# Peter Guthrie Tait and the Scrapbook

1. Introduction

On 22 March 2006 I [EFR] lectured to the Institute of Physics on Peter Guthrie Tait. I gave the lecture at 14 India Street, Edinburgh, the birthplace in 1831 of James Clerk Maxwell, and now owned by the James Clerk Maxwell Foundation. John O'Connor came with me since we knew that P G Tait's Scrapbook would be on display after the lecture.

2. 14 India Street, Edinburgh

The house where James Clerk Maxwell was born is at 14 India Street, Edinburgh about a fifteen-minute walk from the railway station which is in the centre of Edinburgh. The hall of the house is impressive with two marble pillars giving an instant impression of grandeur. The room, entered from a door on the right, is the former dining room. On the wall facing you as you enter are two large portraits, the rightmost one of James Clerk Maxwell, the left most one being a portrait of his school friend P G Tait. Portraits of James Clerk Maxwell's family are on the walls and a Display Cabinet near the windows contains a fine collection of items associated with Maxwell. Documents relating to the purchase of the house, which was built in 1820, are in the Display Cabinet and, especially for the occasion, Tait's school medals are on display. James Clerk Maxwell was born in the first floor room overlooking the stables. By a remarkable coincidence, the family now living in the house above the former stables is descended from Maxwell's friend P G Tait. Shortly after James's birth, the family moved to their house at Glenlair.

3. P G Tait's Scrapbook

Tait's Scrapbook had been placed on the table in the former dining room described above. Mr Murray Tait, the great-grandson of P G Tait, presented it to the James Clerk Maxwell Foundation in 2003. It must have been created by members of his family after his death using papers and newspaper cuttings which Tait had preserved.

The Scrapbook contains obituaries of Tait (these are the first items), newspaper cuttings which contain anything about him, letters he sent to the newspapers, copies of examinations he set, syllabuses for courses he gave, letters sent to him by Maxwell, Thomson and many others, articles about golf which mention his work in that area, poems by Tait, Maxwell and others etc.

There is a police summons for his son Alexander Tait to appear in court. It is dated 1862 when Alexander was six years old!. There is also a letter from Tait who was greatly upset about the summons which related to his children throwing stones in Abbotsford Crescent in St Andrews.

Many pages relate to The Unseen Universe: or Physical Speculations on a Future State by P G Tait and Balfour Stewart, originally penned anonymously and first published in 1875. There are a host of cuttings which are reviews of the book, speculation as to who the authors were, etc. Similar cuttings relate to later editions when the authors gave up their anonymity.

4. From Dalkeith to professor at Edinburgh

P G Tait was born in Dalkeith on 28 April 1831, the son of John Tait, secretary to Walter Francis Scott, fifth duke of Buccleuch, and his wife, Mary Ronaldson. There were three children in the family, with Peter having two sisters. Peter began his studies at Dalkeith grammar school. A tragedy struck the family when his father died in 1840. Following this his mother moved from Dalkeith to Edinburgh where Peter attended Circus Place School for a year before entering Edinburgh Academy in 1841. There were two important aspects of the move to Edinburgh. One was that the family went to live in Somerset Cottage, the home of John Ronaldson, Mary's brother. He was a banker with a keen interest in science, and fostered Peter's scientific interests in astronomy, geology and photography. The other aspect was that he became friendly with Maxwell around the middle of his time at the Academy. Maxwell, although the same age as Tait, was one year ahead. He was registered late for the Academy and there were no places left in Tait's class. Much later Tait wrote:-
From this time forward I became very intimate with him, and we discussed together, with schoolboy enthusiasm, numerous schoolboy problems, among which I remember particularly the various plane sections of a ring or tore, and the form of a cylindrical mirror which should show one his own image unperverted.
There is a notebook in which Tait and Maxwell recorded the "schoolboy problems" he referred to in the above quote. Much of the manuscript is written in beautiful calligraphy. Great care has been taken with these parts and pencil lines have been drawn in and then removed to ensure that all lines are straight and are perfectly left justified. Most of the manuscripts are by Tait and signed 'fecit P G Tait' with a date. The friends became competitive when it came to school prizes. Tait was top of his class in each one of his six years at Edinburgh Academy but, of course, Maxwell was not in the same class. There were school prizes open to all pupils and in 1846 Tait came third overall but first in mathematics, while in the following year Maxwell came first in mathematics with Tait second. Here is an extract from the announcement of the 1846 prizes (taken from the Scrapbook):-

The Academical Club Prize was this year awarded to the successful Competitor in all the departments of study pursued by the Academy. The Competition, which was open to all the Rector's Classes, was conducted in the following manner. The branches of study were divided into five departments, viz. Greek - Latin - Mathematics - English and French - Geography, History and Scripture; and printed Examination Papers, containing questions and exercises on each of these, were successively put into the hands of the Competitors, who returned written answers, without leaving the school-room, and without any assistance of any kind. There were thirty-seven Competitors, and the examination occupied three separate days.

Lewis Campbell (sixth class) came top, Tait (fifth class) came third, Maxwell (sixth class) came sixth equal. In Mathematics Tait (fifth class) came top, Lewis Campbell (sixth class) came second, Maxwell (sixth class) came third. It is indicated that these three did significantly better than six others who also gained distinction in mathematics. Tait also gained distinction in Latin (Maxwell didn't), Lewis Campbell came second in Greek despite going on to have a distinguished career as a professor of Greek, Tait and Maxwell both achieved distinctions in English and French and in Geography, History and Scripture.

In November 1847, Tait entered the University of Edinburgh. Maxwell entered Edinburgh University at the same time at Tait and together they attended the second mathematics class taught by Kelland and the natural philosophy (physics) class taught by James David Forbes. Tait remained at Edinburgh University for only one year before entering Peterhouse, Cambridge in 1848. During a remarkable undergraduate career his tutor was William Hopkins. In January 1852, at the age of twenty, he graduated as senior Wrangler in the Mathematical Tripos. This means that he was placed first among the First Class degrees in mathematics awarded by Cambridge in that year. The full list of results in the Mathematical Tripos of that year are in the Scrapbook:-

List of Honors
at the
Bachelor of Arts' Commencement
January
31, 1852

Examiners: Arthur Cayley, M.A. Trinity College

Wranglers
TAIT Peterhouