1864 Tait published in the North British Review articles 
on " The dynamical theory of heat " and " Energy " which 
were afterwards made the basis of his Sketch of Thermodynamics 
published in 1868. The articles, mainly historical, are written 
from the British point of view, so much so, that he was accused 
of Chauvinism. To this charge he replied, " I cannot pretend 


to absolute accuracy, but I have taken every means of ensuring 
it, to the best of my ability, though it is possible that cir- 
cumstances may have led me to regard the question from a 
somewhat too British point of view. But, even supposing this 
to be the case, it appears to me that unless contemporary his- 
tory be written with some little partiality, it will be impossible 
for the future historian to compile from the works of the present 
day a complete and unbiased statement. Are not both judge 
and jury greatly assisted to a correct verdict by the avowedly 
partial statements of rival pleaders? If not, where is the use of 

A German physician named Mayer was struck by the amount 
of heat developed in the team of horses which pulled the stage- 
coach into his village; and he reflected on the connection between 
the amount of heat developed and the amount of work they 
'had done. From this as a starting point he was led to investi- 
gate the nature of heat, and he arrived at the now accepted 
doctrine that heat is a motion of the small parts of bodies. 
He sought after the exact mechanical equivalent of heat, and 
was able to deduce it by calculation from determinations of 
the specific heat and some other properties of air. He had 
not the means for making any experiments. Tait pointed out 
defects in Mayer's reasoning, and minimized his contribution, 
because he had not made any experiments. Prof, von Helm- 
holtz, in reply, pointed out that Mayer was not in a position 
to make experiments; that he was repulsed by the physicists 
with whom he was acquainted; that he could scarcely procure 
space for the publication of his paper; and that in consequence 
of these repulses his mind at last became affected. Tait felt 
that he had been taking a rather ungracious attitude towards 
one who had suffered much for the sake of truth in science. 

It cannot be denied that Chauvinism was one of the eccentric 
characteristics of Prof. Tait. He had never studied on the 
Continent; he never traveled, I believe, beyond the narrow 
confines of the British Islands; and in his later years, he became 
something of a. recluse. What he said of the life of Rankine, 
applied with still greater force to his own. " The life of a 


genuine scientific man is, from the common point of view, 
almost always uneventful. Engrossed with the paramount 
claims of inquiries raised high above the domain of mere human 
passions, he is with difficulty tempted to come forward in politi- 
cal discussions even when they are of national importance, 
and he regards with surprise, if not with contempt, the petty 
municipal squabbles in which local notoriety is so eagerly 
sought. To him the discovery of a new law of nature, or even 
of a new experimental fact, or the invention of a novel mathe- 
matical method, no matter who has been the first to reach it, 
is an event of an order altogether different from, and higher 
than, those which are so profusely chronicled in the newspaper. 
It is something true and good forever, not a mere temporary 
outcome of craft or expediency. With few exceptions, such 
men pass through life unnoticed by, almost unknown to, the 
mass of even their educated countrymen. Yet it is they who, 
far more than any autocrats or statesmen, are really molding 
the history of the times to come. Man has been left entirely 
to himself in the struggle for creature comforts, as well as for 
the higher appliances which advance civilization; and it is to 
science, and not to so-called statecraft, that he must look for 
such things. Science can, and does, provide the means; state- 
craft can but more or less judiciously promote, regulate or 
forbid their use or abuse. One is the lavish and utterly unselfish 
furnisher of material good; the other the too often churlish 
and ignorant dispenser of it." 

His next book was written in conjunction with Prof. Kelland, 
An Introduction to Quaternions, 1873. Kelland was the 
professor of mathematics, and it was his custom to expound 
to his senior class the elements of quaternions along with 
advanced algebra. Tait, so far as I know, never lectured on 
the subject at the University of Edinburgh. The volume in 
question grew out of Kelland's lectures, and was revised and 
supplemented by Tait. Kelland. was much the older man, 
and had stood to Tait in the relation of instructor. In the 
preface, which was written by Kelland, light is thrown on the 
relation between the joint authors and colleagues: " The 


preface I have written," Kelland says, " without consulting my 
colleagues, as I am thus enabled to say what could not other- 
wise have been said, that mathematicians owe a lasting debt 
of gratitude to Prof. Tait for the singleness of purpose and the 
self-denying zeal with which he /-has worked out the designs 
of his friend Sir William Hamilton, preferring always the claims 
of the science and of its founder to the assertion of his own 
power and originality in its development. For my own part I 
must confess that my knowledge of Quaternions is due exclu- 
sively to him. The first work of Sir William Hamilton 
Lectures on Quaternions was very dimly and imperfectly 
understood by me and I dare say by others, until Prof. Tait 
published his papers on the subject in the Messenger of Mathe- 
matics. Then, and not till then, did the science in all its sim- 
plicity develop itself to me." 

Tait had now co-operated with Steele in writing Dynamics 
of a Particle, with Thomson in a Treatise on Natural Philosophy, 
and with Kelland in the Introduction to Quaternions. There was 
still a fourth literary partnership to follow; this time with 
Balfour Stewart, professor of physics at the Owens College, 
Manchester. In 1875 a volume called The Unseen Universe, 
having as a sub- title " Physical Speculations on a Future State " 
appeared anonymously; but to a physicist it was evidently 
inspired by Tait's Sketch of Thermodynamics and Stewart's 
book The Conservation of Energy. It was asserted in the 
Academy that Tait and Stewart were the authors; and a sub- 
sequent edition appeared with their names on the title page. 
It was to most people a matter of surprise that one who had 
been denouncing metaphysics in season and out of season, 
should turn out to be part author of a book described as " phys- 
ical speculations on a future state." Did not Kant say that 
the three problems of metaphysics are God, freedom, and 
immortality? What is metaphysics but speculation based 
upon physical science concerning things which can never be 
reached directly by the methods of physics? The Unseen 
Universe was metaphysics of the best or worst (however you 
may view it) kind; it was full of Carnot's reversible engine, the 


mechanical equivalent of heat, vortex-atoms and so forth. 
In subsequent editions, and there are many, the physical basis 
disappeared more and more; and the book took more of the 
appearance of a philosophical and theological essay. 

In my- lecture on Clifford * I explained how an anagram 
had appeared in Nature in 1874 an d how that later the anagram 
was explained in The Unseen Universe as follows: " Thought 
conceived to affect the matter of another universe simultane- 
ously with this may explain a future state." The kernel of 
the book is this so-called discovery. Preliminary chapters are 
devoted to a survey of the beliefs of ancient peoples about the 
immortality of the soul; to physical axioms, to an exposition 
of the doctrines and hypotheses concerning energy, matter and 
ether; and to the biological doctrine of development; it is only 
in the last chapter that we come to the " unseen universe." 
What is meant by the " unseen universe? " Matter, according 
to the authors is made up of molecules, which are supposed to be 
vortex-rings made of the luminiferous ether; the luminiferous 
ether is in turn supposed to be made of much smaller mole- 
cules which are vortex-rings of a second ether. These smaller 
molecules with the ether in which they float constitute the 
unseen universe. The authors see reason to believe that the 
unseen universe absorbs energy from the visible universe and 
vice versa; in this way a communication is established between 
them. The human soul is a frame made of the refined mole- 
cules and exists in the unseen universe, although in life it is 
attached to the body. Every thought we think is accom- 
panied by certain motions of the coarse molecules of the brain; 
these motions are propagated through the visible universe, but 
a part of each motion is absorbed by the fine molecules of 
the soul. Consequently the soul as well as the body has an 
organ of memory; at death the soul with its organ of memory 
is simply set free from association with the coarse molecules 
of the body. In this way, the authors considered that they had 
shown the physical possibility of the immortality of the soul. 
So far the book may be considered to be a legitimate and inter- 
* Ten British Mathematicians, p. 89. EDITORS. 


esting metaphysical speculation. But the authors proceeded 
further to apply their speculation, to explain the main doctrines 
of Christianity. Hypotheses about the nature of matter may 
change, and have changed wonderfully since 1875, an d no one 
cares to see sacred truths placed on so precarious a foundation 
as the vortex theory of matter. 

Such was the immediate success of the book, from the point 
of view of sales, that the authors were induced to venture on a 
novel Paradoxical Philosophy: a Sequel to the Unseen Universe. 
The hero is a Dr. Stoffkraft, who goes to Strathkelpie Castle 
to take part in an investigation of spiritualistic phenomena. 
He begins by detecting the mode in which one young lady 
performs her spirit-rapping, but forthwith falls into an " electro- 
biological " courtship of another, and, this proving successful, 
he is persuaded by his wife and her priest to renounce the 
black arts in the lump as works of the devil; and then settles 
down to compose an " Exposition of the Relations between 
Religion and Science," which he intends to be a thoroughly 
matured production. He advocates various materialistic views, 
but the other guests at the castle, who compose the Paradoxical 
Club, have read The Unseen Universe, and work discomfiture 
on Dr. Stoffkraft by arguments drawn from it. 

About this time, 1876, Tait published a volume entitled 
Lectures on Recent Advances in Physical Science. These lectures, 
prepared at the request of a number of professional men, 
chiefly engineers, were delivered in the physics theater of the 
University. They were edited from the report of a stenographer, 
and they give a very good idea of Tait's style as a lecturer. 
He was in his time considered the finest lecturer of the Edin- 
burgh University. On reading these lectures, published only 
twenty-five years ago, one is struck by the greatness of the 
advances made since, especially in the domain of electricity. 
In them there is no mention of the telephone or microphone, 
of the dynamo or incandescent lamp; electric waves and Jf-rays 
are yet undemonstrated. The advances treated of are the doc- 
trine of energy, spectrum analysis, the conduction of heat, 
and the structure of matter. Prof. Tait was accustomed 


to spend his vacation at the ancient city of St. Andrews, on the 
sea coast where there is a magnificent course for golf. On one 
occasion soon after these lectures were published both he and a 
Glasgow professor of theology, a metaphysician of the Hegelian 
school, were invited to a dinner in that city. Tait was very 
naturally drawn out to talk about the subjects on which he 
had been lecturing, and he did so largely and to the delight 
and edification of everyone except the Hegelian, who when he 
could stand it no longer, gravely put the question: " But, Mr. 
Tait, do you really mean to say that there is much value in 
such inquiries as you have been speaking about?" After that 
the subject was changed, and during the rest of the evening 
the mathematician and the metaphysician did little else than, 
as one of the company expressed it, " glour at each other." 

We have seen that Tait attended the meeting of the British 
Association at Aberdeen in 1859; but he was not a frequent 
attendant, for he said that there was too much jabber and 
talk, and that he did not care for great " spreads." At one 
of the Edinburgh meetings (1871) he was president of the section 
of mathematics and physics, on which occasion he delivered an 
address on Hamilton's Calculus of Quaternions and Thomson's 
Principle of the Dissipation of Energy. When the Associa- 
tion met in Glasgow in 1876, he was requested on short notice 
to deliver one of the popular lectures. He took for his subject 
Force, he made a plea for the accurate use of terms in mechanical 
science, a reform which has progressed much since that time. 
He says that force, defined as the rate of change of momentum 
in a body is also the space- variation of potential energy. Another 
point he insisted on is that matter and energy are things have 
objective existence, because their quantity in the universe is 
constant; force on the other hand cannot be a thing, or have 
objective existence, because its quantity is indeterminate. 
" It is only things," he said, " which can be sold." In view of 
this dictum it is interesting to observe that some courts have 
held that an electric current cannot be stolen, as it was not a 
thing. But what is stolen is the energy of the current, and 
according to Tait's ideas energy is a thing. 


In the same lecture Tait gave a succinct statement of his 
philosophy of knowledge. " In dealing with physical science " 
he said, "it is absolutely necessary to keep well in view the all- 
important principle that Nothing can be learned as to the physical 
world save by observation and experiment, or by mathematical 
deductions from data so obtained. On such a text volumes might 
be written, but they are unnecessary, for the student of physical 
science feels at each successive stage of his progress more and 
more profound conviction of its truth. He must receive it, 
at starting, as the unanimous conclusion of all who have in a 
legitimate manner made true physical science the subject of 
their study, and, as he gradually gains knowledge by this 
the only method, he will see more and more clearly the absolute 
impotence of all so-called metaphysics or a priori reasoning, 
to help him to a single step in advance. Man has been left 
entirely to himself as regards the acquirement of physical 
knowledge. But he has been gifted with various senses (with- 
out which he could not even know that the physical world 
exists) and with reason to enable him to control and under- 
stand their indications. Reason, unaided by the senses, is 
totally helpless in such matters. The indications given by the 
senses, unless interpreted by reason, are utterly unmeaning. 
But when reason and the senses work harmoniously together, 
they open to us an absolutely illimitable prospect of mysteries 
to be explored." 

What, it may be asked, is this reason which interprets the 
indications of the senses? Is it not the very a priori knowledge 
which the rational philosophers have ascribed to the mind? 
If so, why all this tirade against so-called metaphysics and 
a priori reasoning? To one who held that all knowledge came 
through the senses, such procedure would be logical, but not to 
the savant who uttered the above theory of knowledge. The 
speculations in the Unseen Universe assume the truth of the 
vortex theory of atoms. According to the ancient idea of the 
atom, it is a hard incompressible sphere. Boscovich removed 
the idea of hardness, and reduced the atom to a mere centre of 
force. Rankine, we have seen, supposed the point surrounded 


by a vortex, whirling round an axis passing through the point. 
Helmholtz investigated the properties of a vortex-ring such as 
skillful smokers emit. The whirling is round the core of the 
ring, and is associated with a progressive motion. Thomson 
replaced Rankine's vortex-atmosphere with Helmholtz's vortex- 
ring; and showed that the properties of the vortex-ring .in a 
perfect fluid would account for the indestructibility, elasticity 
and difference in kind of the atoms. The simplest kind of 
vortex is the unknotted ring. Suppose that one knot is put 
on the ring before the ends are tied; this will give the trefoil 
knot. It has three crossings, and was supposed to figure an 
essentially different kind of atom. 

Professor Tait investigated all the essentially different 
forms up to nine crossings, and contributed his results to the 
Edinburgh Royal Society. u Clever," some said, " but what is 
the use of it." The application was obvious; to elaborate the 
vortex-ring theory of atoms. Since then, however, electrical 
investigations have thrown more light on the subject of the 
atoms, so that Lord Kelvin is for going back to Lucretius. 

In the discharge of his duties as a teacher, Tait was a model 
to his colleagues. The lecture always began punctually at 
seven minutes past the hour, and did not end till the clock 
struck the next hour. Lecturing to undergraduate students 
he never obtruded his own researches, still less made them the 
subject of lectures; he had a conscientious desire to teach them 
thoroughly the appointed subjects. He was also punctual in his 
attendance at the laboratory. In the summer term he came 
about ii o'clock, would discuss results and plans with the 
researchers, take up his own investigation, and generally leave 
about 2 o'clock. In those days the physical laboratory did 
not remain open for long hours from 10 to 3. He had little 
liking for the general business of the University, and in later 
years he was to be found only in his lecture room, or laboratory 
at the University, in his library at home, or in the hall of the 
Edinburgh Royal Society. For many years he was general 
secretary, and did Herculean work for the Society. He never 
sought fellowship in other scientific societies, and the scientific 


honors he received were not in proportion to the greatness of 
his scientific achievements. 

In the summer time, after the close of the University session, 
it was Tait's invariable custom to spend the vacation on the 
links at St. Andrews. He "was an enthusiastic golfer, and exem- 
plified the harmony of theory and practice. He investigated by 
observation and experiment the various physical phenomena, 
the chief of which is the long time during which the golf ball 
remains in the air notwithstanding the slight elevation of its 
path above the ground. To investigate the path and velocity 
of the ball he made a drive and bunker in the basement of the 
University building. He communicated his results to the 
Royal Society of Edinburgh and there stated definitely the 
longest distance to which a golf ball could possibly be driven. 
One of his sons, Frederick Guthrie Tait, acquired great skill 
as a golfer. He was a lieutenant in the famous regiment called 
Gordon Highlanders, and also the champion amateur golfer 
of the British Islands. Such was his fame and prowess that 
to the general public Tait, the eminent mathematician, became 
known to them from being the father of the champion golfer. 
Prof. Tait enjoyed his son's success immensely for the buoyant 
and sanguine temperament of youth remained his throughout 
life. But the champion golfer upset his father's calculations 
of the greatest possible distance by driving a ball five yards 

In the course of his long career Tait was engaged in many 
polemical discussions. Look over the columns of Nature, and 
you will find controversies with Tyndall, Proctor, Zollner, 
Poincare, Gibbs, Heaviside and many others. He was apt 
to take an exaggerated view of men Newton was nothing 
short of a god, Leibnitz nothing better than a devil; whereas 
the truth is that Newton and Leibnitz were both men of many 
virtues but also of some failings. Tait himself was a man of 
many heroic virtues, mixed with a few inconsistencies. In 
these polemical discussions he used exaggerated language, 
which was probably taken more seriously than he intended. 
Anyhow a stranger introduced to him in his retiring room at 


the University, found a very genial and buoyant gentleman, very 
different from any idea imagined from reading his controversial 
letters. As regards those who attended his lectures, he commanded 
their respect and admiration, while the attitude of his research 
students can be expressed only by veneration and love. 

In 1897 his health began to break down before the end 
of the arduous winter session; but it was recuperated by a 
vacation on the links at St. Andrews. He had a splendid 
physique; but it had long been his custom to remain in his 
library to very late hours, reading, or writing at a plain wooden 
desk (which he did standing); these long hours of study and 
mental work eventually told upon his health. 

Lieutenant Tait, the champion golfer, was ordered with his 
regiment to the field of action in South Africa. His regiment 
(the Black Watch) suffered heavily in the engagements at the 
Modder River, directed by the unfortunate Lord Methuen. 
It was reported that Lieutenant Tait had been killed, but his 
fate remained uncertain for six weeks. He was killed at Koo- 
doosberg, where a white cross now marks his grave. The story 
of his life has appeared in a book F. G. Tait: a record. The 
loss was a serious blow to Prof. Tait, already in failing health. 
Early last year he was unable to attend to any of the duties 
of his chair, and he sent in his resignation. It was hoped that, 
freed from teaching duties, his health might recover. At 
the beginning of July, 1901, he went to the seashore near Edin- 
burgh to spend some days at the house of his friend Sir John 
Murray, editor of the " Challenger " reports. On July 4, he 
spent the afternoon in the garden and filled a sheet of foolscap 
with a quaternion investigation; in the evening he suddenly 
became ill and died in the course of a few hours, aged 70 years 
and one month. 

Before his death two volumes of his Collected Works had 
been published and a third will follow. At the time of his 
retirement those who had been trained by him in research took 
steps to prepare an illuminated address, but as they were scat- 
tered over all the world this was not fully finished at the time 
of his death, and it was presented to his widow. The address 


is surrounded by designs emblematic of his principal labors; 
there is a scroll on which are inscribed certain quaternion 
equations, a portrait of Newton, a thermo-electric diagram, a 
deep-sea thermometer, a Crookes' radiometer, and a profusion 
of knots. There are 63 signatures . to the address which reads 
as follows: 

" Dear Professor Tait: We need hardly tell you how deeply 
we share the universal feeling of regret with which the announce- 
ment of your resignation of the chair of Natural Philosophy 
in the University of Edinburgh has been received. Your tenure 
of the chair has extended over a most momentous period in the 
advance of knowledge; and no small part of the progress of 
physical science, which has been so characteristic of that period, 
has been the result of your own work. By your investigations 
and writings you have placed the whole scientific world in 
your debt, and have added prestige to a chair already rendered 
illustrious by your distinguished predecessors. The many 
thousands who have gained from your direct personal teaching 
a real insight with the processes of nature, and a training in 
accuracy of thought and of language, will always recall with 
pleasure and pride that you were their teacher. We whose 
privilege it was to come into closer touch with you in class- 
room or in laboratory, have had our life-work in many cases 
determined and in all cases influenced by the inspiration and 
guidance received there; and no words can fully express the 
feelings of reverence and affection which we entertain towards 
you. Yet, however feeble the expression, we ask you to accept 
it as our tribute of appreciation and of gratitude for all you 
have been to us as an intellectual stimulus and as a moral 
force. Your retirement is an irreparable loss to the University; 
but if, by relieving you from the arduous duties of the chair, 
it enables you to devote yourself more entirely to investigation 
and research, the world will without doubt have the greater 
gain. We wish you many years of health and strength both 
for the enjoyment of a well-earned leisure and for the further 
exercise of an unusually fruitful scientific activity." 

But it was not to be. 



WILLIAM THOMSON, now Lord Kelvin, was born in Belfast, 
Ireland, on the 26th of June, 1824. He is of Scottish-Irish 
descent. His father was James Thomson, then professor of 
mathematics in the Royal Belfast Academical Institution, who 
had a remarkable career; he was descended from a family of 
Thomsons, who had for several generations occupied a farm 
near Ballynahinch, County Down, in the north of Ireland. 
When a boy he endeavored all alone to understand the princi- 
ples of drilling and in this way was led to study mathematics. 
As a result he was sent to a small grammar school in his native 
place, where he rose to be an assistant teacher. Soon he became 
able to attend the University of Glasgow during the winter 
session, by teaching in the local school during the summer. 

After studying in this manner for five years he was appointed 
to a position in the Belfast Institution mentioned, where he 
was promoted to the professorship of mathematics. He was 
the author of an algebra, which was popular with teachers for 
many years, and his reputation was such that in 1832 he was 
appointed professor of mathematics in the University of Glasgow. 

William Thomson was then six years old, and his brother 
James Thomson nearly two years older. They were educated 
together at home by their father, and in 1834 they became 
students together at the University of Glasgow. At the Scot- 
tish Universities the conditions for entrance, were then, and 
still are, rather loose no inferior limit to the age, and no entrance 
examinations to pass. William Thomson, when he entered, 
was but little over ten years of age. He studied for six years. 
*This Lecture was delivered on March 25, 1902. EDITORS, 



but did not take a regular course leading to a degree. He had 
the genius of a mathematician, and his father was not slow to 
discover it. Accordingly he was sent when seventeen years 
of age to the University of Cambridge, where he became a 
student of St. Peter's College, the pldest foundation of that 
University (600 years). His undergraduate career at Cam- 
bridge extended over four years. In his first year he contributed 
a paper signed P. Q. R., to the Cambridge Mathematical Journal, 
in which he defended Fourier's Treatise on Heat from some 
criticisms made by Prof. Kelland of Edinburgh University. 
This paper was followed in the same journal by two others of 
still greater importance: " The uniform motion of heat in 
homogeneous solid bodies and its connection with the mathe- 
matical theory of Electricity " and " The linear motion of heat." 
In the former paper he points out the analogy between the 
theory of the conduction of heat in solid bodies and the theory 
of electric and magnetic attraction; and pursuing this analogy 
he makes use of known theorems about the conduction of heat 
to establish some of the most important theorems in the mathe- 
matical theory of electricity. The latter paper contains the 
foundations of the method which he afterwards applied to find 
limits to the age of the Earth. In his undergraduate career 
Thomson was well-known for his skill in boating; he was also 
president of the musical society. Probably he did not, as 
much as his rivals, concentrate his attention on the subjects 
which would pay in the final examinations; anyhow, he came 
out second wrangler. Although he was unsuccessful in the 
struggle for supremacy as determined by the blind adding of 
marks, one of the examiners declared that the senior wrangler 
was not fit to cut pencils for Thomson. In the subsequent 
more scientific test the competition for the Smith prizes he 
obtained the first place. He was immediately elected a Fellow 
of his college. 

At this time (1845) tne Analytical Society founded by 
Peacock, Herschel, and Babbage had accomplished its reform. 
But in Newton's University experimental investigation in 
physics had died out, the greatest mathematical physicists of the 


day were in Paris Fourier, Fresnel, Ampere, Biot, Regnault. 
So William Thomson went to Paris, and worked for a year in 
Regnault's laboratory, where classical determinations of physical 
constants were being made. Partly as a consequence of this 
step, Thomson has always been very popular with the scientists 
of France. When resident in Paris he published in Lionville's 
Journal a paper on the " Elementary Laws of Statical Electric- 
ity," in which he examined the experiments and deductions 
of Sir. W. Snow-Harris. This investigator had made an experi- 
mental examination of the fundamental laws of electric attrac- 
tion and repulsion, and his results were supposed to disprove 
tne well-known simple laws of Coulomb. Thomson showed 
by pointing out the defects of Harris' electrometers that the 
results, instead of disproving these laws, actually confirmed 
them, so far as they went. From this examination dates 
Thomson's interest in electrometers, which led to the invention 
of the quadrant electrometer, the portable electrometer, and the 
absolute electrometer. 

In 1846 the chair of Natural Philosophy in the University 
of Glasgow became vacant, and William Thomson was appointed 
at the early age of 22. I have heard it said that in the matter 
of appointments at Glasgow the principle of nepotism was 
powerful; in this case it was fortunate. Thomson's father was 
still the professor of mathematics, and remained so for three 
years longer; his brother, James Thomson, a few years later, 
became professor of engineering. At the same time Thomson 
was made editor of the Cambridge and Dublin Mathematical 
Journal (hitherto the Cambridge Journal). Among the con- 
tributors who supported him in this enterprise were Stokes, 
Cayley, Sylvester, De Morgan, Boole, Salmon, Hamilton, of 
whom only two now survive Sir George Stokes, and Rev. 
George Salmon, Provost of Trinity College, Dublin. 

While Thomson was a student at Cambridge, Joule made his 
investigations which determined the dynamical equivalent of 
heat. Thomson had made a special study of Fourier's Treatise 
on Heat, and had begun to apply his methods; consequently, 
on his return to Glasgow it was not long before he took up the 


dynamical theory of heat. His first contribution, read before 
the Royal Society of Edinburgh in 1849, was a critical account 
of Carnot's memoir " Reflexions sur la puissance motive du feu." 
Joule's measurements were at first almost ridiculed, and had few 
hearty supporters; but one of thes was Thomson. Carnot's 
theory of the heat-engine assumed that heat is a species of 
matter; Thomson set to himself the task to modify the theory 
to suit the doctrine that heat consists in the motion of the small 
particles of a body. His great stumbling block in the way of 
accepting the dynamical theory of heat was the difficulty .of 
accurately defining temperature. Founding on Carnot's work 
Prof. Thomson put this matter upon a perfectly satisfactory 
scientific basis. Before he propounded his absolute scale of 
temperature, purely empirical scales founded on the behavior 
of various gases, liquids, and solids, had each its advocate, 
and there seemed to be no satisfactory reason for preferring 
one to another. Once he propounded the absolute scale, no 
question has ever since been raised but that it is the only rational 
scale to adopt as the absolute one. To carry out this idea he 
made experimental investigations in conjunction with Joule 
on the thermodynamic properties of air and other gases, and as 
a result showed how to define a thermodynamic scale tempera- 
ture having the convenient property that air thermometers 
and other gas thermometers agree with it as closely as they 
agree with one another. 

His thermodynamic investigations led to the doctrine of the 
dissipation of energy announced by him in 1852. " During any 
transformation of energy of one form into energy of another 
form there is always a certain amount of energy rendered unavail- 
able for further useful application. No known process in nature 
is exactly reversible, that is to say, there is no known process 
by which we can connect a given amount of energy of one form 
into energy of another form, and then, reversing the process, 
reconvert the energy of the second form thus obtained into 
the original quantity of energy of the first form. In fact, during 
any transformation of energy from one form into another, 
there is always a certain portion of the energy changed into 


heat in the process of conversion, and the heat thus produced 
becomes dissipated and diffused by radiation and conduction. 
Consequently, there is a tendency in nature for all the energy 
in the universe of whatever kind, gradually to assume the 
form of heat, and having done so, to become equally diffused. 
Now, were all the energy of the universe converted into uni- 
formly diffused heat, it would cease to be available for producing 
mechanical effect, since for that purpose we must have a hot 
source and a cooler condenser. This gradual degradation of 
energy is perpetually going on; and, sooner or later, unless 
there be some restorative power, of which we at present have 
no knowledge whatever, the present state of things must come 
to an end." Maxwell imagined a restorative process which 
might be applied by intelligent demons. Suppose a portion 
of gas to be confined in a closed space, it will have a uniformly 
diffused temperature. Suppose a partition stretched across 
with a little door guarded by an intelligent demon. The mole- 
cules by their impacts and collisions really have different veloc- 
ities; what is uniform is the mean velocity. If the demon 
in charge opens the door so as to let the swift molecules in B 
go into A. and die slow molecules in A go into B, the degrada- 
tion of the temperature will be gradually restored. 

In 1852 he was married to Miss Margaret Crum, daughter 
of Walter Crum, Esq. of Thomliebank; a devout lady much 
attached to the Presbyterian Church. As a consequence, he 
resigned his fellowship in St. Peter's College; but he was after- 
wards made an honorary fellow. About this time he organized 
the first physical laboratory in Great Britain. He had an 
abundance of experimental problems for his students to tackle 
particularly on the properties of metals. About four years 
after Thomson located at Glasgow, submarine telegraphy became 
an object of practical science. In the working of a submarine 
cable between England and Holland, it was observed that the 
signals were more difficult to receive than those from the end 
of an aerial line. Faraday was the first to investigate the cause 
of this overlapping of the signals. At first there was a great 
deal of confusion; speed of signaling was mixed up with velocity 


of transmission; the duration of the signal was not distin- 
guished from the time required to traverse the cables. Thomson 
investigated the phenomenon, and found that it was due to 
the capacity of the cable; and he deduced the practical result 
that with cables of equal lateral .dimensions the retardations 
are proportional to the squares of the lengths. This law became 
known generally as the " law of squares." A Mr. Whitehouse, 
experimenting with a cable 1125 miles in length, found that 
the maximum effect of a signal communicated instantaneously 
at one end was received at the farther end in one second and a 
.half. Applied to these data the " law of squares " said that 
as the distance from Ireland to Newfoundland is twice the length 
of the experimental cable, the time in which a signal com- 
municated instantaneously would be received at the further 
end is 2.5 2 seconds: that is, six seconds. It became evident 
that if only five signals could be sent in a minute, the 
financial success of an Atlantic cable was very doubtful, so 
Whitehouse fought manfully against the " law. of squares." 
He said, " I can only regard it as a fiction of the schools, a 
forced and violent adaptation of a principle in physics, good 
and true under other circumstances but misapplied here." 
He also made experiments and published results which seemed 
entirely opposed to the law. To this Prof. Thomson replied 
in the Athenaum newspaper (Nov. i, 1856), reiterating the 
application of the " law of squares " to submarine telegraphy, 
and showing that the experiments cited really confirmed the 
law they were supposed to disprove. He further maintained 
that, notwithstanding the law of squares, Atlantic telegraphy 
was possible, and stated his conviction that increase of the 
electric pressure was a development in the wrong direction. 
Prof. Thomson showed that the condition for rapid signaling 
consisted in being able to observe the first beginning of the 
electric current at the far end, and to stop the signal as soon 
as it had risen to this observable value. To realize these con- 
ditions he invented the delicate reflecting galvanometer in 
which the minute turning of the magnet is magnified by the 
motion of a spot of light. Maxwell wrote a parody on Tenny- 


son's " Blow, bugle, blow," and called it " A Lecture to a Lady 
on Thomson's Reflecting Galvanometer": 

The lamplight falls on blackened walls, 

And streams through narrow perforations, 

The long beam trails o'er pasteboard scales 

With slow-decaying oscillations 

Flow, current, flow, set the quick light-spot flying, 

Flow current, answer light-spot, flashing, quivering, dying. 

O look! how queer! how thin and clear, 

And thinner, clearer, sharper growing 

The gliding fire! with central wire, 

The fine degrees distinctly showing. 

Swing, magnet, swing, advancing and receding, 

Swing magnet! Answer dearest, " What's your final reading?" 

O love! you fail to read the scale 

Correct to tenths of a division. 

To mirror heaven those eyes were given, 

And not for methods of precision 

Break, contact, break, set the free light-spot flying; 

Break contact, rest thee magnet, swinging, creeping, dying. 

In the above verses Maxwell describes the process of taking 
a quantitative reading for the amount of a steady electric 
current; for signaling, all that is necessary is to observe the 
direction towards which the spot of light is going to move. 
It was by the reflecting galvanometer that the historic message 
through the first Atlantic cable was received: " Europe and 
America are united by telegraphic communication. Glory to 
God in the highest, on earth peace and goodwill towards men." 

Prof. Thomson was personally engaged in the laying of the 
first cable. It transmitted several messages, then stopped. 
It served to prove the feasibility of the project which many 
engineers up to that time regarded as chimerical. By the 
labors of Thomson, Varley, Jenkin and others the construction 
of the cable was improved, as well as the mechanical means for 
laying it, and in 1866 a new cable was successfully laid, and 
the old one of the previous year raised from the depths and 


repaired. On his return from this labor in 1866, Prof. Thomson 
along with others of his distinguished coadjutors, received the 
honor of knighthood. Subsequently he invented a recording 
receiver for long cables, called the siphon recorder. We have 
seen that in 1860 Thomson and Tail entered upon the prepara- 
tion of their treatise on natural philosophy, which was planned 
to extend to four volumes, but of which the first and last appeared 
in 1867. In this interval of years Thomson was likewise engaged 
on the Atlantic Cable, and in writing several cosmological 
papers, which have ever since been famous subjects for dis- 
cussion: they were on the age of the Sun, the physical state 
of the interior of the Earth, and the age of the Earth as an abode 
for life. 

The last mentioned subject was treated of in a paper " On 
the secular cooling of the Earth," read before the Royal Society 
of Edinburgh in 1862. He introduced the subject as follows: 
" For eighteen yea'rs it has pressed on my mind, that essential 
principles of thermodynamics have been overlooked by those 
geologists who uncompromisingly oppose all paroxysmal 
hypotheses, and maintain not only that we have examples now 
before us on the Earth, of all the different actions by which its 
crust has been modified in geological history, but that these 
actions have never, or have not on the whole, been more violent 
in past time than they are at present. It is quite certain the 
solar system cannot have gone on, even as at present, for a few 
hundred thousand, or a few million years, without the irrevo- 
cable loss (by dissipation, not by annihilation) of a very con- 
siderable proportion of the entire energy initially in store for 
Sun heat, and for Plutonic action. It is quite certain that the 
whole store of energy in the solar system has been greater in 
all past time than at present; but it is conceivable that the 
rate at which it has been drawn upon and dissipated, whether 
by solar radiation, or by volcanic in the Earth or other dark 
bodies of the system, may have been nearly equable, or may 
even have been less rapid, in certain periods of the past. But 
it is far more probable that the secular rate of dissipation has 
been in some direct proportion to the total amount of energy 


in store at any time after the commencement of the present 
order of things, and has been therefore very slowly diminishing 
from age to age. I have endeavored to prove this for the Sun's 
heat, in an article recently published in Macmillari's Magazine 
(March, 1862), where I have shown that most probably the 
Sun was sensibly hotter a million years ago than he is now. 
Hence, geological speculation, assuming somewhat greater 
extremes of heat, more violent storms and floods, more luxuriant 
vegetation, and harder and coarser grained plants and animals, 
in remote antiquity, are more probable than those of the extreme 
quietist, or * uniformitarian * school. A middle path, not 
generally safest in scientific speculation, seems to be so in this 
case. It is probable that hypotheses of grand catastrophes 
destroying all life from the Earth, and ruining its whole surface 
at once, are greatly in error; it is impossible that hypotheses 
assuming an equability of sun and storms for 1,000,000 years can 
be wholly true." 

He proceeded in the paper cited, to apply Fourier's results 
to deduce a limit to the age of the Earth. Suppose a solid 
slab of uniform thickness and of great lateral dimensions to 
be originally heated to a temperature F, one side to be kept 
exposed to a temperature 0, and the other to be kept exposed 
to a temperature V. Let k denote the conductivity of the 
solid, when measured in terms of the thermal capacity of the 
unit of volume; and let v denote the temperature at any dis- 
tance x from the surface at any time / from the beginning of 
the cooling. Fourier showed that under these conditions, 

Here means the gradient of temperature, along a line normal 

to the face; it is the rate of change of the temperature as you 
go along the direction of x. This formula does not apply to 
any time prior to the beginning of the cooling, for then / will be 
negative and the formula involves the square root of /. 

But what application has this result to the case of the Earth? 


No doubt there still are people who think that the Earth is an 
infinite slab; but if the investigation has any application, it 
is to a solid globe, originally at one uniform temperature, exposed 
to a cooling agent at the surface. But the case of the Earth 
is reduced to the simple case of the slab by the following con- 
siderations. It had been ascertained by the observations of 
Forbes on underground temperature that change of temperature 
due to day and night, or summer and winter, disappears at 
about 24 feet below the surface; and observations in coalpits 
and borings show that the temperature thereafter increases 
at the rate of about one degree Fahrenheit per 50 feet of descent; 
but Fourier's results show that this rate will practically vanish 
at a small depth compared with the distance to the Earth's 
centre. Hence a spherical plate of the Earth if such thickness 
may be treated as a plate of the kind specified. The best 
value of k then known was 400; hence for the case of the Earth, 




When / is very large and x small, the exponential factor is 
negligible; and we know that then is ; hence 


50 354V 7 * ' 

v 50 

Suppose V, the original temperature of the Earth, when it had 
just solidified, to be 7000 F., the temperature of melting rock, 
then / = 98,000,000 years. 

Prof. Thomson concluded that the age of the Earth as a possible 
abode for life must lie between 400,000,000 years and 20,000,000 
years. These results came like a bolt from the blue sky on the 
geologists and biologists of the day. The former supposed that 


physical changes went on in the past at the slow rate at which 
they take place now; and by a simple application of the rule of 
three, to the sedimentary rocks, demanded as much time as the 
above for a small portion of the secondary period. In the Earth 
they discovered no trace of a beginning, no indication of an 
end; and some of them, leaving the solid crust of the Earth, 
and looking out into the Universe could see no signs of age or 
decay in the solar system. The biologists too were explaining 
the evolution of forms by unlimited amounts of time. The 
great Darwin spoke of the proposed limitation of geological 
time as one of his " sorest troubles." It was indeed inevitable 
that a clash should come. 

Four years later, 1866, Sir William Thomson read another 
paper to the Edinburgh Society, " The doctrine of uniformity 
in geology briefly refuted." It contained only a few sentences 
and was a formal indictment of the fundamental doctrine of 
the geologists. The geologists put up Prof. Huxley to defend 
them; which he did in an address to the Geological Society 
of London in 1869. We have seen in a previous lecture how 
much Huxley knew of the nature of mathematics; he was 
scared at a few italic letters, particularly if they were small, 

not to mention the more formidable . He could not discuss 


Thomson's arguments scientifically, all he could do was to make 
fun of them, and encourage his colleagues in their indifference. 
He said, as an introduction, " I do not suppose that at the 
present day any geologist would be found to maintain absolute 
uniformitarianism, to deny that the rapidity of the rotation of 
the Earth may be diminishing, that the Sun may be waxing 
dim, or that the Earth itself may be cooling. Most of us, I 
suspect, are Gallios, ' who care for none of these things,' being 
of opinion that, true or fictitious they have made no practical 
difference to the Earth, during the period of which a record is 
.preserved in stratified deposits." If researches which are the 
outcome of dynamical reasoning, combined with observational 
and experimental data, applied to determine the constancy 
of the length of the day, the intensity of sunshine in different 


ages, the age and temperature of the Earth are not geology, 
it is difficult to adduce anything which has a right to that 
title. Yet Huxley in the name of the geologists said that 
they were intellectual Gallios, caring for none of these things. 
It is certainly a very remarkable, fact that one who fought 
all his life against ecclesiastical Callios as regards evolution 
should, in the matter of the application of physical science 
to a geological problem, borrow their precise attitude and 

The controversy has gone on ever since, and has enlivened 
many a meeting of the British Association. The geologists 
say to Lord Kelvin "Look at our arguments." Lord Kelvin 
says to the geologists " Look at mine." The former call out 
" cosmogonist " ; the latter replied "geological calculus." As 
a result of the controversy the uniformitarian doctrine has 
disappeared; but no agreement has been reached about the 
age of the Earth when it became an abode for life. Kelvin's 
reasoning can be attacked only by questioning the values 
which are assumed for the constants, or by denying the con- 
ditions which are assumed to be true in applying Fourier's prob- 
lem to the case of the Earth. The former course was adopted 
a few years ago by Prof. Perry; by modifying the constant k 
he increased the time about tenfold. It is the only course 
which presents any avenue of escape such as the geologists 
desire to see. Is the Earth a body which was once molten 
hot, and has been subsequently left to cool, without any further 
generation of heat in the interior by oxidation of its contents? 
If the geologists had more mathematical training, they might 
be able to make better use of their data. As it is their reasoning 
is too much of this character: the Mississippi now carries 
down so much mud in a year, how long will it take at this rate 
to reduce the whole valley to the level of the Gulf of Mexico? 
This is a specimen of " logical calculus." A very slight 
knowledge of mathematics suffices, however, to show that 
natural changes take place at a variable rate which depends 
at any time on the amount to be changed, and until one gets a 
clear idea of a logarithm and an exponential he will not be able 


to reason to much purpose on the time required for any of the 
works of Nature.* 

Sir William Thomson's labors in connection with the laying 
of the Atlantic cables called for his presence on board ship, 
and thus attracted his attention to the art of navigation, if 
indeed he could live in Glasgow without being in some measure 
drawn into it. He became a skillful yachtsman, and he used 
his yacht for testing improvements in the means of navigation. 
His achievements in this direction are numerous and important, 
but the principal ones are his improved mariner's compass, and 
his improved sounding line. The use of iron in the construction 
of ships introduces a serious interference with the compass 
needle; the needle may direct itself towards a point in the ship 
instead of a point in the Earth. The action of the ship's mag- 
netism must be cancelled; and this is no easy matter in the case 
of the ordinary mariner's compass. The improved compass 
of Sir William Thomson had instead of one large needle, a 
number of very small needles placed parallel to one another; 
and instead of a heavy continuous card a light card with the 
centre wholly cut away. It is more steady, more free to move, 
and more easily protected from the ship's magnetism. His 
sounding-line consists of a sinker of 20 to 30 pounds, carried 
by a strong steel wire. The greatest vertical depth of the 
sinker beneath the surface is recorded by an instrument which 
measures the greatest water pressure; and it is read after the 
instrument has been brought back on board ship. In the old 
method of casting the lead the depth is determined from the 
length of rope run out. With the old method a ship must be 
brought to a standstill, if any trustworthy measure is desired 
in deep water; with the improved line, a steamer may be run- 
ning at a speed of 20 knots. 

Connected with navigation is his invention of a machine 
for calculating the heights of the tides at a given port. " It 
is essentially a mechanical contrivance by which the sum of 

* One desiring to follow this celebrated controversy further should consult 
the article on Geology in the Eleventh Edition of the Encyclopaedia 
Britannica. EDITORS. 


a Fourier series is obtained by mechanical means. The tides 
for a given part for a whole year can be wound out of it in four 
hours, thus facilitating their prediction to an extraordinary 
degree. The form in which it gives the prediction being a 
continuous curve on paper, it enables the height of the water 
at any moment to be ascertained by inspection, while any 
arithmetical result that could possibly be worth the trouble 
of calculating, would only give the times of high and low water." 

Sir William Thomson was for many years a member of the 
Committee of the British Association, which had in charge the 
development of an absolute system of units. He was the 
champion of the centimeter as opposed to the metre; and his 
argument was that it was important that the density of water 
should be unity, not 1,000,000. Electrical measurement was 
then in its infancy. Looking at the question in the light of 
recent development, we see that the adoption of the centi- 
meter was a mistake for the desired system of C.G.S. electric 
units is too small for practical purposes, and the actual system 
which is used involves the fundamental units multiplied by 
some power of ten. Hence electrical computations now include 
the metric system proper, the C.G.S. system, and the practical 
electric system. Sir William Thomson designed many instru- 
ments for the purpose of electrical measurements, and for the 
manufacture of these instruments established a large workshop 
in Glasgow, under the management of James White. This has 
been a principal source of his fortune. 

When I was at work in Tait's laboratory, Sir William 
Thomson was president of the Royal Society of Edinburgh; 
and I have often heard him read papers and make addresses. 
These meetings brought him to Edinburgh frequently, and it 
was his custom to visit the laboratory of his colleague Tait. 
He must originally have been about six feet high. But for 
many years his height has been diminished by a stiff leg which 
was brought about in the following way. He broke his leg 
when skating on the ice, and would not remain at rest until it 
had recovered properly. Otherwise his appearance was athletic. 
Compared with Tait, he was not so elegant a speaker, but his 


papers have more of the stamp of a genius. He has strong 
opinions on most subjects, and like most Irishmen, he is not 
afraid of a controversy. If Tait made a move and was not 
immediately successful, he was apt to retire resolved to have 
nothing further to do with it; not so Thomson; if baffled, he 
returns to the attack again and again On social matters he 
has strong conservative opinions; at a club meeting after the 
regular meeting of the Royal Society of Edinburgh he was 
asked: " Sir William! what do you think? Should a man be 
allowed to marry his widow's sister." " No sir, the Bible 
forbids it, and I hope the law of the land will continue to 
forbid it." 

Sir William Thomson visited America at the time of the 
Centennial Exposition at Philadelphia, 1876, and he brought 
back to Scotland a wonderful account of Graham Bell's tele- 
phones. In 1884 he made another visit, to deliver a course 
of lectures at the Johns Hopkins University. This course of 
lectures, twenty in all, treated of the wave-theory of light, 
principally with the outstanding difficulties of the theory, and 
they partook largely of the nature of conferences. " Discussion 
did not end in the lecture-room ; and the three weeks over which 
the lectures extended, were like one long conference." He 
was also a member of the Commission which solved the problem 
of harnessing Niagara. 

In 1892 he was created a member of the House of Lords, 
under the title of Baron Kelvin. He took his title from the 
stream which flows past the hill on which the University of 
Glasgow is built. In 1896 the jubilee of his professorship was 
celebrated with great eclat at Glasgow. The exercises lasted 
three days and there were present representatives from all the 
scientific institutions of Great Britain, and from many of the 
scientific institutions of other countries. After a further tenure 
of three years, he resigned his chair. He now spends his time 
mostly at his country seat at Largs on the coast of Ayrshire, and 
at his house in London. The degrees and honors conferred 
upon him are numbered by hundreds, and the enumeration of 
these honors might be most briefly made by mentioning the 


few not conferred; he is still open, I believe, to receive some 
distinguished mark of recognition from the geologists. 

Lord Kelvin has been twice married, but there is no direct 
heir to inherit either his genius or title. Notwithstanding the 
fact that he has long been the acknowledged leader of science 
in Great Britain, and indeed in Europe, his disposition has 
remained simple and kindly. A multitude of honors, and great 
fame and power has not spoiled the grandson of the small Irish 
farmer. He is still active in the production of scientific papers, 
and although now nearly 78 years of age is making preparations 
to again cross that ocean which has been the scene of so many 
of his exploits, and which is now much more safely navigated 
through the instrumentality of his inventions.* 

* Lord Kelvin died on December 17, 1907, in the 84th year of his age. 
His activity in scientific discussions did not diminish with age. He revised 
the lectures on the wave-theory of light which he had delivered at Johns 
Hopkins University and published them in 1904. In that year also he was 
elected Chancellor of the University of Glasgow. He continued to take an 
active part in the work of scientific societies; only a few months before his 
death he delivered at the meeting of the British Association a long and search- 
ing address on the electronic theory of matter. He was buried in Westminster 
Abbey a few feet south of the grave of Newton. EDITORS. 



CHARLES BABBAGE was born at Totnes in Devonshire on 
December 26, 1791. His father was a banker and was able to 
give his son a moderate fortune. Being a sickly child he received 
a somewhat desultory education at private schools, first at 
Alphington near Exeter, and later at Endfield near London. 
It appears that he instructed himself in the elements of Algebra, 
and that he early manifested a great fondness for it. 

When he entered Trinity College, Cambridge, in 1810, he 
was already acquainted with the text books of Lacroix and 
other French writers; he had also read the book of Woolhouse 
which aimed at introducing into Cambridge the Leibnitzian 
notation for the differential calculus. Among his contemporary 
graduates he found congenial spirits in Peacock and Herschel, 
and the three friends, along with some juniors such as Whewell, 
were wont to breakfast together each Sunday morning and 
discuss philosophical subjects. At one of these philosophical 
breakfasts the "Analytical Society" was formed, the object 
of which as stated by Babbage was " to advocate the principles 
of pure d-ism in opposition to the J0/-age of the University. 
Babbage was skillful in getting up what the politicians call 
a good cry. It was while he was yet an undergraduate that an 
idea occurred to him which ruled the whole of his subsequent 
career. One evening he was sitting in the rooms of the Analyti- 
cal Society at Cambridge, his head leaning forward on the table 
in a dreamy mood, with a table of logarithms lying open before 
him. Another member, coming into the room and seeing him 
half asleep, called out " Well, Babbage, what are you dreaming 
* This Lecture was delivered on April 21, 1903. EDITORS. 


about?" to which he replied " I am thinking that all these 
mathematical tables might be calculated by machinery." 

In the last year of his undergraduate career, he migrated 
from Trinity College to Peterhouse, and did not compete for 
honors, believing Herschel* sure of tjje first place, and not caring 
to come out second. He took merely a pass degree in 1815, 
and thereafter resided in London, where philosophical break- 
fasts continued to be a feature of his house. In the year follow- 
ing the text-book of Lacroix Differential and Integral Calculus, 
translated by Herschel, Peacock, and Babbage, was published 
by the Analytical Society; and four years later a volume of 
Examples on the Calculus. Lacroix had also written on the 
calculus of Finite Differences, and both Herschel and Babbage 
were attracted to the subject. The latter immediately con- 
tributed three papers on " The Calculus of Functions " to the 
Royal Society and he was elected a Fellow at the age of 

He married, and made a tour of the Continent. He visited 
Paris and studied the details of the arrangement by which the 
celebrated French tables had been computed under the direc- 
tion of Prony; and he copied the logarithms to fourteen places 
of figures of every 5ooth number from 10,000 to 100,000 from 
the manuscript tables deposited in the observatory at Paris. 
These tables were computed at the time of the Revolution, 
in order to facilitate the application of the decimal division 
of the degree which had been adopted. In executing the task 
Prony received a valuable hint from Smith's Wealth of Nations 
where the " division of labor " is exemplified. He adopted the 
idea; appointed three classes of mathematical workers; first, 
five or six analyists to investigate the best formulae; second, 
seven or eight mathematicians to calculate arithmetical values 
at suitable intervals; and third, sixty or eighty arithmeticians 
(said to have been tailors on a strike) to compute intermediate 
values by the method of differences. The tables thus computed 
fill seventeen large folio volumes. 

On his return to London he was encouraged by Wollaston 
(a pioneer in electrical science) to set about the realization 


of his idea of a difference machine for computing tables. What 
is the fundamental idea of the method of differences? Write 
down the square numbers in the first column, the differences 

First Second Third 

Differences Differences Differences 




16 9 2 o 

25 II 2 

36 13 


between the successive squares in the second column, and the 
differences of the first difference in the third column; these 
last are constant, consequently the next differences are all zero. 
To compute a table of squares, then, it is only necessary to add 
to a square the preceding first and second differences, thus 
49+13 + 2 = 64, etc. In the case of logarithms and other 
transcendental functions there is no difference which becomes 
zero, but when a certain number of figures only are required, 
there is a difference which is zero within a certain range. Hence 
within that range the same process of calculation may be applied 
as for a function which has a certain order of differences con- 
stant. To calculate tables by a machine only a device for 
adding is required; to insure accuracy in the printed tables 
Babbage thought it necessary that the machine which computes 
the results should also print them. 

By 1822 Babbage had constructed a small model having 
two orders of differences and applicable to computing numbers 
of from six to eight places. It could compute squares, tri- 
angular numbers, values of # 2 +#+4i, and values of any function 
of which the second difference was constant and not greater 
than about 1000. He exhibited this model to the Royal Astro- 
nomical Society and was subsequently awarded a gold medal 
on account of it. He also wrote a public letter to Sir Humphrey 
Davy, then president of the Royal Society, explaining the 
utility of his invention. Through what had been published the 


Government was induced to apply to the Royal Society for an 
opinion on the merits and utility of the invention; it appointed 
a committee which reported favorably. The Government 
advanced 1500 and work was started in 1823. Babbage 
superintended the work, and he employed a mechanical engineer, 
named Clement, whose workshop was in Lambeth, to execute 
his plans. The construction of a Difference Engine was begun 
having six orders of differences, each consisting of about 
twenty places of figures, and provided with mechanism to print 
the results. It was called an Engine, because after being 
started with the proper differences for computing a table the 
results would be produced merely by power applied to a shaft. 
Three years later (1826) the Lucasian professorship of 
mathematics at Cambridge became vacant. There were three 
candidates; French, who was the head of one of the colleges; 
Airy, afterwards astronomer royal; and Babbage. The appoint- 
ment is made by the heads of the colleges, and in this case they 
were quite prepared to appoint a candidate from their own 
number who was more proficient in divinity and Hebrew than 
in mathematics. This was Newton's chair, but since his time 
mathematics had declined at Cambridge and was only now 
beginning to revive. Babbage threatened legal proceedings, 
with the result French retired and Airy was elected. Airy 
resided and lectured, the first Lucasian professor who had done 
so for many years; two years later he changed to the professor- 
ship of Astronomy, and his former rival Babbage was elected. 
This was in 1828; although Babbage held this professorship 
until 1839 he did not reside or lecture; his mind was completely 
absorbed with anxiety about the success and fame of his com- 
puting machine. However, with a view of delivering a course of 
lectures, he collected the material and published a book called 
Economy of Machinery and Manujacture which he dedicated to 
the University of Cambridge. The object of the volume is to 
point out the effects and the advantages which arise from the 
use of machines; to endeavor to classify their modes of action 
and to trace the consequences of applying machinery to super- 
sede the skill and power of the human arm. Babbage wrote 


many books, but this is considered his most finished production; 
it has been described as a " hymn in honor of machinery." 

The work on the Difference Engine went on for five years 
with little interruption, and the expenses had amounted to 
nearly 7000, of which the Government had advanced less than 
half, the remainder having come out of Babbage's pocket. 
Before proceeding further he wished to have a complete under- 
standing with the Government, which was eventually reached 
after a delay of two years. The Government repaid Babbage 
what he had advanced, arranged to pay certified bills, leased 
a part of the grounds belonging to Babbage's house, and erected 
thereon a fireproof office and workshops. While these were in 
course of erection, the work continued for three years longer in 
Clement's workshop. At the end of this time (1833) a portion 
of the Difference Engine was assembled, and found to fulfill all 
Babbage's expectations and even more. 

The Royal Society, like the University of Cambridge, had 
also declined as a scientific center since the days of Newton. 
The president had often been one of high rank rather than 
eminent in science. At this time the reforming party put up 
Sir John Herschel as a candidate for the presidency in opposi- 
tion to the Duke of Sussex, but the royal candidate was success- 
ful. Babbage was one of the leading reformers; he prepared 
and printed a book called The Decline of Science in England 
which proved highly beneficial in that it led in a short time 
to the foundation of the British Association for the Advancement 
of Science. 

After the drawings and parts of the computing machine 
were removed to the fireproof premises adjoining Babbage's 
house, the engineer Clement made a claim for compensation 
for the removal of his business from Lambeth, a claim which 
Babbage declined to entertain as being extravagant. Whereupon 
Clement stopped the work on the machine, disbanded the 
specially trained workmen, and carried off all the tools, includ- 
ing those specially designed by Babbage and paid for by the 
Government. This he could do according to English law; 
he offered to sell the special tools to Babbage but the latter 


declined purchasing. Notwithstanding this bad break, the 
Government were willing to proceed; and the construction 
was actually in an advanced state. Among the workmen dis- 
charged by Clement was Joseph (afterwards Sir Joseph) Whit- 
worth who later amassed a fortune ; fey utilizing as a mechanical 
engineer the training which he got from Babbage. 

While the work was suspended owing to change of workshop, 
Babbage experimented much with the portion of the engine 
which had been assembled; and his inventive mind conceived 
the idea of a much more general machine which he called an 
Analytical Engine. He immediately set to work to plan 
how it could be realized, and he considered that he had hit 
upon a much simpler mechanical invention for adding than the 
one adopted in the Difference Engine. Unfortunately instead 
of proceeding to complete the Difference Engine as the plans 
adopted and followed for ten years, as the Government desired 
him to do, he waited for an opportunity to explain about his 
new invention. However superior his new ideas might be, he 
ought to have perceived that the heads of the Government 
and that Government frequently changing were not capable 
of appreciating their value, and that they would judge of the 
matter from the business point of view, saying " You wish 
us to abandon the construction of an engine which has cost 
17,000 and wish us to undertake a new and more elaborate 
engine; we cannot justify such expenditure to the House of 

It was very unfortunate that Babbage did not see the practi- 
cal necessity of completing the first engine on the plans adopted. 
By the course he adopted he gave his scientific enemies a chance 
to defeat the realization of his great invention. The matter 
was not finally settled until 1842 nine years after the con- 
struction was suspended. He was then informed by the Premier 
and the Chancellor of the Exchequer that they abandoned the 
undertaking, and that he might have what had been constructed 
for his own property. Babbage declined to accept it; the 
portion assembled was placed in a museum; the loose parts 
sold or melted down. Babbage appears to have thought that 


the Ministers acted on their own judgment, but it was not so; 
Airy, the astronomer at Greenwich, records in his Autobiography 
that he was consulted and that he pronounced the Difference 
Engine to be worthless. Naturally the ministry attached great 
weight to this opinion, for the immediate value of this engine 
was claimed to be the construction of astronomical and nautical 

The portion of the Difference Engine which was put together 
has been exhibited at various Expositions in London, and is 
now in the Science and Art Museum at South Kensington; 
I saw it, and heard it explained, on the occasion of the Loan 
Exhibition of Scientific Apparatus in 1876. It consists of three 
columns; each column contained six cages, each cage one figure 
wheel. Each figure wheel has the numbers o to 9 placed around 
the circumference and may be set by hand at any one of the 
numbers. The right-hand column is for the resulting number, 
the middle column for the first difference, and the left-hand 
column for the second difference. Suppose any sets of proper 
numbers to be placed upon the three columns, then the mechan- 
ism is such that four half turns of the handle two backwards 
and two forwards causes the first difference to be added to the 
previous result and the second difference to be added to the first 
difference ; hence if the machine printed the results, mere turning 
of the handle would produce the entire table of numbers or 
all the results requiring to be interpolated between two given 
values. To make the portion assembled more useful, slight 
departures from the general plan were adopted. The three 
upper wheels of the left-hand column were separated from the 
rest of the machine and employed to count the natural numbers, 
that is, to register the number of calculations made and give' 
the numbers corresponding with the terms of the table computed. 
A wheel at the top of the central column indicated when each 
calculation is complete and also the position of the handle when 
the figure wheel was to be adjusted. 

About this time (1829) the Earl of Bridgewater died, leaving 
a sum of 10,000 to trustees to be expended in the production 
of books " on the Power, Wisdom, and Goodness of God as 


manifested in the Creation," the writers to be selected by the 
President of the Royal Society. He, acting with certain bishops, 
selected eight authors, assigned to each a portion of the subject 
with an honorarium of 1250. Babbage was not one of the 
number, but in 1837, after the eight treatises had appeared, 
he published a volume entitled The Ninth Bridgewater Treatise. 
In design the book is grand and much superior to the regular 
treatises, but in execution it is like many others of Babbage's 
works, a magnificent torso. He was moved to write the book 
by a chapter in Whewell's Bridgewater volume where it is 
maintained that long application to mathematical and physical 
reasoning disqualifies the mind from duly appreciating the force 
of that kind of reasoning which alone can be adduced in favor of 
Natural Theology. Babbage thought that such reasoning 
tended to promote the prejudice that the pursuits of exact 
science are unfavorable to religion; he shows on the contrary 
that his pursuits had led him to new views of the truths of 
Natural Theology. 

The most remarkable part of Babbage's book is where he 
takes up Hume's conception of a law of nature, and the conse- 
quences as to miracles which he deduced from it. According to 
Hume cause and effect are nothing more than invariable sequence; 
and a law of nature rests upon experience or repeated observation 
just as the reliability of a witness does. Babbage points to his 
Difference Engine (that is, the part completed) and remarks 
that it may be adjusted to produce the natural numbers. He 
asks a supposed observer how often a natural number must 
be produced to infer that this is the whole law of the machine; 
one hundred times? one thousand times? one million times? 
Babbage answers that according to the constitution and given 
adjustment of the machine it will produce the natural number 
up to 1,000,001; but after that it will give the triangular num- 
bers and that after 2761 turns a further complexity will be 
introduced. These additional complexities are necessary con- 
sequences of the nature and given adjustment of the machine; 
and no amount of mere induction from given instances could 
detect the inner necessary connection. Hence casual connection 


and repeated sequence are not the same thing. He went on 
to prove by his Analytical Engine (existing only in drawings) 
that "It is more probable that any law, at the knowledge of 
which we have arrived by observation, shall be subject to one 
of those violations, which, according to Hume's definition, 
constitutes a miracle, than that it should not be so subjected." 
He rests this proposition on the statement that his Analytical 
Engine could be set to compute the successive terms of a given 
algebraic law, but so that one chosen term would be different, 
and then to resume the production of the true terms ever after. 
Provision could be made by the maker of the machine for a 
single suspension of the law at a given point. 

Babbage devoted 37 years of his life to perfecting the inven- 
tion of the Analytical Engine and no inconsiderable part of his 
fortune was spent thereon. This invention must be carefully 
distinguished from the Difference Engine; they are often popu- 
larly confounded but are confused in some scientific writings. 
When the fragment of the Difference Engine was put together 
in 1833, Babbage found that, as he had anticipated, it possessed 
powers beyond those for which it was intended, something in 
the same way as algebra displays powers beyond those of 
generalized arithmetic for which it was designed. Babbage 
saw that, by interposing a few connecting wheels, the column 
of Result could be made to influence the last Difference, and he 
proposed to arrange the axes circularly so that these columns 
should be near each other. He called this arrangement " the 
engine eating its own tail." This soon led to the idea of con- 
trolling the engine by entirely independent means, and to the 
idea of an engine which could calculate the numerical values of 
any function which the mathematician can express in a series 
of integral powers. 

.To realize the first idea that is, to make the adjustment 
of the engine automatic he had recourse to the device of 
punched cards similar to those invented by Jacquard for the 
weaving loom. The machine was to consist of three parts; 
first, the store; second, the mill; third, the cards. The store 
was to consist of 100 columns each of fifty wheels for indicating 


the given numbers, intermediate numbers, and resulting number. 
The mill was to consist of mechanism which would add two 
numbers, subtract a less number from a greater, multiply two 
numbers, or divide one number by another, according to the 
kind of gearing brought into operation. The cards were of 
three kinds; Number cards to communicate given numbers 
to the store; Directive cards to transfer numbers from the 
store to the mill and from the mill to the store; Operation cards 
to call for addition, subtraction, multiplication, division. For 
example, to compute numerical values of (ab-\-c)d, seventeen 
cards in all were required, as follows: 

Number Directive Operation 

Card Card Card 

1 Places a on column i of store. 

2 Places b on. column 2 of store. 

3 Places c on column 3 of store. 

4 Places d on column 4 of store. 

1 Brings a from store to mill. 

2 Brings b from store to mill. 

1 Multiplies a and b = p. 

3 Takes p -to column 5 of store. 

4 Brings p into mill. 

5 Brings c into mill. 

2 Adds p and c = q. 

6 Takes q to column 6 of store. 

7 Brings d into mill. 

8 Brings q into mill. 

3 Multiplies d and q = r. 

9 Takes r to column 7 of store. 
10 Takes r to printing apparatus. 

Each form of calculation would require a special set of 
cards strung together in proper order; just as the particular 
pattern for a woven fabric requires its own set of Jacquard 
cards, and they would be applied to the calculating machine 
in the same manner. The great improvement in the construction 
of the engine proper was the invention of the principle of the 
Chain, by which the carriage of the tens is anticipated. This 
part of the design was actually constructed. For subtraction 
the adding rotations were reversed; multiplication was to be 
effected by successive additions, and division by successive 
subtractions. It is obvious that the machine could treat of 


transcendental functions only when expressed in a series of powers. 
Irrational quantities would be represented approximately. 

To express the complicated relations among the various 
parts of the machine, Babbage invented what he called a 
" mechanical notation " explained in a paper published in the 
Philosophical Transactions for 1826, entitled " On a method of 
expressing by signs the action of machinery." It consists of 
three divisions; first, Notation for the parts; second, Represen- 
tation of trains; third, Representation of cycles. He denoted 
pieces and points of the frame by upright letters, the former 
capitals and the latter small letters; movable pieces and their 
points by slant letters, capitals and small letters respectively. 
On account of the great number of movable pieces he employed 
indices, placing them to the left above the letters. The train 
is designed to show how motion is transmitted from the prime 
motor to the final driven piece. The several pieces are marked 
on a diagram by trial so that each pair of driver (point) and 
driven (piece) may be connected by arrows; after a number 
of trials the pieces are so placed as to make the connecting 
arrows the shortest. In a cycle he aimed at representing the 
time during which each piece moved and the time of action 
of each of its working points. The period of the machine is 
represented by a vertical line divided into proper subdivisions 
on the nature of the machine; to each piece and to each working 
point is allotted a parallel line, and those portions of the period 
are marked off during which there is no movement of the piece 
or the point, thus giving a synoptic view of the motion of the 
machine. To make drawings, perfect the notations, and test 
mechanical contrivances, he turned his coach house into a 
forge and foundry, transformed his stables into a workshop, 
and expended a large sum in employing skilled vorkmen. 

In 1840 he received a letter from M. Plana, nephew of 
Lagrange, urging him to come to a meeting of Italian philoso- 
phers which was to be held in Turin. Babbage went, furnished 
with models, drawings, and notations of his Analytical Engine, 
and explained them to the Italian mathematicians, among 
whom was M. Menabrea. Subsequently Menabrea wrote an 


account of the invention in French, which was afterwards 
translated into English aftd embellished with notes by Lady 
Lovelace, nee Augusta Ada Byron, daughter of the poet Byron. 
This lady did not inherit the poetic genius of her father, but 
was remarkable for exact mathematical attainments, which 
were also possessed by her mother. ' 

Babbage himself never wrote an extended account of the 
Analytical Engine; the memoir of Menabrea with the notes 
of Lady Lovelace gives the most complete account regarding 
it. In 1848 he made drawings for a new Difference Engine 
in which the adding was to be effected by his new contrivance. 
He was anxious to discharge whatever imagined obligation 
might be supposed to rest upon him in connection with the 
original undertaking, and an entirely practicable proposal was 
laid before the Premier (Lord Derby) by Lord Rosse, a mathe- 
matical nobleman. The Premier turned the matter over to 
his Chancellor of the Exchequer, Benjamin Disraeli, who gave 
an adverse decision. The wrath of Babbage at the novelist 
was unbounded; he denounced him as the Herostratus of 
Science. A few years later a Difference Engine, suggested by 
Babbage's plans, was actually constructed in Sweden by a 
printer named Scheutz; it performed successfully the kind of 
work for which it was designed. The original Scheutz machine 
was bought by the Dudley Observatory at Albany, N. Y., and 
was used to a slight extent about 1878; a copy of it constructed 
for the English Government has been used for the calculation 
of insurance tables. 

After the death of Babbage in 1871 what he had accomplished 
on the Analytical Engine was transferred for safe-keeping 
to the Museum at South Kensington. The British Association 
appointed a committee to examine it; in 1878 they reported 
that the part assembled was only a small portion of the mill 
sufficient to show the methods of addition and subtraction; 
that the drawings were complete in exhibiting every movement 
essential to the design of the machine. They concluded that the 
labors of Babbage, first on the Difference Engine, and after- 
wards on the Analytical Engine were a marvel of mechanical 


ingenuity; that the realization of the latter would be of utility; 
that the complete design is not more than a theoretic possibility; 
and that the mill portion of it might be constructed at reason- 
able expense. 

Babbage was distinguished for his skill in solving ciphers. 
He wrote a paper " On the properties of letters occurring in 
various languages " and it appears that these researches gave 
the keys which he used. In 1851 he communicated to the 
Trinity House a note respecting occulting lights in lighthouses. 
His idea of making each lighthouse publish its own name was 
forthwith adopted by the English and American Governments. 
The application of, the same idea to solar light led to the inven- 
tion of the heliograph, first brought into practice by the Russians 
at Sebastopool and which figured so prominently in the siege of 

Babbage's last book, published in 1864, was a kind of auto- 
biography entitled Passages from the Life of a Philosopher. Like 
many of his works it was brilliant in conception but incomplete 
in execution. In his later years he came before the public as 
the implacable foe of organ grinders. He estimated that one- 
fourth of his entire working hours had been wasted through 
audible nuisances to which his highly strung nerves rendered 
him peculiarly sensitive. 

Charles Babbage died on October 18, 1871 in the 8oth 
year of his age. To the public he was known as an eccentric 
and irritable person, as a crank on the subject of calculating 
machines. But his books show true nobility of nature; his 
engines exhibit marvelous mechanical ingenuity. He sowed 
many valuable seeds which less able but more thrifty minds 
turned to advantage. As a reformer he accomplished much 
for exact science, especially in the foundation of the Astronomical 
Society, the British Association, and the Statistical Society. 
The money expended by the Government on his machine was 
fully repaid, according to Lord Rosse, by the improvement 
in mechanical tools which he made incidentally in his designs. 
The main defect in his character was a want of persistence and 
an imperfect adjustment of his aims to what was practicable. 



WILLIAM WHEWELL was born at Lancaster, England, on 
May 24, 1794. His father was a master carpenter and had 
several children. William was educated first at the grammar 
school of his native town, and was afterwards sent to that at 
Heversham in order to qualify for an Exhibition to Trinity 
College, Cambridge. The winning of this exhibition of 50 
was his first scholastic success. At these schools great atten- 
tion was paid to- classical studies, including versification in 
both Latin and Greek, and he also received a good start in 
mathematics. He entered Trinity College in October, 1812. 
The Analytical Society was then in existence and he became 
one of the group which met on Sunday mornings to breakfast 
and to discourse on philosophical subjects. One of the prin- 
cipal honors which he gained in his undergraduate career 
was the Chancellor's medal for the best poem on Boadicea, 
in the course of which he celebrates the praises of beauty: 

O beauty! heaven born queen! thy snowy hands 
Hold the round earth in viewless magic bands; 
From burning climes where riper graces flame 
To shores where cliffs of ice resound thy name, 
From savage times ere social life began 
To fairer days of polished, softened man; 
To thee, from age to age, from pole to pole, 
All pay the unclaimed homage of the soul. 

Whewell did not concentrate his attention exclusively on 
the subjects of the final examination, but he came out second 
wrangler. The next year (1817) he won a fellowship, took 

* This Lecture was delivered on April 23, 1903. EDITORS. 


private pupils, and began to read extensively with a view of 
following in the footsteps of Francis Bacon. He was soon 
appointed one of the mathematical tutors of his college. His 
connection with the Analytical Society suggested his first work 
An Elementary Treatise on Mechanics, in which the continental 
notations for the calculus is used. It was a great advance on 
any existing text-book on the subject used at Cambridge; 
subsequently it passed through several editions and became 
much altered. In 1820 Whewell was one of the moderators 
at the tripos examinations, and, following the example of Peacock 
the year before, he made use of the d notation. He was not 
an ardent reformer like Peacock; he appeared to have waited 
until the success of the movement was apparent. Although 
his first book was on Mechanics, his main design, even then, 
was a work on the inductive philosophy in which he should take 
full advantage of what had been accomplished in the .physical 
sciences since the time of Bacon. For this reason we find him 
at an early age studying Locke's Essay on Human Understand- 
ing and Kant's Critique of Pure Reason. 

In those days a fellowship expired at the end of seven years 
unless the holder took holy orders. Whewell took orders in 
1826; in the same year he and Airy, the Lucasian professor of 
mathematics, made observations in a mine in Cornwall to 
determine the mean density of the earth. Bacon, more than 
two centuries earlier, had suggested swinging a pendulum in a 
deep mine for this purpose. Airy and Whewell attempted 
to determine the time of oscillation of a pendulum at the bot- 
tom of the mine about 1200 feet deep and to compare it with 
that of another pendulum on the surface. An accident to the 
pendulum vitiated the first series of observations. Two years 
later they made a second series, which was also unsuccessful 
on account of an accident in the mine. Nearly thirty years 
later Airy, however, made successful observations at another 
mine from which he deduced 6.565 as the mean density of the 
earth as compared with wate r . At the time when Whewell 
took orders the professorship of mineralogy at Cambridge fell 
vacant; it appears to have been occupied as a sinecure. Whewell 


saw in it a position where he might have opportunity to study 
one of the sciences comprehended in his scheme of inductive 
philosophy. He held the appointment for several years, 
delivered lectures, founded a museum and wrote an essay on 
mineralogical classification.. In 1830 he published a book on 
the architecture of Gothic churches, in which he gave a theory 
explaining how the Gothic style had been derived from Grecian 
and Roman architecture. 

It suited the philosophic plans of the professor of mineralogy 
to study the new and allied science of geology. In 1830 the 
first volume of Lyell's Principles of Geology appeared in which 
was adopted and extended the doctrine of uniformity first 
published by Hutton. Whewell believed in the older doctrine 
of successive catastrophes; in a review of the bo.ok he said: 
" Hutton, for the purpose of getting his continents above water, 
or of manufacturing a chain of Alps and Andes, did not disdain 
to call in something more than the common volcanic eruptions 
which he read of in newspapers from time to time. He was 
content to have a period of paroxysmal action, an epoch of 
gradual distraction and violence, to usher in one of restoration 
and life. Mr Lyell throws away all such crutches; he walks 
alone in the path of his speculations; he requires no paroxysms, 
no extraordinary periods; he is content to take burning moun- 
tains as he finds them; and with the assistance of the stock of 
volcanoes and earthquakes now on hand, he undertakes to trans- 
form the earth from any one of its geological conditions to any 
others. He requires time, no doubt; he must not be hurried 
in his proceedings. But if we will allow him a free stage in the 
wide circuit of eternity, he will then ask no other favor." 
Whewell here seems to adopt that view of geological time which 
has since been advocated by Kelvin. This same year there 
appeared HerschePs work Preliminary Discourse on the Study 
of Natural Philosophy. Herschel's object was to extend and 
correct the inductive philosophy of Bacon in the light of 
later achievements. Whewell was, from his own plans deeply 
interested in this work and he wrote a review in which he 
remarked that Herschel had said nothing of Bacon's condem- 


nation of the method of anticipation of nature, as opposed to 
what he considers as the true method of interpretation of 
nature. As a matter of fact Herschel was too wise to follow 
Bacon in his condemnation of anticipation; he knew that the 
guidance of theory was needed for the interpretation of facts. 

Whewell was one of the eight persons selected to write the 
Bridgewater Treatises. His subject was " Astronomy and 
General Physics considered with reference to Natural Theology/' 
and he received 1000 as well as the profits of the volume. 
His treatise is divided into three parts: (i) Terrestrial adapta- 
tions, (2) Cosmical, arrangements, (3) Religious views. In the 
first part he aims at demonstrating how the laws and facts of 
nature work in harmony to secure the well being of man, animals, 
and plants; and the inference is drawn that such arrangement 
testifies to the existence of an intelligent and beneficent Creator. 
In the second part he shows how all the universe is subject to 
a law of continual decay. The third part has two remarkable 
chapters on inductive and on deductive habits, the former, he 
held, had a stronger tendency to religion. This volume was 
the most popular of the eight Bridgewater Treatises, and it 
went through seven editions. 

Soon after the British Association was founded in 1831 
Whewell became one of the most active members; to him 
is due the important suggestion of the preparation, by committees 
or specially appointed individuals, of reports upon subjects of 
scientific importance and their publication in full in the Pro- 
ceedings. In 1833 he was one of the secretaries of the meeting 
of the Association held at Cambridge and it fell to him to 
deliver an address similar to the presidential addresses of later 
years. By this time Whewell had acquired the reputation 
through his philosophical researches of being the best authority 
in Great Britain on scientific language. Faraday in his elec- 
trolytic researches had encountered a number of new ideal 
and for these he wished to have suitable names. Wheweli 
suggested anode, cathode, anion, cation, ion, words which, with 
their derivatives, are now familiar not only to the electrician, 
but to people of general culture. Other electrical terms sug- 


gested by Whewell to Faraday were paramagnetic and diamagnetic. 
To Lyell, the geologist, he suggested eocene, miocene, pliocene. 

In 1833 Whewell published in the Transactions of the Royal 
Society the first of a series of memoirs on the tides. In its 
preface he says: "No one appears to have attempted to 
trace the nature of the connection among the tides for the 
different parts of the world. We are, perhaps, not even yet 
able to answer decisively the inquiry which Bacon suggested 
to the philosophers of his time, whether the high water extends 
across the Atlantic so as to affect contemporaneously the shores 
of America and Africa, or whether it is high on one side of the 
ocean when it is low on the other, at any rate such observations 
have not yet been extended and generalized." To this subject 
Whewell applied his method of the colligation of facts, more 
commonly called the reduction of observations. His main 
object was to reduce the enormous series of observations con- 
cerning the tides which had accumulated, and in this work 
he had the aid of skilled computers paid by the Admiralty 
or by the British Association. He began by constructing a 
map of cotidal lines for the whole globe, that is, lines drawn 
on the surface of the ocean and passing through all the points 
where it is high water at the same time. The succeeding 
memoirs were devoted to the discussion of observations at 
London, Liverpool, Plymouth, and other ports. There were 
fourteen of these memoirs and Airy thus estimates their 
value: "Viewing the two independent methods introduced 
by Mr. Whewell, of reducing the tabular numbers to law by a 
process of numerical calculation, and of exhibiting the law to 
the eye without any mathematical operation by the use of 
curves, we must characterize them as the best specimens of 
reduction that we have ever seen." Whewell did not grapple 
with the theory of the tides, that he left to use his own words 
" to bolder and stronger mathematicians." Neglect of the 
role played by theory, especially mathematical theory, in the 
discovery of truth, is the weak point in Whewell's philosophy. 
The reduction of observations to empirical laws is only one step 
in the process and not the most important. 


In 1835 Whewell published a pamphlet on mathematics 
in liberal education one of the fruits of his philosophical 
studies. In it he maintains that mathematics is superior to 
formal logic as an educational discipline, and he discusses faults 
in teaching by which its benefits are diminished. In reply 
to the pamphlet an article appeared in the Edinburgh Review, 
written by Sir William Hamilton, professor of logic and mathe- 
matics at Edinburgh, which became notorious as a wild and 
indiscriminate attack on mathematical work by a person only 
slightly acquainted with it. In the succeeding number Whewell 
asks for the titles of some treatises on practical logic and philos- 
ophy which the reviewer would recommend for their educa- 
tional efficiency as rivals to the well-known mathematical 
treatises. In this tilt between the expounder of the renovated 
Baconian logic and an official representative of the old scholastic 
logic, the modern champion came off victorious. 

In 1837 Whewell finished the first part of his History of the 
Inductive Sciences. In this book he notes the epochs when the 
great steps were made in the principal sciences, the preludes 
and the sequels of these epochs, and the way in which each step 
was essential to the next. He attempts to show that in all 
great inductive steps the type of the process has been the same. 
The prominent facts of each science are well selected and the 
whole is written with a vigor of language and a facility of illus- 
tration rare in the treatment of scientific subjects. This book 
was, however, introductory to his Philosophy of the Inductive 
Sciences which appeared three years later; its preparation 
had indeed gone along with that of the History. In this work 
Whewell explained the process of induction, the elements of 
which it consists, what conditions it requires, and what facilities 
it calls into play. He maintains that, in order to arrive at 
knowledge or science, we must have besides impressions of 
sense, certain mental bonds of connection, ideal relations, or 
ideas. Thus space is the ideal relation on which the science of 
geometry depends; time, cause, likeness, substance, life, are 
ideal relations on which other sciences depend. WhewelPs 
philosophy was, in fact, a blending of Kant and Bacon. 


Bacon recommended that a great collection of facts should 
be made regarding every branch of human knowledge, and con- 
ceived that, when this had been done by common observers, 
philosophers might extract scientific truth from these facts by 
the application of a right method. ,.;As an example of such an 
investigation Bacon collected facts bearing on the nature of 
heat and he arrived at the conclusion " That heat is an expan- 
sive, restrained motion, modified in certain ways, and exerted 
in the smaller particles of the body." This true conclusion 
was designated by Bacon as a " first vintage/' in other words 
as a guess, but it was regarded by Whewell as an unfortunate 
conclusion, and he asks " Where is the motion in a red-hot 
iron?" Whewell made a great advance on the method 
of Bacon by claiming that ideas are as indispensable as 
the facts themselves, and that facts are collected in vain 
except they be duly unfolded by ideas; his defect was that 
he stopped short at ideas, instead of proceeding to theories 
and equations. 

In 1841 he was president of the British Association for the 
meeting at Plymouth. His address was characteristic; he 
compared the Association to Solomon's House, imagined by 
Bacon in The New Atlantis, the principal difference being that 
the Association depended upon voluntary support, whereas 
the philosophers of Solomon's House were to be paid by the 
state. This House had caves and wells, chambers and towers, 
baths and gardens, parks and pools, dispensatories and fur- 
naces, and other provisions for experiment and observation. 
" There were also many classes of persons to conduct the busi- 
ness of the college: merchants of light, mystery men, depre- 
dators, pioneers or miners, dowry men or benefactors, inocu- 
lators, and finally interpreters of nature who elevate the truths 
of experiment into general laws which are the highest form 
of human knowledge." The imaginary teacher who thus 
described Solomon's House to a traveler also said: " The end 
of our foundation is the knowledge of causes and secret motions 
of things." But Whewell said: " Knowledge is to be dealt 
with as the power of interpreting nature and using her forces, 


not as a power of exciting the feelings of mankind and providing 
remedies for social evils." 

In the interval between the publication of the History and 
the Philosophy Whewell took a step which may appear erratic, 
but which in reality was a step toward the accomplishment 
of his great plan. He accepted the Chair of Moral Philosophy. 
In a letter he explained that this was done so that he might 
ultimately extend his inductive principles to some of the meta- 
physical sciences. He proposed to resign his position as a 
mathematical tutor and to take a college living in the country. 
In 1841 he was 47 years old and engaged to be married. But 
finally, instead of retiring to the country, he bought a house 
in Cambridge. Shortly after he was married, and within a 
week he was appointed Master of his college the foremost 
scientific college in England. He never occupied the house 
which he had bought; henceforth his home was Trinity College. 

While Master of Trinity he published anonymously the book 
Plurality of Worlds, to which I referred in the lecture on H. J. S. 
Smith.* Fontenall and Chalmers had maintained the affirma- 
tive that there is a plurality of worlds. Whewell maintained 
the negative and his book went rapidly through five editions. 
Brews ter in More Worlds than One then took the affirmative 
side, this title being said to give " the Creed of the Philosopher 
and the Hope of the Christian." In more recent times Proctor 
wrote Other Worlds than Ours setting forth the results of scientific 
researches. Only a few months ago Whewell's old position 
was maintained in the Fortnightly Review by Mr. Wallace, 
but in a matter of astronomical reasoning Proctor is a much 
safer guide than Wallace. Whewell was Master of Trinity 
College for 25 years; much of his time was taken up by the 
duties of administration, especially on account of the reform 
of the college which the Government carried out. His writing 
during this period was mainly on moral science, but he also 
brought out the second and third editions of his Philosophy 
of the Inductive Sciences. One of his acts was to present a 
statue of Bacon to Trinity College. 

* Ten British Mathematicians, p. 92. EDITORS. 


Whewell was noted for his power as a University preacher. 
He was a man of splendid physical development. A Cambridge 
legend tells of a prize-fighter who had exclaimed " What a 
man was lost when they made you a parson! " No doubt his 
friends imagined him hale and hearty at a very advanced age; 
but it was not to be. He was fond of horseback exercise and 
it was this recreation which cut short his career. His horse 
bolted and threw him, and the injuries were such that he died 
in a few days. His death occurred on March 6, 1866, in the 
72d year of his age. He was twice married, but, having no 
children, bequeathed the most of his fortune to Trinity College. 

He was very fond of argument and in early life, at least, 
somewhat rough in manner. De Morgan wrote : " The Master 
of Trinity was conspicuous as a rough customer, an intellectual 
bully, an overbearing disputant. The character was as well 
established as that of Sam Johnson, but there was a marked 
difference. It was said of Johnson that if his pistol missed 
fire he would knock you down with the butt end of it; but 
Whewell, in like case, always acknowledged the miss, and 
loaded again or not as the case might be. ... I knew him 
from the time when he was my teacher at Cambridge, more 
than forty years ago. As a teacher he was anything but 
dictatorial, and he was perfectly accessible to the proposal 
of objections. He came into contact with me in his slashing 
way twice in our joint lives, and on both occasions he acknowl- 
edged himself overcome by that change of manner and apolo- 
getic mode of continuance which I had seen him employ toward 
others under like conditions." The great variety of his studies 
struck some of his contemporaries as peculiar; for instance 
Sydney Smith said at a breakfast party with reference to 
Whewell: " That man's forte is science and foible omnis- 
cience." There was, however, as we have seen, a method in 
his madness. In his day he was a Grand Master; in more 
recent times some have asked what contributions did he make 
to science. His enduring monument is the Renovation of the 
Baconian philosophy. 

Whewell, like Bacon, set forth a series of aphorisms giving 


the essentials of his philosophy. I will quote four of these: 
"I. Man is the interpreter of nature, Science the right inter- 
pretation. . . . VIII. The Sensations are the objective, 
the Ideas are the subjective part of every act of perception or 
knowledge. XI. Observed facts are connected so as to pro- 
duce new truths by superinducing upon them an Idea; and 
such truths are obtained by Induction. XII. Truths once 
obtained by legitimate Induction are Facts; these facts may 
be again connected so as to produce higher truths; and thus 
we advance to successive Generalizations." On the title page 
of his later books you may find a picture of a hand transmitting 
a torch to another hand, with a motto of four Greek words 
underneath. The words are from Plato, who in allusion to an 
Athenian ceremony says: " Holding torches they will pass 
them on one to another." Whewell adopted the picture for 
his coat of arms with the motto lampada tradam. 



GEORGE GABRIEL STOKES was born August 13, 1819, at 
Skreen, County Sligo, Ireland. His father was the rector of 
the parish, a clergyman of the Church of England in Ireland, 
When twelve years of age he was sent to a school in Dublin 
and two years later to Bristol College in the West of England. 
At this time the principal of that college was Dr. Jerrard whose 
researches on the solution of equations of the fifth degree were 
discussed by Sir William Rowan Hamilton at the Bristol meet- 
ing of the British Association in 1836. In 1837 young Stokes 
entered Pembroke College, Cambridge, and four years later 
graduated as senior wrangler, won the first Smith's prize, and 
was elected to a fellowship. During all his school and college 
years he had won distinction in mathematical studies. 

He now did what was a great novelty in those days turned 
one of his rooms into a physical laboratory. The University 
had no lecture rooms for its professors, far less laboratories 
or museums. Being a powerful analyst as well as a skillful 
experimenter he immediately entered on a period of fruitful 
scientific production. He chose as channels of publication 
the two institutions which had been recently inaugurated at 
Cambridge, namely, the Cambridge Philosophical Society, and 
the Cambridge and Dublin Mathematical Journal. To the 
former he contributed two papers on pure mathematical analysis, 
namely, " on the critical values of the sums of periodic series," 
based on Fourier's analysis of periodic functions; and another 
" On the numerical calculation of a class of definite integrals 
and infinite series," in which he was able to calculate the first 

* This Lecture was delivered on April 28, 1903. EDITORS. 


fifty roots of an equation of which Airy had been able to cal- 
culate only two. Other memoirs followed: " On the theories 
of the internal friction of fluids in motion and of the equilibrium 
and motion of elastic solids," in which he shows for the first 
time how to take account of the equations of motion, of differences 
of pressure in different directions due to the viscosity of the 
fluid; and the resulting equations constitute the complete 
foundation of the hydrokinetics of the present day. " On the 
theory of oscillatory waves," in which he investigates the steep 
waves of the deep sea where the elevations are narrower 
than the hollows and the height of an elevation exceeds the 
depth of a hollow. " On the formation of the central spot of 
Newton's rings beyond the critical angle," his earliest investi- 
gation in the wave- theory of light. " On the dynamical theory 
of diffraction," containing the mathematical theory of the prop- 
agation of motion in a homogeneous elastic solid; also ^an 
experimental investigation from which he concluded that the 
plane of polarization is the plane perpendicular to the direction 
of vibration in plane-polarized light, agreeing with Fresnel's 
position as opposed to that of MacCullagh. 

To the Cambridge and Dublin Mathematical Journal he con- 
tributed the following papers: " On the motion of a piston 
and of the air in a cylinder"; " On a formula for determining 
the optical constants of doubly refracting crystals"; " On 
attractions and on Clairault's theorem." A series of notes on 
hydrodynamics was prepared supplementary to a report on that 
subject which he presented to the British Association in 1846. 
Shorter papers he communicated to the Philosophical Magazine, 
two of which are the aberration of light and the constitution 
of the luminiferous ether viewed with reference to that phenom- 
enon. On the theory of the emission of light, the explanation 
of aberration is simple; in these papers he attempts an explana- 
tion which shall be in accordance with the undulatory theory 
without making the startling supposition that the earth in its 
motion round the sun experiences no resistance from the ether. 

In 1849 the Lucasian Chair of Mathematics at Cambridge 
fell vacant the chair filled by Sir Isaac Newton 180 years 


earlier. From 1828 to 1839 this chair was occupied by Charles 
Babbage who neither lectured nor resided; his successor, 
Joseph King, seems also to have made it a sinecure. But now 
tjie electors who are the heads of the colleges saw in Stokes 
a young, talented, and enthusiastic investigator who might 
worthily follow in the steps of Newton. At the time of the 
election Peter Guthrie Tait was an undergraduate and twenty- 
five years later he recorded his impression of the event: " To 
us, who were mere undergraduates when he was elected to the 
Lucasian professorship, but who had with mysterious awe 
speculated on the relative merits of the men of European fame 
whom we expected to find competing for so high an honor, 
the election of a young, and to us unknown, candidate was a 
very striking phenomenon. But we were still more startled, 
a few months afterwards, when the new professor gave public 
notice that he considered it part of the duties of his office to 
assist any member of the University in difficulties he might 
encounter in his mathematical studies. Here was, we thought 
(in the language which Scott puts into the mouth of Richard 
Coeur de Lion) "a single knight fighting against the whole 
melee of the tournament." But we soon discovered our mis- 
take, and felt that the undertaking was the effort of an earnest 
sense of duty or the conscience of a singularly modest but 
exceptionally able and learned man. And as our own knowl- 
edge gradually increased and we became able to understand 
his numerous original investigations, we saw more and more 
clearly that the electors had indeed consulted the best interests 
of the University, and that the proffer of assistance was some- 
thing whose benefits were as certain to be tangible and real 
as any that mere human power and knowledge could guarantee." 
Tait himself benefited by this proffer of assistance; so did 
Thomson and Clerk Maxwell. In fact Prof. Stokes is regarded 
as the principal founder of the Cambridge school of mathe- 
matical physicists, one of the main glories of the British mathe- 
maticians of the nineteenth century, the only other name having 
any claim to the position being that of William Hopkins who 
tutored them all. Thus at the age of 35 years Stokes was placed 


in the position where he was to do his life work. At that time 
the salary attached to the chair was small; the colleges collected 
all the revenues, and the University proper had very little for 
the payment of her officers. 

Before his appointment to the Lucasian chair, Stokes had 
contributed a paper to the Transactions of the Royal Society 
of London: " On the theory of certain bands in the spectrum." 
He was now (1851) elected a Fellow of the Society. Two years 
later he was appointed one of the secretaries, an office which 
he continued to hold for thirty years. In 1852 he contributed 
an important paper " On the change of refrangibility of 
light " for which he received a Rumford medal, and which is 
considered his greatest contribution to science. Sir John 
Herschel had discovered a phenomenon, now called fluorescence, 
in the behavior of a solution of sulphate of quinine when a 
beam of light strikes on it. Viewed by transmitted light, the 
liquid appears colorless and transparent like water, but viewed 
by reflected light it exhibits a peculiar blue color. This blue 
color comes from a narrow stratum of the liquid adjacent to 
the surface by which the light enters. Light, which has once 
produced this effect, though unaltered apparently by trans- 
mission through the liquid, cannot produce the blue stratum 
in a posterior solution. Stokes reasoned that certain invisible 
rays in the beam are changed into visible rays the blue rays; 
which means that certain waves of a length too small to be seen 
are, by incidence on the molecules of the solution, transformed 
into waves of greater length so as to become visible. How 
the change takes place is not known; but what Stokes did 
establish was that the appearance of the visible blue light was 
due to disappearance of certain invisible light rays. In the 
substances which Stokes examined, the change was in every 
case to greater wave-length; on which he based an induction 
that the change was always from smaller to greater wave- 
length, an induction which in more recent years has been 

Soon after he contributed to the Cambridge Philosophical 
Society a paper " On the effect of the internal friction of fluids 


on the motion of pendulums." In this he investigates the motion 
of a pendulum which has for its bob a globe and moves in a 
viscous fluid contained in a spherical envelope concentric with 
the bob when at rest; and also the motion of a globe moving 
uniformly with a small -velocity through a mass of viscous 
fluid. He applies the result of ; the second investigation to 
explain the suspension of clouds in the air; and determined 
from the known viscosity of air the terminal velocity of an 
exceedingly minute globule of water falling through it. Up 
to this time the motion of a pendulum had been corrected for 
buoyancy and for the inertia of the air; Stokes supplied the 
correction for viscosity. 

In 1857 he married, and in consequence of the provision of the 
statute governing the colleges, his fellowship became vacant. 
On account of this diminished income he took more work, such 
as Lectures at the School of Mines in London. When the 
colleges were reformed (about 1875) fellows engaged in teaching 
in the University were allowed to retain their fellowships after 
marriage; and in the case of Stokes the provision was applied 
extro-actively, and he was reinstated a Fellow of Pembroke 
College. Professor Stokes not only lectured to the junior 
members of the University and advised the senior members in 
questions of applied mathematics, but he was also very help- 
ful to scientists in general. He was in applied mathematics 
and physics what Cayley was in pure mathematics a valuable 
referee and advisor in the work of others. He had the true 
spirit of a philosopher, more anxious to see science advance 
than that he should have priority in the advancement. Lord 
Kelvin has stated that before he removed from Cambridge in 
1852, Stokes explained to him the principles of spectrum analysis 
upon which solar and stellar chemistry has been founded, a 
work which was afterwards carried out fully by Balfour Stewart 
and Kirchoff. The following is the account which Stokes 
himself gives. 

In 1849 Foucault accidentally observed that in a solar beam 
which had traversed the electric arc between two carbon poles, 
the double dark line D appeared darker than usual, and the 


bright D line was seen in precisely the same place in the spectrum 
of light coming from the electric arc; Stokes was informed by 
Foucault of this observation a few years later. It seemed to 
Stokes that a dynamical illustration of how a medium could 
act both by emission and absorption for light of a definite 
refrangibility was not far to seek. He says: " I imagine a 
series of stretched wires, like pianoforte wires, all turned to the 
same note. The series, if agitated, suppose by being struck, 
would give out that note, which on the other hand it would be 
capable of taking up if sounded in air. To carry out the anal- 
ogy, we have only to suppose a portion of the molecules con- 
stituting the vapor of the arc to be endowed with a capacity of 
vibrating in a definite manner, that is according to a definite 
time of vibration. But what were these molecules? It is 
well known that the bright D line in flames is specially char- 
acteristic of compounds of sodium, though from its very general, 
occurrences some had doubted whether it were not really due 
to something else. But in what condition must we suppose 
the sodium in the arc to be? The compounds of sodium, such 
as common salt, carbonate of soda, etc., are colorless; and it 
would be contrary to the analogy of what we know as to the 
relation of gases and vapors to their liquids or solutions to 
suppose that a gas which does exercise absorption should be 
merely the vapor of a heated solid which does not. On this 
ground it seemed to me that the substratum which exercised 
the selective absorption in Foucault's experiment must be 
free sodium. This might be conceivably set free from its 
compounds in the intense actions which go on in the sun or in 
the electric arc; but I had not thought that a body of such 
powerful affinities would be set free in the gentle flame of a 
spirit lamp nor experienced that the fact of that flame emitting 
light of the indefinite refrangibility of D entails of necessity 
that it should absorb light of that same refrangibility." 

In 1869 Stokes was president of the British Association 
at a meeting in Exeter. His address was devoted chiefly to 
recent progress in spectrum analysis to which Mr. Huggins 
had just applied Doppler's principle in the theory of sound 


and deduced that Sirius is receding from the Sun at the rate 
of 30 miles per second. Stokes closed his address with some 
observations on life and mind these being characteristic of his 
philosophical attitude which was that of the golden mean. 
He says " What this something wjKich we call life may be, is a 
profound mystery. We know not how many links in the chain 
of secondary causation may yet remain behind; we know not 
how few. It would be presumptuous indeed to assume in any 
case that we had already reached the last link, and to charge 
with irreverence a fellow worker who attempted to push his 
investigations yet one step farther back. On the other hand, 
if a thick darkness enshrouds all beyond, we have no right 
to assume it to be impossible that we should have reached even 
the last link of the chain, a stage where further progress is 
unattainable, and we can only refer the highest law at which 
we stopped to the fiat of an Almighty Power. . . . When 
from the phenomena of life we pass on to those of mind we 
enter a region still more profoundly mysterious. We can 
readily imagine that we may here be dealing with phenomena 
altogether transcending those of mere life, in some such way 
as those of life transcend, as I have endeavored to infer those 
of chemistry and molecular attractions, or as the laws of chemical 
affinity in their turn transcend those of mere mechanics. Science 
can be expected to do but little to aid us here, since the instru- 
ment of research is itself the object of investigation. It can 
but enlighten us to the depth of our ignorance and lead us to 
look to a higher aid for that which most nearly concerns our 

In 1880 the Cambridge University Press began the republi- 
cation in collected form of Stokes' Mathematical and Physical 
Papers. In this publication he introduced for the first time the 
solidus notation for division, originally introduced by De Morgan 
in his article on the Calculus of Functions in the Encyclopedia 

Metropolitan. If a fraction like y, or a differential coefficient 

such as --r, is mentioned in the text, the printing of such expres- 


sions requires a good deal of " justification " on the part of the 
compositor. To avoid this expense and the loss of space Stokes 
introduced the linear notation a/b and dy/dx. The symbol: 
and -j- likewise indicate division but he did not use them in the 
text. He did not use / in writing out centered equations, 
excepting where it is needed to simplify the index of an exponen- 
tial function. He considered it convenient to enact that the 
solidus shall as far as possible take the place of the horizontal 
bar for which it stands and accordingly that the quantities 
immediately preceding and following shall be welded into one, 
the welding action to be arrested by a period. For example 
m 2 -n 2 /m 2 +n 2 is to mean (m 2 -n 2 )/(m 2 +n 2 ), and a/bed 

means -=-^, but a/bc.d means -r-d. 
bed be 

This solidus notation for algebraic expressions occurring 
in the text has since been used in the Encyclopedia Brittanica, 
in Wiedemann's Annalen and quite generally in mathematical 
literature. The solidus may be viewed as a symbol of opera- 
tion, denoting reciprocal in the same way as ^/~ denotes square 
root and as denotes reverse. The expression fa is a sufficient 
notation for the reciprocal of a; in i/a the figure i is redundant, 
just as in o a the o is redundant. The horizontal bar serves 
the two-fold purpose of a vinculum and a sign for reciprocal. 
When the reciprocal idea is detached and denoted by /, rules 
for the manipulation of / can be enunciated; thus i/a = a; 
(/a)(/b) = iab, just as VaV^ = Vab. The notation of algebra 
is in fact planar; its complete reduction to a linear form is 
not a simple matter and was not tackled by Stokes, but this 
has been attempted by later writers, some of whom write exp x 
for e x . One indeed has proposed to use \ for involution 
and t instead of a bracket so that c\(d+e) 3 would be written 

In the winters of 1883-4-5 Prof. Stokes delivered in Aber- 
deen, Scotland, three courses of lectures on Light, under the 
auspices of the Burnett trust. In 1 784 John Burnett, a merchant 
of Aberdeen, died, bequeathing a portion of his property to 
establish prizes for the best and next best essay on the following 


subject: " That there is a Being, all powerful, wise, and good, 
by whom everything exists; and particularly to obviate diffi- 
culties regarding the wisdom and goodness of the Deity; and, 
this in the first place, from considerations independent of written 
revelation of the Lord Jesus; and from the whole to point out 
influences most necessary for and useful to mankind." The 
prizes were to be competed for at intervals of forty years; and 
awards were actually made on two occasions. On account of 
the length of the interval the trustees began to think that the 
endowment might be better applied, and they obtained authority 
to change the funds so as to appoint special lecturers who should 
be appointed for three years, the courses to be given at intervals 
of five years and to cover subjects with special regard to the object 
of the testator. Prof. Stokes was the first lecturer appointed. 

The subject of his first lecture was the Nature of Light. 
He brings out prominently Newton's difficulty in the hypothesis 
of undulation that light should produce rays and sharp 
shadows while sound does not; and Brewsters' difficulty that 
space should be filled with an ether in order that the light of 
yon twinkling star may come to us. And he concludes with 
this lesson: " It may be said, if the former emission theory 
is nowadays exploded, why dwell on it at all? Yet surely 
the subject is of more than purely historical interest. It teaches 
lessons for our future guidance in the pursuit of truth. It 
shows that we are not to expect to evolve the system of nature 
out of the depths of our inner consciousness, but to follow the 
painstaking inductive method of studying the phenomena 
presented to us, and be content gradually to learn new laws 
and properties of natural objects. It shows that we are not 
to be disheartened by some preliminary difficulties from giving 
a patient hearing to a hypothesis of fair promise, assuming of 
course that those difficulties are not of the nature of contradic- 
tions between the results of observation and experiment and 
conclusions certainly deducible from the hypothesis on trial. 
It shows that we are not to attach undue importance to great 
names, but to investigate in an unbiased manner the facts which 
lie open to an examination." 


In his second course of lectures he treated of light as a means 
of investigation. One of the objects taken up was the nature 
of comets. He held that the nucleus consists, in its inner 
portions at least, of vapor of some kind in an incandescent 
state. To explain the cause of this incandescence he brings 
forward the " greenhouse theory." The glass of a greenhouse 
is transparent to the higher but opaque to the lower forms of 
radiation, and hence acts as a trap for the sun's rays. The nucleus 
of the comet he supposed to be surrounded by an envelope of 
some kind, transparent to the higher but opaque to the lower 
forms of radiation. Thus solar heat can get freely at the 
nucleus, but cannot escape until it has raised the nucleus, 
in part at least, to incandescence. The coma and tail are formed 
by the condensation of small quantities of this vapor, so that 
they are mere mists of excessive tenuity. Prof. Tait preferred 
his own " brickbat theory "; he considered that Stokes' theory 
made the comet resemble the huge but barely palpable Efreet 
of the Arabian Nights, who could condense himself so as to 
enter the bottle of brass with the seal of Solomon the son of 
David. (Nature, August 20, 1885.) 

The third course of lectures treated of the beneficial effects 
of light. As regards the special application contemplated by 
Burnett, he concludes: " If we shut our eyes to the grandeur 
of Nature and do not attempt, through the things that are made, 
to acquire higher conceptions of the eternal power and God- 
hood of the Maker, our conceptions of the Divine Being are apt 
to become too anthropomorphic. If on the other hand we con- 
fine our attention to the study of Nature in all its immensity, 
our conceptions of its Author are in danger of merging in a 
sort of pantheistic abstraction in which the idea of personality 
is lost." Tait remarked with reference to these sentences 
that the first Burnett lectures had set a noble example to suc- 
cessors, and that Stokes had supplied a valuable warning not 
only to them but " to the rapidly changing quaternion of neo- 
teleologists that were soon to be set to work in the Scottish 
Universities." He referred to the new institution of the Gifford 


The second volume of Stokes' Mathematical and Physical 
Papers was published in 1883; the third in 1901. This long 
delay was due to the fact that his time was engrossed by scientific 
business; in his later years he seems to have had little ambition 
in the direction of scientific publication. In 1885 Prof. Stokes 
after having discharged the duties of Secretary of the Royal 
Society for thirty years, was elected President, which office 
he held for the usual period of five years. For twenty years 
after 1887 he represented the University of Cambridge in 
Parliament. In 1889 he received the honor of a baronetcy. 

In 1891 Sir George Stokes was made one of the changing 
quaternion to which Tait referred; he was appointed, by the 
University of Edinburgh, lecturer on the Gifford foundation. 
Lord Gifford, one of the judges of the High Court of Justice 
in Scotland, died about 1887, leaving by his will a sum of money 
to each of the Scottish Universities. The object of the endow- 
ment was to appoint for one or two years a thinker, who might 
not belong to an); Christian denomination provided only he 
was a true and reverent inquirer after truth, to deliver a course 
of public lectures on some point bearing on Natural Theology, 
treating the subject just as any other science. Stokes delivered 
two courses of lectures in 1891 and 1893. Trained in Cam- 
bridge University where little attention was paid to philosophy, 
he seems to have felt a difficulty in treating Natural Theology 
" just as any other science " and he could not speak with the 
same authority as when he was discoursing on light. 

Four years ago (in 1899) the University of Cambridge 
celebrated in brilliant style the jubilee of his professorship. 
Delegates were invited from the learned societies; sixty-eight 
of them, mostly British, were represented. The celebration 
of the jubilee began with the delivery of the Rede lecture by 
Prof. Cornu of the ecole poly technique of Paris; the endowment 
for this lecture dates back to 1524. The subject was appropriate 
to the occasion: "The wave- theory of light, its influence on 
modern physics." At an evening reception a bust of Stokes 
was presented to Pembroke College and a replica to the Uni- 
versity. The presentation was made by Lord Kelvin who 


said that Sir George Stokes had published in his own name 
but a very small part of the good he had done to the world. 
At the principal function, which was held in the Senate house, 
the delegates were received by the Vice Chancellor of the 
University; they presented the addresses of which they were 
bearers and these were handed to Sir George. In reply he said 
that he often thought, in reviewing his long life, that he might 
have worked harder, and he attributed his longevity to his 
comparative idleness a remark which was cheered by the 
undergraduates in the gallery. A special meeting of his early 
love, the Cambridge Philosophical Society, was held and the 
papers there presented are published in a memorial volume. 

In the summer of 1902 he was elected to the mastership of 
Pembroke College. Later in the year he took part with Lord 
Kelvin in making the presentation of a portrait of Prof. Tait 
to St. Peter's College. He died on February i, 1903, in the 
84th year of his age. In many respects the life of Stokes resem- 
bles that of Newton. Both were skilled experimenters, especially 
in optics; of Stokes it used to be said that if you gave him 
sunlight and three-quarters of an hour, there was no experiment 
in optics he could not perform. Both Newton and Stokes filled 
the Lucasian chair of mathematics; both represented Cam- 
bridge University in Parliament; both filled the offices of 
Secretary and President of the Royal Society; both received 
the dignity of Sir, and both lived to an advanced age. They 
also resembled one another in type of mind and in religious 
views; but Stokes never sat down to produce a work at all 
commensurate in labor or in importance with the Principle,. 



GEORGE BIDDELL AIRY was born at Alnwick in North- 
umberland on the 27th of July, 1801. His father, William 
Airy, was collector of the Excise duties for that district; his 
mother, Anna Biddell Airy, was the daughter of George Biddell, 
a well-to-do farmer in Suffolk. In 1810 William Airy was trans- 
ferred to the county of Essex, and the family then settled in 
Colchester, the county town. Here George was first sent 
to a private school, where he got a good introduction to elemen- 
tary mathematics; afterwards he was sent to the grammar 
school where he was initiated in Latin and Greek to the extent 
of being able to write Latin prose. He also got the usual instruc- 
tion in Latin verse, but he did not excel in that kind of com- 
position. On one occasion his father brought him a present 
from London, which had much influence on his future career 
a terrestrial and a celestial globe. From this event he dated 
his interest in astronomy. Arthur Biddell, his mother's brother, 
lived on a farm at Playford, in Suffolk, and was a man of some 
scientific and literary culture, besides being interested in his- 
torical and antiquarian matters. George spent his holidays 
in this uncle's company and especially in his library; from 
this source originated an interest in mechanics, optics, poetry 
and antiquities. There he found the means of constructing 
a telescope for himself. 

At school he distinguished himself, especially in memory 
work. Although not wanting in courage, he did not take an 
interest in athletic sports. It was the custom for each boy 
once a week to repeat a number of lines of Latin or Greek 

* This Lecture was delivered on April 7, 1904. EDITORS. 


poetry, the number depending very much on his own choice. 
Airy repeated 100 lines every week; on one occasion he repeated 
more than 2000 lines. The schoolmaster was impressed with 
his powers and suggested to his father that the boy should be 
sent to Cambridge; who, on inquiry, concluded that the expense 
was too great for his straitened circumstances. However, the 
uncle took up the problem, and with the help of a Cambridge 
alumnus got the boy prepared in classics and mathematics 
for the entrance examination to Trinity College. In these 
preliminary examinations he acquitted himself so well, that 
a reputation for scholarship preceded his going there to reside. 
In 1819, when 18- years old, he commenced residence as a sizar 
of Trinity College. By a sizar is meant a poor student who is 
exempted from some of the expenses he does not pay for 
dinner in hall; the sizars dine after all the rest, on the remains 
of the Fellows' dinner. Newton himself started in that same 
college as a sizar. George Peacock, who was then a mathe- 
matical tutor of the college, became his warm friend and adviser; 
he gave him a copy of Lacroix's Differential Calculus , trans- 
lated by himself, Babbage, and Herschel, and also a copy of his 
Collection of Examples. At this time the Differential Calculus 
was beginning to prevail over Fluxions; Airy had got instruction 
in the old method, but he took to the new with great industry. 
At a breakfast party at Peacock's he met Whewell, who was 
a resident fellow graduate of the University. 

Airy employed part of his first vacation in writing out a 
paper on the geometrical Interpretation of V i. He got the 
suggestion of " perpendicular " from some book; the aim of 
his essay was to apply that theory. Peacock to whom he 
showed the essay was much pleased. Mr. Hustler, his tutor, 
on the contrary disapproved of his employing his time on such 
speculations. The former was a philosopher and reformer, 
the latter an official and disposed to consider everything that is, 
is right. Airy however, whether by the influence of Hustler 
or otherwise, did not go very deep into the subject. He after- 
wards wrote: " I have not the smallest confidence in any 
result which is essentially obtained by the use of imaginary 


symbols. I am very glad to use them as conveniently indicating 
a conclusion which it may afterwards be possible to obtain by 
strictly logical methods; but until these logical methods shall 
have been discovered, I regard the result as requiring further 
demonstration." Here -we note a; want of confidence in mathe- 
matical deduction which appears to have been characteristic 
of Airy and his generation of mathematicians. 

In his first year Airy read WhewelPs textbook on Mechanics, 
just published, the first innovation made in the Cambridge 
system of Physical Science for many years, and which made 
partial use of the differential notation (d). By the beginning 
of his second year he was so far advanced that he took two 
private pupils for instruction in mathematics men of his 
own year. By this means he became able to defray all his 
expenses without help from his relatives. In his early career 
as a student he started the custom of keeping on his desk a 
quire of scribbling paper sewed together; and on the current 
quire everything was written translations from the Greek, 
prose translations into Latin, mathematical problems, memo- 
randa of every kind. These quires were carefully preserved. 
This habit of writing out everything made him an accurate 
and ready man, and placed him far ahead of his contemporaries 
in the college examinations. He adopted the rule of writing 
on his quire every day a translation into Latin of three or four 
sentences; this he did in preparation for the final University 
examinations. While he was an undergraduate Babbage's 
difference machine was much talked of : in his last undergraduate 
year (1822) Airy studied the subject and made a sketch of a 
computing machine. About the same time he prepared a 
paper on the construction of a reflecting telescope with silvered 
glass; a paper which brought him an introduction to Mr. (after- 
wards) Sir John Herschel, and Mr. (afterwards) Sir James South, 
two of the active astronomers of the day. 

In Airy's time a candidate for B. A. was required to pass 
a University ordeal, which was a survival of the ancient system 
of examination. The candidate at the end of his second and 
third years was required to state three theses which he was 


prepared to defend in Latin against as many opponents. For 
instance Airy submitted the following theses : 

(1) Recte statuit Newtonus in Principiis suis Mathematicis, libro 
primo, sectione undecima. 

(2) Recte statuit Woodius de Iride. 

(3) Recte statuit Paleius de Obligationibus. 

An apponent was appointed to attack each thesis. The dis- 
cussion was carried in the Latin language under the direction 
of a Moderator; and when the high men were engaged, the 
spectacle was sufficiently interesting to draw a great crowd 
of undergraduates. The statutes framed in the time of Queen 
Elizabeth, required that a candidate should keep a certain 
number of such acts; at this time all excepting the two men- 
tioned were gone through as a matter of form. Airy's practice 
in Latin enabled him to acquit himself with high distinction. 
A few years later the respondent and opponents reduced the 
procedure to a farce by concocting their arguments beforehand, 
and the system was suppressed in 1830. This procedure explains 
the term wrangler and senior wrangler ; the contest was originally 
a wrangle in the Latin language. In Airy's time there was a 
further tripos examination conducted partly in writing, partly 
viva voce in English. Airy came out Senior Wrangler, very 
far ahead of the next man. The year before Peacock had 
introduced a paper of questions entirely on the Differential 
Calculus, a procedure which definitely established the study 
of the continental mathematics at Cambridge University. 

After graduating as B.A., Airy continued to read for the 
fellowship examination, and to take pupils, generally four in 
number. He was now elected a member of the Cambridge 
Philosophical Society. During the vacation he went on a 
geological tour in Derbyshire, visiting among other places 
Edensor, near Chatsworth, the principal residence of the Duke 
of Devonshire. His introduction was to the rector, the Rev. 
Richard Smith, a Cambridge man; he fell in love with the 
eldest daughter, and within two days proposed an engagement 
to marriage. This was before he entered the competition 
for fellowship, and in view of the rules then in force about the 


tenure of fellowship, was a rather bold step. No engagement 
was then made. In 1824 he was elected a fellow of his college. 
He also obtained the post of assistant mathematical tutor, 
and in addition took some private " pupils. While engaged 
in this work he prepared a volume called Mathematical Tracts, 
on subjects which were either deficient at the University, or 
else not presented in readable form, namely, Lunar Theory, 
Figure of the Earth, Precession and Nutation, and the Cal- 
culus of Variations. The volume was printed by the University 
Press, and brought its author both reputation and some money. 
This book, published in 1826, applied the continental notation 
of the calculus and it exerted a great influence on the study 
of mathematical physics at Cambridge. 

Whewell was senior to Airy in academic standing by seven 
years. In 1826 they made experiments on gravity in the Dol- 
coath mine in Cornwall. One pendulum was swung at the top 
of the mine, the other at the bottom. After numerous observa- 
tions of their periods in these positions, the one down below 
was sent up to be compared with the other at the top; when 
it emerged at the top, the experimenters were surprised and 
mortified to find the basket on fire, and hence the observations 
had to be abandoned. This same year the Lucasian profes- 
sorship of mathematics fell vacant; a Head of one of the colleges 
sought to capture it as a sinecure; Charles Babbage, who had 
taken only a poll degree at Cambridge, also applied; and so 
did Airy. Babbage and the Head mutually destroyed one 
another, with the result that Airy was elected. Airy improved 
his academic standing, but not his income; the salary was only 
100, and the position involved the giving up of some tuition 
work. He was not yet in a position to sacrifice his fellowship 
by marriage. He immediately issued a printed notice that 
he would give prof essional lectures in the next term. There had 
been no lectures on Experimental Philosophy (Mechanics, 
Hydrostatics, Optics) for many years. The University in 
general looked with great satisfaction on such vigorous reform; 
but there were difficulties to surmount; no allotted term 
for the lectures, no allotted hour of the day, scarce any available 


lecture-room. In this contest Airy and Babbage first came 
into conflict. 

It was the next year (1827) that Airy's path first intersected 
that of Hamilton. Dr. Brinkley, the professor of astronomy 
at Dublin had been made a bishop. Airy went over to Dublin 
to see about the appointment: finding that the electors desired 
to appoint W. R. Hamilton, although still an undergraduate, 
he retired. The following year the Plumian professorship of 
astronomy and experimental philosophy at Cambridge fell 
vacant, the salary of which was 300. Airy applied, and 
before he was elected took the extraordinary course of applying 
for an increase of salary. He was anxious to secure an income 
on which he could marry a difficult thing in the constitution 
of the University. His good fortune did not fail him; he was 
elected and the salary raised to 500. He had now charge of the 
College Observatory, and a residence, to which two years later 
he brought Richarda Smith from Edensor. For eight years he 
lived and worked in the Cambridge Observatory. One of his 
first scientific works was a repetition along with Whewell of the 
pendulum experiments in the Dolcoath mine. Misfortune 
again attended the inquiry. A few days after the observations 
had been started, a mass of rock settled in the mine, stopping 
the pumps and allowing the water to accumulate; sufficient 
time was not left to complete the observations, and the result 
was again nugatory. After one year at the Observatory Airy 
began to publish his astronomical observations, first of all 
devising an orderly system of exhibition, then " quite a novelty 
in astronomical publications." 

In 1832 a committee of the newly founded British Associa- 
tion asked Airy to prepare the report on Astronomy for the next 
meeting to be held at Oxford. This he did, and read part of 
it at the meeting. Mr. Vernon Harcourt, secretary of the 
Association, deprecated the tone of the report as relating to 
English astronomers; but Airy refused to alter a word. About 
this time Sir James South, the astronomer, on removing to a 
house in Kensington, bought a 1 2-inch achromatic telescope in 
Paris and employed Troughton & Simms of London to mount it 


equatoreally. South was not satisfied with the work, and 
refused to pay, and a lawsuit followed in which the English 
astronomers of the day were called on as expert witnesses. 
Airy and Sheepshanks were on the side of the contractors; 
Babbage on the side of South. .^The court appointed an arbi- 
trator, who decided against South; whereupon he dismantled 
the telescope and issued the following notice: 


To shyock toymakers, smokejack makers, mock coin makers, etc. 
Several hundred weights of brass etc., being the metal of the great equa- 
toreal instrument made for the Kensington Observatory by Messrs. 
Troughton & Simms, are to be sold by hand on the premises; the wooden 
polar axis of which, by the same artists, with its botchings cobbled up 
by their assistants, Mr. Airy and the Rev. R. Sheepshanks, was purchased 
by divers vendors of old clothes, and dealers in dead cows and horses, 
with the exception of a fragment of mahogany specially reserved at the 
request of several distinguished philosophers, on account of the great 
anxiety expressed by foreign astronomers to possess them, was converted 
into snuff boxes as a souvenir piquant of the state of the art of astronomical 
instrument making in England during the nineteenth century. 

This dispute occasioned by one who eventually proved to be 
insane, led to much quarreling among the astronomical scientists 
of the day. De Morgan as a friend of Airy and Sheepshanks 
was publicly insulted by South, and on asking an explanation 
from him received what was virtually a challenge to a duel. 
Babbage, on the other hand, by his support of South, inflicted 
much damage on his own career. South, who was on the board 
of visitors, attacked Airy's administration of the observatory 
in public. 

In 1835 Airy received an exceptional favor from the British 
Government; a pension of 300 was settled on his wife. Airy 
was a liberal, the Government conservative. No personal 
or political obligation was imposed; it was given avowedly 
as an encouragement to science. Later in this year a liberal 
Government came into power; they offered him the appoint- 
ment of astronomer royal at the Greenwich Observatory, which 


at that time had fallen into a very inefficient state. He accepted 
and then they offered him Knighthood, which he declined on 
the ground of not being wealthy enough. When Airy took 
charge of the Cambridge Observatory, it had only one instru- 
menta transit instrument, and no assistant. By the date 
when he left for Greenwich the University had erected a Mural 
Circle and a small Equatoreal, and he had induced the Duke 
of Northumberland a great patron of science to purchase 
and erect what was then the finest equatoreal telescope in 

At Greenwich Observatory Airy appointed two new assist- 
ants, and he speedily introduced his system of order. He 
introduced thirty printed skeleton forms for observations and 
computations; procured a copying press; punched four holes 
in papers and tied them flat in packets and subordinate packets. 
Later he got from a manufacturer a machine to punch the 
holes; and his system was an anticipation of the device which 
is now common in offices. All papers were carefully preserved 
in their proper place; and in his later years the ruling passion 
for order was so great, that he took more pains to classify a 
letter properly than to master its purport. About this time 
the difficulty of navigating iron ships was pressed on the Govern- 
ment; they asked Airy to make experiments on a ship. He 
made a series of observations, reduced them, and prepared 
magnets and iron correctors to neutralize the disturbance 
mechanically. He was successful in substituting mechanical 
for tabular correction; but the sluggishness of the large magnet 
of the compass remained a difficulty. Subsequently Sir William 
Thomson introduced instead of the large magnet a number 
of small magnets, and put a patent on it; but Airy got nothing 
from the Government for solving the main part of the problem. 
Being a very methodical man Airy kept a diary. Under 
September 15, 1842 he entered the following: " The Chan- 
cellor of the Exchequer asked my opinion on the utility of 
Babbage's calculating machine, and the propriety of expending 
further sums of money on it. I replied, entering fully into 
the matter, and giving my opinion that it was worthless." 


Fortified with this opinion, the Government broke off definitely 
with poor Babbage. 

Airy's successor at the Cambridge Observatory was named 
Challis. In 1844 Prof. Challis introduced to Airy by lettei 
the senior wrangler of the previous year named J. C. Adams, 
who in consequence of having read Airy's report on recent 
progress in astronomy to the British Association had several 
years before formed the design of investigating the unexplained 
irregularities in the motion of the planet Uranus, and who was 
now, his undergraduate years over, busily engaged on the 
solution. Adams wished to be furnished with the Greenwich 
observations of Uranus; these were promptly supplied. A 
year later Challis wrote a letter of introduction to Airy beginning : 
" My friend Mr. Adams, who will probably deliver this note to 
you, has completed his calculations respecting the perturbation 
of the orbit of Uranus by a supposed ulterior planet, and has 
arrived at results which he would be glad to communicate to 
you, if you could spare him a few moments of your valuable 
time." Provided with this letter, Adams called at the Royal 
Observatory; Airy was absent in France. A month later, 
when Airy had returned, Adams called again; the astronomer 
royal was taking his midday walk, but would be back soon. 
Adams called an hour later; the astronomer was at dinner, 
and granted no interview. Adams left a paper giving the results 
of his investigation the mass, position, and elements of the 
orbit of the new planet. A few days later Airy sent him a 
letter inquiring whether his theory likewise accounted for 
the irregularities in the radius-vector of Uranus. Adams did 
not reply; he felt mortified, and he thought the question trivial. 
Airy wrote no further letter to Adams; but a few months later, 
when Leverrier communicated similar results in a letter, he 
replied hailing Leverrier as the true predicter of the new 
planet. It was Airy's custom to turn off visitors without 
seeing them; interviews interfered too much with his pet order. 
He forgot his official position, and how he himself had been 
assisted. Adams was very unfortunate in the man to whom 
he confided his results. Prof. Challis made use of the Cam- 


bridge telescope to search for the planet; but he was anticipated 
by a Berlin astronomer who followed Leverrier's prediction. 
Challis actually mapped the planet as a star twice, but had 
not compared his maps. A great controversy arose; the 
attitude is neatly expressed by the couplet : 

When Airy was told, he wouldn't believe it; 
When Challis saw, he couldn't perceive it. 

In the early forties there raged in England the " battle of 
the gauges." Of the railroads built some had adopted a broad 
gauge (6 feet), some a narrow gauge (4 feet 8J inches). The 
inconveniences of the diversity were beginning to be felt acutely, 
and the Government appointed a commission of which Airy 
was a member. The commissioners reported in favor of the 
universal use of the narrow gauge; their recommendation 
was opposed effectively in Parliament by the broad gauge 
interest, supported by Babbage, who devised very ingenious 
instruments and made much more scientific observations than 
Airy. However the narrow guage gradually became the solu- 
tion of the difficulty. In the fall of 1848 Lord Rosse invited 
a number of astronomers to his castle at Parsonstown, Ireland, 
in order that they might inspect his large reflecting telescope. 
They were entertained for two weeks, Airy and Hamilton 
were the principal experts. Airy was able to remove a fault 
in the mounting of the great mirror, for in practical astronomy 
he was immensely superior to Hamilton; but as a calculator 
and scientific genius Hamilton was as much superior. It was 
on this occasion that Hamilton, influenced by Airy's sarcastic 
remarks, broke his abstinence resolution. 

In 1851 Airy presided over the British Association, at the 
meeting held in Ipswich. The next year he communicated a 
paper to the Royal Society on the " Eclipses of Agathocles, 
Thales, and Xerxes." And he also lectured on the subject 
at the Royal Institution. In 1854 he renewed the attempt 
to determine by pendulum vibrations the intensity of gravity 
at the bottom of a mine; this time he chose the Harton coal 
mine in the north of England, and for his assistants observers 


from the different astronomical observatories of the country. 
The observations were successful; they gaye the result that 
gravity is increased at the depth of 1260 feet by i/ipoooth 
part: from which he estimated the density of the Earth to be 
6.565. Airy not only supplied IJansen with the Greenwich 
observations of the Moon for the purpose of constructing his 
Lunar Tables, but he had them printed at the expense of the 
British Government and secured for him a personal grant 
of 1000 against the opposition of Babbage and South, who 
were on the Board of Visitors for the Observatory. 

Airy came into conflict with Prof. Cayley about the kind 
of questions that ought to be set at the Cambridge Tripos 
Examination. Airy held that " The papers were utterly per- 
verted by the insane love of problems, and by the foolish impor- 
tance given to wholly useless parts of algebraical geometry. 
For the sake of these every physical subject and every useful 
application of pure mathematics was cut down or not men- 
tioned." When invited to make an address at Cambridge, 
he seized the occasion to renew the attack; he also wrote to 
the board of mathematical studies. He wished to introduce 
into the list of subjects for examination Partial Differential 
Equations, Probabilities, Mechanics in a form which verges on 
practical application, Attractions, Figure of the Earth, Tides, 
Theory of Sound, Magnetism but not (for the present) Mathe- 
matical Electricity. In the correspondence which followed 
Cayley said, " I think that the course of mathematical study 
at the University is likely to be a better one if regulated with 
a view to the cultivation of science as if for its own sake, rather 
than directly upon consideration of what is educationally best 
(I mean that the' best educational course will be so obtained) 
and that we have thus a justification for a thorough study of 
pure mathematics. In my own limited experience of examina- 
tions the fault which I find with the men is a want of analytical 
power, and that whatever else may have been in defect Pure 
Mathematics has certainly not been in excess." Later Airy 
criticized the questions set for the Smith prizes in 1879 in a 
letter addressed to the members of the Senate. He singled 


out the following question, " Using the term circle as extending 
to the case where the radius is a pure imaginary, it is required 
to construct the common chord of two circles." This drew 
forth from Cayley a rejoinder in which he gave a solution of 
the problem. To which Airy replied, " I am not so deeply 
plunged in the mists of impossibles as to appreciate fully your 
explanation in this instance, or to think that it is a good criterion 
for University candidates." The dispute ended in the intro- 
duction of mathematical physics into the course of study. 

Airy was a liberal in religious attitude. He sympathized 
with the agitation which led to the abolition of religious tests 
for M.A. degree at the Universities of Oxford and Cambridge. 
He also supported his fellow mathematician Colenso when he 
was attacked for his writings on the Pentateuch. With respect 
to Colenso he wrote, " He has given me a power of tracing out 
truth to a certain extent which I never could have obtained 
without him. And for this I am very grateful. As to the 
further employment of this power he and I use it to totally 
different purposes. But not the less do I say that I owe to 
him a new intellectual power." During the years 1872-3 Airy 
was president of the Royal Society. In 1872 he was knighted 
by Queen Victoria; he had declined the honor three times 
before. In 1873 he was consulted by Barlow and Bouch the 
engineers for the construction of a railway bridge across the 
Firth of Tay, on the subject of the wind pressure that should be 
allowed for. This bridge was blown down in 1879 with a pas- 
senger train on it, no one surviving to tell the tale. Airy's 
report was subsequently much referred to at the official inquiry 
into the causes of the disaster. 

In 1 88 1 when 80 years old (20 years over the limit assigned 
by Osier for good work!) Airy resigned the office of astronomer 
royal and the Government, on account of his exceptional 
public services, granted him a pension almost equal to his 
salary. He died on the 2d of January, 1892 in the 9ist year 
of his age. His life had been one of great activity; he was 
the author of eleven volumes and of 518 papers extending from 
1822 to 1887. With regard to his habits while he was at Green- 


wich Observatory, he generally worked in his office from 9 
to about 2 30, then took a walk, dined at about 3 130, and after- 
wards slept for about an hour. In the evening he worked in 
the same room with his family. " His powers of abstraction 
were remarkable; nothing seemed to disturb him, neither 
noise, singing nor miscellaneous conversation. . . . With his 
natural love of work and with the incessant calls upon him, 
he would soon have broken down, had it not been for his system 
of regular relaxation. Two or three times a year he took a 
holiday, generally a short run of a week or ten days in the 
spring, a month in the early autumn and about three weeks 
in the winter." Airy did valuable work and exerted great 
influence; especially we may look upon him as the founder 
at Cambridge of the modern school of mathematical physics. 



JOHN COUCH ADAMS was born on the 5th of June, 1819, at a 
farmhouse seven miles from Launceston in Cornwall. His 
father was a tenant farmer, and so had been his ancestors 
for several generations. His mother, nee Tabitha Knill Grylls, 
owned a small estate, inherited from an aunt named Grace 
Couch; hence the middle name of the mathematician. John 
Couch Adams was the oldest of seven children; he had three 
brothers and three sisters; his brother William Grylls Adams 
became a professor of physics, and has attained to scientific 
distinction although not comparable to that of his brother. 
Adams was thus of the old Welsh stock located in the south- 
western peninsula of England. He received his primary edu- 
cation at the village school near the farm, where at ten years 
of age he studied algebra. In his own home there was a small 
library, which also had been inherited by his mother, and 
which included some books on astronomy. He constructed a 
simple instrument to determine the elevation of the sun. " It 
consisted of a vertical circular card with graduated edge, from 
the centre of which a plumb bob was suspended. Two small 
square pieces of card, with a pinhole in each, projected from 
the circular disc at right angles to its face at opposite ends of a 
diameter. The card was to be so placed that the sun shone 
through the pin holes, and the elevation was read off on the 

At twelve years of age he was placed in a private school 

taught by the Rev. John Couch Grylls, a cousin of his mother, 

the subjects of instruction being classics and mathematics. Here 

* This Lecture was delivered on April 8, 1904. EDITORS. 



he had access to a public library, where he studied more books 
on astronomy, and also Vince's Fluxions, then the principal 
testbook at Cambridge on the higher mathematics. Thus 
early was he introduced to Newton's methods. While at this 
school he watched for three wee}es for a predicted return of 
Encke's comet; at last he saw it (1835) an d he wrote home, 
" You may conceive with what pleasure I viewed this, the first 
comet which I had ever had a sight of, which at its visit 380 
years ago threw all Europe into consternation, but now affords 
the highest pleasure to astronomers by proving the accuracy 
of their calculations and predictions." The following year 
an annular eclipse of the Sun took place. For the people on 
the farm he made a calculation of the times of the eclipse for 
that meridian and latitude, and also a diagram of the eclipse 
as it would appear to them. Next year his account of observa- 
tions of an eclipse appeared in the London papers. He was 
now 1 8 years old, and had shown such signs of mathematical 
power that preparations were made to send him to Cambridge, 
In 1839, when 20 years old, he entered St. John's College; 
while an undergraduate he was invariably the first man of his 
year in the college examinations. It was his custom to keep 
a memorandum book, in which at the end of his second college 
year (July 3, 1841) he made the following entry: " Formed a 
design, in the beginning of this week, of investigating as soon 
as possible after taking my degree, the irregularities in the 
motion of Uranus, which are yet unaccounted for, in order 
to find whether they may be attributed to the action of an 
undiscovered planet beyond it; and if possible thence to deter- 
mine the elements of its orbit, etc., approximately, which would 
probably lead to its discovery." His attention had been drawn 
to the phenomenon by reading Airy's report on Astronomy 
to the British Association (1831-2); but no explanation is 
suggested there. Meanwhile he kept to the beaten path of 
training for the Tripos; as a result in 1843 he won the first 
place in that examination, the first Smith's prize and a fellow- 
ship from his college. After taking his degree, Adams attempted 
a first solution of his problem on the assumption that the orbit 


was a circle with a radius equal to twice the mean distance of 
Uranus from the Sun an assumption suggested by Bode's 
law. The result showed that a good general agreement between 
his theory and observation might be obtained. He now in 
1844, if not before, acquainted Prof. Challis, Airy's successor 
with his scientific enterprise; and through him made a request 
to Airy for the errors of the tabular geocentric longitude 
of Uranus for 1818-26, with the factors for reducing them to 
errors of heliocentric longitude. Airy at once supplied all 
the results of the Greenwich observations of Uranus from 
1754 to 1830. 

With these improved data Adams now undertook a more 
elaborate discussion of the problems, retaining however the 
former assumption with respect to the mean distance; and by 
September of the following year (1845) ne na d the investiga- 
tion completed. He communicated the results to Prof. Challis 
in the form of a note giving numerical values for the new planet, 
of its mean longitude at a given epoch, the longitude of its 
perihelion, the eccentricity of its orbit, its mass and its 
geocentric longitude for the last day of the month but without 
any account of his method. Challis on the 22d of September 
wrote to Airy a letter to introduce Adams; the first sentence 
in that letter has been already quoted in my lecture or Airy. 
Challis further said that he considered Adams' deductions to 
be made in a trustworthy manner. Challis had the best facilities 
in England to search for the predicted planet, yet he turned 
the matter over to Airy. Provided with the letter Adams 
called at the Greenwich Observatory, and met with the experi- 
ences described in my last lecture. Adams was naturally of a 
shy disposition and he felt mortified. In reply to the paper 
of results that he had left at the Observatory, Airy sent, a 
fortnight later, a letter to Adams: " I am very much obliged 
by the paper of results which you left here a few days since, 
showing the perturbations on the place of Uranus produced by 
a planet with certain assumed elements. ... I should be 
very glad to know whether this assumed perturbation will 
explain the error of the radius- vector of Uranus." The prin- 


cipal result was that the mean longitude of the planet for 
ist of October, 1845, was 323 34'. Adams was hurt at the 
reception which his results had obtained; regarding Airy's 
question as of trifling importance he did not send any answer 
immediately but applied himself ,to a new calculation on the 
assumption of a smaller mean distance. 

That same November a French astronomer, M. Leverrier, 
presented a paper to the French Academy on the perturbations 
of Uranus produced by Jupiter and Saturn, and concluded that 
these were quite incapable of explaining the observed irregu- 
larities. In June of the next year he presented his second 
paper which showed that there was no other possible explanation 
of the discordance, except that of an exterior planet. Further, 
like Adams, he assumed the distance to be double that of 
Uranus, and calculated that its longitude at the beginning 
of the next year (1847) would be 325. Leverrier communi- 
cated his results by letter on the 24th of June to Airy, who 
on comparison found that there was only about one degree of 
difference in the predicted places of Adams and Leverrier. 
The next day (June 29) a meeting of the Board of Visitors took 
place at the Greenwich Observatory; Sir John Herschel and 
Prof. Challis were present as visitors. In the course of a dis- 
cussion, Airy referred to the probability of shortly discovering 
a new planet, giving as his reason the close coincidence of Adams' 
and Leverrier's predictions. Early in July Airy thought it 
time that a search should be made for the planet. He con- 
sidered the Cambridge telescope the best for the purpose, and 
he asked Prof. Challis whether he would undertake it, and the 
latter agreed to do so. Airy suggested the formation of three 
successive maps of the stars down to the 4th magnitude, in a 
band of the heavens 30 long by 10 wide having the predicted 
place of the planet as its centre. When the successive sets of 
observations were mapped, the planet could be detected by its 
motion in the interval. 

At the end of August Leverrier presented his third memoir 
to the French Academy in which he gave the calculated elements 
of the orbit of the planet. He also restricted as far as possible 


the limits within which the planet should be sought; he pre- 
dicted that it would have a visible disc, and sufficient light to 
make it conspicuous in ordinary telescopes. By this time 
Adams had completed his new investigation on the assumption 
of a distance 1/30 less than before; the results agreed still 
better with observation. In a letter to Airy he communicated 
the new results, answered his question about the errors of the 
radius- vector, and intimated that he was thinking of presenting 
a brief account of his investigation at the coming meeting of 
the British Association. Airy at this time was again absent 
on the Continent; the British Association met; Adams came 
with his paper, but the section of mathematics and physics had 
adjourned the day before he arrived. Had he been present 
at the beginning of the meeting he would have heard Sir John 
Herschel say in his address on resigning the chair to his suc- 
cessor, after referring to the astronomical events of the year, 
which included a discovery of a new minor planet: " The 
year has done more. It has given us the probable prospect of the 
discovery of another planet. We see it as Columbus saw 
America from the shores of Spain. Its movements have been 
felt, trembling along the far-reaching line of our analysis, with 
a certainty hardly inferior to that of ocular demonstration/' 

In this same month of September Leverrier sent his pre- 
dictions to Dr. Galle of the Berlin Observatory in a letter 
received September 23, 1846. Dr. Galle was already provided 
with a map of the part of the heavens prescribed, and that 
very evening he found a star of the eighth magnitude which 
did not exist on the map; observation on the following evening 
showed that its motion was nearly the same as that of the 
predicted planet. On October ist Chain's heard of the dis- 
covery of the planet at Berlin. He then found that he had 
actually noted it on August 4 and August 12, the third and 
fourth nights of his search, so that had the observations been 
compared as the work proceeded, the planet might have been 
discovered by him before the middle of August. The discovery 
of the planet by Dr. Galle, in consequence of Leverrier's pre- 
diction, was received with the greatest enthusiasm by astron- 


omers of all countries, and in France the planet was at once 
called Leverriers' planet or even " Leverrier." Sir John 
Herschel was the first to speak for Adams. He wrote a letter 
to the AthencBum in which he recalled his works at the South- 
ampton meeting, and explained fthat the ground of his con- 
fidence was the near coincidence of the results of two independent 
investigations that by Leverrier, and another by a young 
Cambridge mathematician named Adams. He invited Adams 
to place his calculations in full before the public; this Adams 
did on the i3th of November, 1846, in a memoir read before the 
Royal Astronomical Society. 

At the time of Galle's discovery Airy was on the Continent. 
On returning to Greenwich he wrote to Leverrier (October 14, 
1846), " I was exceedingly struck with the completeness of your 
investigations. May you enjoy the honors which await you! 
and may you undertake other work with the same skill and the 
same success, and receive from all the enjoyment which you 
merit! I do not know whether you are aware that collateral 
researches had been going on in England, and that they had 
led to precisely the same result as yours. I think it probable 
that I shall be called on to give an account of these. If in this 
I shall give praise to others, I beg that you will not consider 
it as at all interfering with my acknowledgment of your claims. 
You are to be recognized beyond doubt as the real predicter 
of the planet's place. I may add that the English investiga- 
tions, as I believe, were not quite so extensive as yours. They 
were known to me earlier than yours." Leverrier naturally 
felt much hurt by Herschel's article and Airy's letter. He 
could not understand why Adams had not published his results. 
Other French astronomers were at first very unwilling to admit 
that Adams had any rights whatever in connection with the 
planet, but later, at the suggestion of the great French astron- 
omer Arago, the name Neptune was adopted and has since 
been universally used. It was now time for Prof. Challis 
to publish what he knew of the matter. He gave in the A thenceum 
for October 17 an account of Adams' investigations, and it 
was then publicly known for the first time that Adams' con- 


elusions had been in the hands of Airy and Challis since 1845, 
and that Challis had actually been engaged in searching for the 
planet. The British astronomers were divided in opinion; some 
held that the fact that Adams' results had not been publicly 
announced deprived him of all claims in relation to the dis- 
covery. The Royal Society of London rather hastily (1846) 
awarded it highest honor, the Copley medal, to Leverrieral one; 
and in the Royal Astronomical Society a majority of the Council 
were in favor of awarding their gold medal to him; but a suffi- 
cient minority of the Council protested. Two years later 
the Royal Society made some amends by awarding the Copley 
medal to Adams. 

In 1847 the Queen with Prince Albert visited the University 
of Cambridge; on this occasion the honor of knighthood was 
offered to Adams, then 28 years old, but he felt obliged to decline 
for the same reason as Airy had done before. The members of 
St. John's College, in honor of the brilliant achievement of one 
of their number founded the Adams prize, to be awarded 
biennially for the best essay on some prescribed subject in 
pure or applied mathematics; its value is about 225. In 
this year also, Prof. Benjamin Pierce of Harvard College 
published a paper in which he criticized the methods of Adams 
and Leverrier, contending that the period of Neptune differed 
so considerably from that of the hypothetical planet that the 
finding of the planet was partly due to a happy accident. 
Adams, on the occasion of the republication of his memoir in 
Lionville's Journal in 1877, replied that the objection did not 
hold on account of the perturbations considered lying within 
a fraction of the synodic periods of Neptune and Uranus. In 
this year Leverrier attended the meeting of the British Asso- 
ciation at Oxford, in the company of Airy. The two discoverers 
of Neptune met then, and ever after manifested a high apprecia- 
tion for each other. In 1876 when Adams was president of the 
Royal Astronomical Society he made an address on presenting 
a second gold medal to Leverrier for his theories of the four 
great planets, Jupiter, Saturn, Uranus, and Neptune. 

Adams was by nature a calculator, not an observer or experi- 


menter. Hence it is not surprising to find that his next 
research work was the determination of the constants in Gauss' 
theory of terrestrial magnetism a subject to which he devoted 
much time in his later years, and which he left unfinished. In 
1851 Adams was elected president of the Royal Astronomical 
Society. In 1852 his fellowship : at St. John's College expired, 
because he had not taken clerical orders; he was however 
elected to a fellowship at Pembroke College, which he retained 
till his death. In 1853 Adams communicated to the Royal 
Society his celebrated memoir on the secular acceleration of the 
Moon's mean motion. Halley was the first to detect this 
acceleration by comparing the Babylonian observations of 
eclipses with those of Albatagnius and of modern times, and 
Newton referred to his discovery in the second edition of the 
Principia. The first numerical determination of the value 
of the acceleration is due to Dunthorne, who found it to be 
about 10" in a century. Laplace was the first to deduce the 
acceleration theoretically from Newtonian principles; the 
result is given by an infinite series of which he calculates only 
the first term. Plana, an Italian mathematician, found the 

next term to be --^-m 4 ; Adams by his investigation found 

1 2o 

it to be w 4 , which reduced the value of the first term 


from 10" to 6". This paper gave rise to a violent controversy; 
those opposed holding that the result was contradictory to 
observation. But Adams was safe; his result depended entirely 
on algebraical considerations on the solution of a differential 
equation, not on observation; consequently his result finally 

In 1858 Adams' life at Cambridge was interrupted; he was 
appointed professor of mathematics in the University of St. 
Andrews, Scotland. At the end of a year he returned to Cam- 
bridge as Lowndean professor of astronomy and geometry. 
As Lowndean professor he lectured during one term in each 
year, generally on the lunar theory, but sometimes on the 
theory of Jupiter's satellites, or the figure of the Earth. Two 


years later he succeeded Challis as the Director of the Cambridge 
Observatory and settled down as a married man. Henceforth 
the center of his scientific activity was the Observatory house, 
where Airy and Challis had lived, situated on an eminence 
about a mile west of Cambridge on the Huntington road. The 
observatory was well equipped, thanks to Airy's efficient 
incumbency; but Adams was by nature a calculator, and 
the instruments were not much used during his tenure of 

In 1866 Adams took up the problem of the November 
meteors, drawn thereto by the remarkable display of that year. 
Prof. Newton of Yale had published a memoir in the American 
Journal of Science and Arts in which he collected and discussed 
the original accounts of thirteen displays of these meteors in 
years ranging from A.D 902 to A.D. 1833; ne inferred that these 
displays recur in cycles of 33.25 years, and that during a period 
of two or three years at the end of each cycle a meteoric shower 
may be expected. He concluded that the most natural explana- 
tion of these phenomena is, that the November meteors belong 
to a system of small bodies describing an elliptic orbit about 
the Sun, and extending in the form of a stream along an arc 
of that orbit which is of such a length that the whole stream 
occupies about one-tenth or one-fifteenth of the periodic time in 
passing any particular point. He showed that in one year the 
group must have a periodic time of either 180.0 days, 185.4 days, 
354.6 days, 376.6 days or 33.25 years. Prof. Newton found 
that the node of the orbit of the meteors is gradually increasing; 
that the rate is 52 ; '.4 with respect to the fixed stars; and he 
remarked that with this datum and the position of the radiant 
point, computation might be able to determine which of the 
five periods is the correct one. He considered 354.6 days the 
most probable. Adams then took up the problem. He found 
that none of the first four periods satisfied the data, while the 
fifth one of 33.25 years did. He concluded that he had settled 
the question of the periodic time of the November meteors 
beyond a doubt. The elements of their orbit obtained by 
Adams agreed very approximately with those of a comet 


observed in 1866, and it seemed probable that the meteors and 
the comet constituted one moving aggregation. In 1899, 
thirty-three years later, an exceptional display of meteors was 
predicted on the strength of Adams' result; there was much 
popular lecturing on the subject beforehand; the citizens of 
London on the predicted niglft went to bed having previously 
arranged with the policeman on the beat to call them up, but 
their slumbers were not disturbed. 

Eleven years later (1877) Adams recognized the merits 
of an American astronomer George W. Hill, who was then 
an assistant in the office of the American Nautical Almanac, 
and whose eminence as an astronomer is now universally recog- 
nized in the world of science. Hill in 1877 published a paper 
on the motion of the moon's node in the case when the orbits 
of the Sun and Moon are supposed to have no eccentricities, 
and when their mutual inclination is supposed to be definitely 
small. He made the solution of the differential equations 
depend on the solution of a single linear differential equation 
of the second order which is of a very simple form. This 
equation is equivalent to an infinite number of algebraical linear 
equations, and Hill showed how to develop the infinite deter- 
minant corresponding to these equations in a series of powers 
and products of the small quantities forming their coefficients. 
Adams in his unpublished investigations had discovered the 
same infinite determinant, and was thus in a position to immedi- 
ately recognize the value of Hill's work. This same year (1877) 
Adams communicated to the British Association at Plymouth 
the results of a calculation of Bernoulli's numbers. Ber- 
noulli's numbers are the coefficients of x n /nl in the expansion of 

- 2 + 3 - ..-.n 

which 1 = B 2 = - . B g = . The first fifteen 


B's were calculated by Euler, the next 16 by Rothe; and in 
this communication Adams supplied the following 31 numbers. 
The difficulty of this calculation may be judged from the facts. 
that the denominator of 32 is 510 and the numerator is a 


number of 42 figures. By means of these numbers and cal- 
culations which Adams made of the logs, of 2, 3, 5 and 7 to 263 
places, he made a calculation of Euler's constant 0.577215 
to 263 places. He also made a calculation of the modulus of 
the common logarithms to the same number of places. Mr^ 
Shanks had previously calculated the above logarithms and 
the modulus of the common logarithms to 205 places, and 
Euler's constant to no places of decimals. 

In 1 88 1 on Airy's retirement from the Royal Observatory, 
the appointment was offered to Adams, but he declined it. 
He was not a business man, and probably already felt the effects 
of age. In 1884 he visited America, coming as a delegate to 
the International Prime Meridian Conference held at Wash- 
ington. He also took part in the British Association meeting 
at Montreal, and the American Association meeting in Phila- 
delphia. In 1889 he was afflicted by a severe illness, and after 
two further attacks he died on the 2ist of January, 1892, in the 
73d year of his age. He was buried in the Cambridge cemetery, 
which is not far from the Observatory. A medallion of Adams 
has been placed in Westminster Abbey close to the grave of 

A Cambridge physician who knew him well thus sketches 
his character: " His earnest devotion to duty, his simplicity, 
his perfect self-lessness, were to all who knew his life at Cam- 
bridge a perpetual lesson, more eloquent than speech. From 
the time of his first great discovery scientific honors were 
showered upon him, but they left him as they found him 
modest, gentle, and sincere. Controversies raged for a time 
around his name, national and scientific rivalries were stirred 
up concerning his work and its reception, but he took no part 
in them, and would generously have yielded to other's claims 
more than his greatest contemporaries would allow to be just. 
With a single mind for pure knowledge he pursued his studies, 
here bringing a whole chaos into cosmic order, there vindicating 
the supremacy of a natural law beyond the imagined limits of 
its operation; now tracing and abolishing errors that had crept 
into the calculations of the acknowledged masters of his craft, 


and now giving time and strength to resolving the self made 
difficulties of a mere beginner, and all the while with so little 
thought of winning recognition or applause that much of his 
most perfect work remained for long, or still remains, 



of March, 1792, at the village of Slough, near Windsor, England. 
His father was Sir William Herschel, a native of Hanover, 
Germany, who migrated in his youth to England, became an 
organist and choir master at Bath, at the same time as an 
amateur astronomer constructed powerful reflecting telescopes 
by means of which he discovered a new planet Uranus, and was 
invited by George III to become astronomer to the court at 
Windsor. He finally established himself in the village of Slough, 
in a house where there was a suitable grassplot for the erection 
of his celebrated large reflecting telescope. The mother of 
John Herschel, nee Mary Baldwin, was the only daughter of 
a London merchant, had been a widow, and had brought to 
his father a moderate fortune. His father's salary as court 
astronomer was only 200, but he made much money from the 
construction of telescopes. John was their only child, and 
was thus the heir to considerable wealth. He received his 
primary education at a private school at Hitcham, Bucking- 
hamshire, and was then sent to the great public school Eton 
in the neighborhood of Windsor; he remained there for a few 
months only, but when his mother saw him maltreated by a 
strange boy he was taken home and placed under the care of 
Mr. Rogers, a Scottish mathematician. He must have studied 
the classics thoroughly for at an advanced age he translated the 
whole of the Iliad into English hexameters. His father realized 
the importance of training in mathematics. At that time 
mathematical science had declined in England, through adula- 
tion of Newton and antipathy towards Leibnitz, but still flour- 

* This Lecture was delivered on April n, 1904. EDITORS. 


ished in Scotland. Herschel himself says, " In Scotland the 
torch of abstract science had never burnt so feebly nor decayed 
so far as in England; nor was a high priest of the sublimer muse 
ever wanting in those ancient shrines, where Gregory and 
Napier had paid homage to her power." At that time, a Scots- 
man named Ivory was almost the sole British mathematician 
who was in touch with the great mathematical progress being 
made on the Continent, especially in France. John Herschel 
possessed the great advantage of living in a home where the 
chief languages of the Continent were understood, and in which 
relations with abroad were still maintained. 

At the age of 17 Herschel entered St. John's College, Cam- 
bridge. His principal undergraduate friends were Charles 
Babbage and George Peacock, and all three were impressed 
with the decline of mathematical science in England. Herschel 
thus describes the situation: " Students at our universities, 
fettered by no prejudices, entangled by no habits, and excited 
by the ardour and emulation of youth, had heard of the existence 
of masses of knowledge from which they were debarred by the 
mere accident of position. There required no more. No 
prestige which magnifies what is unknown, and the attraction 
inherent in what is forbidden, coincided in their impulse. The 
books were procured and read, and produced their natural 
effects. The brows of many a Cambridge moderator were 
elevated, half in ire, and half in admiration, at the unusual 
answers which began to appear in examination papers. Even 
moderators are not made of impenetrable stuff; their souls 
were touched, though fenced with sevenfold Jacquier, and 
tough bullhide of Vince and Wood. They were carried away 
with the stream, in short, or replaced by successors full of their 
newly-acquired powers. The modern analysis was adopted 
in its largest extent." The three undergraduates accomplished 
their object by forming an Analytical Society. The Society 
published a volume of memoirs but more important still they 
translated and published Lacroix's smaller Treatise on the 
Differential Calculus, to which Herschel added an appendix 
on Finite Differences. 


While undergraduates both Babbage and Herschel attended 
the lectures of the professor of Chemistry, they helped the 
professor to prepare his experiments, and they set up private 
laboratories for themselves. Herschel finished his under- 
graduate career in 1813 by being a senior wrangler; he also won 
the first Smith's prize. He was immediately elected to a fellow- 
ship in his college. While an undergraduate he wrote a paper 
on "A remarkable application of Cotes' Theorem," which 
was published in the Transactions of the Royal Society, and 
he had no sooner graduated than he was elected a Fellow of that 
Society. It was his father's desire that he should enter the 
church, but he himself preferred the profession of the law; 
so in 1814 he was entered as a student of Lincoln's Inn, London. 
Residence in the metropolis brought him into intimate relations 
with the principal scientists of the day; among whom was 
Wollaston; the physicist (who was the first to notice two or 
three of the most conspicuous dark lines of the solar spectrum) 
and South, the astronomer. By Wollaston he was influenced 
to take up chemistry and optics, and by South to turn his at- 
tention to the unfinished researches of his father. The professor 
of chemistry at Cambridge whom he had assisted was killed 
accidentally; Herschel applied for the chair, but unsuccess- 
fully. After two years spent in London he returned to Slough 
with the definite purpose of taking up astronomical research. 
To this step lines written by himself doubtless refer: 

To thee, fair Science, long and early loved, 

Hath been of old my open homage paid; 

Nor false, nor recreant have I ever proved, 

Nor grudged the gift upon thy altar laid. 

And if from thy clear path my foot have strayed, 

Truant awhile, 'twas but to turn, with warm 

And cheerful haste; while thou dids't not upbraid, 

Nor change thy guise, nor veil thy beauteous form, 

But welcomedst back my heart with every wonted charm. 

During the six following years he worked at pure mathe- 
matics, astronomy, experimental optics and chemistry. It 
was in these years that he made his principal contributions to 


pure mathematics. Several of the papers which he contributed 
to the Royal Society dealt with the calculus of finite differences; 
for these he received the Copley medal in 1821. In astronomy, 
he revised the catalogue of double stars made by his father; 
this work he did in conjunction .-with (Sir James) South and 
with the help of two refracting telescopes the property of that 
scientist. The resulting catalogue, printed in the Philosophical 
Transactions, brought its author the gold medal of the recently 
instituted Astronomical Society of London; also the Lalande 
prize for astronomy (of the Paris Academy) for 1825. Herschel 
along with Babbage took an active part in the foundation of the 
Royal Astronomical Society; he wrote its inaugural address, 
and was its first foreign secretary, while his father was its first 
president. In optics he investigated the absorption of light 
by colored media and the action of crystals upon polarised 
light. In chemistry (1819, when philosophical chemistry was 
perhaps at its lowest ebb in England) he rediscovered the hypo- 
sulphite salts, and ascertained their leading properties, the 
principal of which is dissolving the nitrate of silver a property 
applied by Daguerre twenty years later to fixing photographic 
pictures. In 1821 he traveled in Italy and Switzerland with 

In 1822 his father died. His mother continued to reside 
at Slough, and the younger Herschel now succeeded to all the 
property, astronomical and otherwise, of his father. His 
mother survived for ten years, and throughout this interval 
Herschel made his home at Slough, with the exception that for 
three years, 1824-7, while he was secretary of the Royal Society 
he had also a house in London. Towards the end of this interval 
he married, the object of his choice being Margaret Brodie 
Stewart, the daughter of a clergyman of the north of Scotland; 
in this as in many other matters Herschel was a fortunate man. 
In 1830 he was put forward as the scientific candidate for the 
presidency of the Royal Society, the titled candidate being the 
royal Duke of Sussex; in which contest rank prevailed, but the 
principle which Herschel stood for ultimately prevailed. In 
this interval he accomplished much work in astronomy. In 


1825 he received from his aunt, Caroline Herschel, a copy of 
her zone catalogue of nebulae; in his reply he said, " Those 
curious objects I shall now take into my especial charge; 
nobody else can see them." He referred to his being the owner 
of a 20-foot " front view " reflector constructed by himself with 
his father's aid in 1820. With this instrument he made a great 
review of all the nebulae visible in England, the result being a 
catalogue of 2307 nebulae, of which 525 were discovered by 
himself; presented to the Royal Society in 1833. Herschel 
also continued the search for double stars, using the larger 
telescope which belonged to South; he discovered 3346 pairs, 
and made extensive measurements of known pairs. 

For Lardner's Cabinet Cyclopedia he prepared an article 
on astronomy which was subsequently rewritten and published 
in 1849 as a book under the title Outlines of Astronomy. This 
book went through many editions, and was translated into 
many languages, even the Roman, Chinese and Arabic. For 
this Cyclopedia Herschel also prepared an introductory volume 
under the title Preliminary Discourse on the Study .of Natural 
Philosophy. By Natural Philosophy he does not mean Physics 
only but it includes the experimental and observational sciences, 
namely, in the order of Herschel's book, Mechanics, Optics, 
Astronomy, Geology, Mineralogy, Chemistry, Heat, Electricity, 
Zoology, Botany. Herschel advanced several of these sciences, 
and had a special knowledge of all, excepting perhaps the two 
last; he was thus rarely well fitted to write on their logic and 
methods. The work treats of the methods of scientific research 
since the time of Francis Bacon. On the title page is a picture 
of Bacon and the words Natures minister et inter pres taken from 
his first aphorism; (these words, as all in this audience know, 
are also in the motto of Lehigh University). In it will be 
found many of the philosophic ideas which were elaborated by 
the British mathematicians whose lives we have discussed. 
Here we find the idea, afterwards elaborated by Clerk Maxwell, 
that the atoms of the chemist bear the characters of " manu- 
factured articles"; here we find the thought, elaborated by 
Tait in verse, that Nature presents to us in a confused and 


interwoven mass the elements of all our knowledge and that 
it is the business of the philosopher to disentangle, to arrange, 
and to present them in a separate and distinct state. In the 
works of these great scientists there is abundant evidence that 
this Discourse formed a guide arid inspiration, as indeed it 
did to all the British scientists of the nineteenth century. The 
Discourse was translated into French, German and Italian, 
and was reprinted in 1851. 

After his mother's death Herschel prepared to carry out a 
long cherished project a survey of the heavens in the southern 
hemisphere. The Government offered Mm a free passage in a 
ship-of-war; he preferred to pay his own way. On the i3th of 
November, 1833, he set sail with his family and instruments 
for the Cape of Good Hope, and arrived in the course of two 
months. He secured a house at Feldhausen, six miles from 
Cape Town, and there he erected his 2o-foot reflector and 
7-foot refractor, and applied them to the double stars and 
nebulae. He constructed a scale of brightness by fixing the 
relative brightness of nearly 500 stars, using for this purpose 
" the method of sequences." He made comparisons not only 
at the Cape, but on the voyage out and back. With an acti- 
nometer of his own invention he made the first satisfactory 
measures of direct solar radiation. 

While Herschel was busy at the Cape, an article appeared 
day by day in the New York Sun pretending to give an account 
of some great astronomical discoveries he had made. It 
announced that he had discovered men, animals, etc., in the 
Moon, and gave much detail. The paper by this enterprise, 
increased its circulation five fold, and secured a permanent 
footing. The article printed separately had a large sale, and 
was translated into various languages. The author was R. A. 
Locke, the editor of the newspaper; but De Morgan thought it 
had been written by a professional astronomer. 

While engaged with the stars, Herschel had also time to 
help the development of the educational system of the colony. 
He was instrumental in initiating an excellent system of national 
education. Consulted on the course of study for a South 


African College he gave his views in a letter which stated that 
too much time was givem to the classical languages in the great 
English schools; that he attached great importance to all those 
branches of practical and theoretical knowledge whose possession 
goes to constitute an idea of a well-informed gentleman, namely, 
knowledge of the actual system and the laws of nature, both 
physical and moral; that in a free country it is important for 
every man to be trained in political economy and jurisprudence; 
that mathematics is the best training in reasoning, provided 
that it is supplemented with the inductive philosophy. He 
concluded, " Let your College have the glory for glory it will 
be to have given a new impulse to public instruction by 
placing the Novum Organum for the first time in the hands 
of young men educating for active life, as a textbook, and as a 
regular part of their College course." 

After four years of work at the Cape Herschel returned to 
England, arriving in the middle of March, 1838. A great 
banquet was given him by his scientific contemporaries to 
which Hamilton came expressly from Dublin. Many honors 
came to Herschel; he had been knighted in 1831 and now he 
was made a baronet by Queen Victoria, on the occasion of her 
coronation (June, 1839); and from Oxford University, as 
one of the lions of the day he received the degree of D.C.L. 
In 1840 he removed his residence from Slough to the country 
house of Collingwood, near the village of Hawkhurst, in the 
County of Kent; and this remained almost without interruption 
the scene of his future labors. For eight years his principal 
work was the reduction of the results of his four years of obser- 
vation at the Cape. From this retreat he was called forth one 
year to address the students of Marischel College, Aberdeen, 
as their lord rector. In the ancient universities the rector was 
the chosen head of the student body; in the Scottish Uni- 
versities the office survives in an altered form. The rector is 
elected by the students, usually on political grounds, and his 
principal duty is to deliver an address at the beginning of his 
term of office. The leading politicians of the day were candi- 
dates for the honor. Occasionally as in the case of Herschel, 


Carlyle, Carnegie, the choice of the students is guided by other 
than political reasons. In 1843 Herschel made a reproduction 
of an engraving of the Slough 4o-foot reflector which was the 
first example of a photograph on glass. He was the first person 
to use the terms positive and negative for photographic repro- 
ductions. His discovery in 1845 of the " epipolic " dispersion 
of light produced by sulphate of quinine and some other sub- 
stances led the way to Stokes' explanation of the phenomena 
of fluorescence. 

In 1845 Herschel was called on to preside at the second 
Cambridge meeting of the British Association. Since his own 
student days, Cambridge had made great progress in mathe- 
matical science. The " d-ists " had long since triumphed over 
the J0/-ards. The Cambridge Philosophical Society had been 
founded for the reading and publication of scientific memoirs; 
the Cambridge Mathematical Journal had been founded; and 
the University Observatory had been made an up-to-date 
institution. His immediate predecessor in the chair was another 
" d-ist ", George Peacock, now dean of Ely; and after the close 
of the meeting Herschel and Hamilton were guests at the 
deanery, on which occasion both essayed their poetic power. 
Two years before the Quaternion theory had been published, 
and Herschel referred to it in his presidential address. The 
closing passage of this address is characteristic of the man: 
" In these our annual meetings, to which every corner of Britain 
almost every nation in Europe sends forth as its repre- 
sentative some distinguished cultivator of some separate 
branch of knowledge; where I would ask, in so vast a variety 
of pursuits which seem to have hardly anything in common, 
are we to look for that acknowledged source of delight which 
draws us together, and inspires us with a sense of unity? That 
astronomers should congregate to talk of stars and planets 
chemists of atoms geologists of strata is natural enough; 
but what is there of equal mutual interest, equally connected 
with and equally pervading all they are engaged upon, which 
causes their hearts to bum within them for mutual communica- 
tion and unbosoming? Surely, were each of us to give utterance 


to all he feels, we would hear the chemist, the astronomer, the 
physiologist, the electrician, the botanist, the geologist, all 
with one accord, and each in the language of his own science 
declaring not only the wonderful works of God disclosed by it, 
but the delight which their disclosure affords him, and the 
privilege he feels it to be to have aided in it. This is indeed a 
magnificent induction a consilience there is no refusing. It 
leads us to look around, through the long vista of time, with 
chastened but confident assurance that science has still other 
and nobler work to do than any she has yet attempted; work 
which, before she is prepared to attempt, the minds of men must 
be prepared to receive the attempt; prepared, I mean, by an 
entire conviction of the wisdom of her views, the purity of 
her objects, and the faithfulness of her disciples." 

In 1846 on resigning the chair at Southampton he announced 
that science was about to triumph in a remarkable way by 
predicting the position of a new planet. The following year, 
1847, the Results of his observations at the Cape of Good Hope 
were published in one large quarto volume, the expense of 
publication being borne by the Duke of Northumberland; 
there may be found an extended catalogue of southern stars 
and nebulae, with elaborate drawings and discussions of their 
relative and variable brightness. In 1850 the office of Master 
of the Mint, an office which had been held by Sir Isaac Newton, 
was changed from a political to a scientific appointment; and 
Herschel was appointed. He did not break up his home, but 
stayed himself in London as much as was necessary. He 
did not like the separation from his family, and after five years 
resigned. While holding this office, he also accepted a place 
on the Cambridge University Commission. After retiring from 
the Mint, he lived for sixteen years longer as the Sage of Colling- 
wood. He was ever ready to help a younger or less fortunate 
man of science. He had an unbounded admiration for the 
genius and character of Sir W. R. Hamilton; he gave him 
practical counsel in the preparation of the " Elements of Quater- 
nions," and in an indirect way assisted him financially in the 
education of his eldest son a very unworthy recipient as events 


turned out. We have seen how he was the first to recognize 
the work of Adams; it is not wonderful then that he retained 
his great popularity to the last. 

Herschel and his mathematical friends all advocated strenu- 
ously the decimalisation of the coinage; that is, to retain the 
pound as the standard fundamental unit of financial value, and 
to retain or adopt only such sub-units as were decimal parts of 
it; the florin is the tenth part, and the farthing nearly the 
loooth part (very approximate ^ cent). Others advocated 
the shilling for the fundamental unit ( = quarter dollar); the 
latter were called Little-endians, the former Big-endians. How- 
ever both Big-endians and Little-endians were downed by the 
non-progressive element. In 1863 a bill was introduced into 
Parliament to legalize the French metrical system. Herschel, 
while favoring decimalisation, did not approve of changing the 
fundamental units. He argued that the French meter was not 
the io,ooo,oooth part of a quadrant of the Earth's meridian 
passing through Paris, but simply the metre des Archives; and 
that its authority was precisely of the same kind as the standard 
yard preserved in London. He also pointed out that the inch 
was very nearly the 500,500,000^1 part of the Earth's polar 
axis, and argued that the polar axis was a better natural unit 
than an arbitrarily chosen meridian. These arguments are 
the source of inspiration of Rankine's song about the Three- 
foot Rule, sang at the British Association. This is the point 
of contest at the present day both in America and Great Britain; 
it is not decimalisation but the choice of the fundamental units. 
The opposition comes from those who do not understand that 
the whole system of scientific arithmetical calculation for 
instance in electrical engineering, depends on the choice of the 
fundamental units; and that whatever the advantages or dis- 
advantages of the fundamental French units, whole systems 
of derived units have been established upon them, and adopted 
by international conferences. 

Sir John Herschel died at Collingwood on the nth of May, 
1871, in the 8oth year of his age. The greatest tribute, in my 
opinion, to his character is the fact that amid the animosities 


and feuds which troubled the lives and impaired the usefulness 
of many of the mathematicians of the earlier part of the nine- 
teenth century, Herschel succeeded in retaining the love of all; 
he was equally the friend of South and Airy, of Babbage and 
Whewell. His home at Collingwood was the ideal home not 
of a selfish bachelor wedded to science, but of a devoted husband 
and loving father. " He never lost his taste for simple amuse- 
ments; was in his element with children; loved gardening, 
and took an interest in all technical arts." His family consisted 
of three sons and nine daughters. His sons have continued, 
though not in so brilliant a manner, the scientific reputation 
of the Herschel family. He was buried in Westminster Abbey 
near the grave of Sir Isaac Newton. On his monument there 
is his motto Coelis Exploratis and a reference to Psalms 
CXLV, 4, 5- 


Adams, J. C., 114, 119-50 

Airy, G. B., 74, 85, 95, 106-118, 120, 

124, 129 

Ampere, A. M., 57 
Aristotle, 24 

Babbage, C. 56, 71-83, 95, 108, 112, 132, 


Bacon, F., 85, 89, 90, 91, 92, 135 
Berard, J. R., 27, 28 
Berkeley, G., 13 
Boole, G., 10, 57 
Bond, G. P., 15 

Campbell, L., 9 
Carnot, J. W. L., 25, 57 
Cassini, J. D., 15 
Cavendish, H., 19 
Cayley, A., 116 
Challis, J., 114, 115, 121 
Clairault, A. C., 95 
Clausius, R. J. E., 27, 42 
Clerk, J, 7 

Clerk-Maxwell, J., 7, 10 
Clifford, W. K., 47 
Colenso, J. W., 117 
Coulomb, C. A., 14 
Crookes, W., 34, 54 

Darwin, C., 65 

Davy, H., 73 

Descartes, 10 

De la Roche, 27 

De Morgan, A., 35, 56, 57, 92, 112, 136 

Dewar J., 15 

Elder, J., 36 
Euler, L., 128 

Faraday, M., 9 
Foucault, J. B. L., 98 
Fourier, J. B. J., 56, 57, 63, 64 
Forbes, J. D., 10, 12, 14, 16, 24, 39, 41 
Fresnel, A. J., 57, 98 

Gatle, J. G., 123, 124 
Galileo, G., 15 
Gibbs, J. W., 52 
Gifford, Lord, 104 
Grylls, J. C., 119 

Halley, E., 126 

Hamilton, W., 10, n, 89, in 

Hamilton, W. R., 16, 18, 39, 40, 46, 49, 

57, 94, 138, 139 
Harcourt, V., in 
Hay, D. R., 10 
Helmholz, H. L. F., 44 
Herschel, J. F. W., 15, 20, 35, 36, 70, 

72, 75i 86, 107, 130-141 
Herschel, W., 131 
Hertz, H. R., 18, 21 
Hill, G. W., 128 
Huggins, W., 99 
Hume, D., 24, 78 
Huxley, T. H., 65 
Huygens, C., 15 

Jacquard, J. R., 79, 80 
Jenkin, F., 24 
Joule, J. P., 24, 85 

Kant, E., 85 

Kelland, P., 10, 12, 45, 56 

Kelvin, Lord, 43, 51, 56-70, 86, 105 

Laplace, P. S., 126 
Leibnitz, G. W., 131 




Leverrier, U. J. J., 114, 122, 124, 125 
Locke, J., 85 
Locke, R. A., 136 

Macfarlane, A., 3, 34, 42, 68, 77 
Maxwell, J. C., 7-21, 37, 38,. 43, 61, 


Mayer, J. R., 25, 44 
Menabrea, 81, 82 
Michelson, A. A., 18 
Mill, J. S., 13 
Murray, J., 53 

Napier, M., 36 

Newton, H. A., 127 

Newton, I., 12, 23, 25, 54, 70, 74, 95, 

105, 107, 120, 129, 139, 141 
Nicol,W., 12 

Peacock, G., 56, 70, 85, 107, 108, 132, 


Perry, J., 66 
Pierce, B., 125 
Plana, M., 81 
Plato, 93 

Proctor, R. A., 91 
Prony, G. C. F., 72 

Rankine, W. J. M., 22-37, 42, 140 
Regnault, H. V., 57 

Routh, E. J., 13 
Rosse, Lord, 82, 83, 115 

Salmon, G., 57 
Scheutz, L., 82 
Sheepshanks, R., 112 
Smith, D. E., 3 
Smith, H. J. S., 91 
Snow-Harris, W., 57 
South, J., 108, in, 134, 141 
Steele, W. J., 38, 46 
Stewart, B., 24, 46 
Stokes, G., 57, 94-105 
Sylvester, J. J., 57 

Tait, F. G., 52, 53 

Tait, P. G., 9, 12, 16, 18, 30, 38-54, 

i3, 105 

Thomson, D., 10 
Thomson, J., 57 
Thomson, W., 19, 26, 27, 28, 36, 40, 

41, 42, 43, 49, 56-70, 95, 113 
Tyndall, J., 20, 52 

Vince, S., 120, 132 

Whewell, W., 12, 18, 84-93, 108, no, 


Whitworth, J., 76 
Wollaston, W. H., 113 

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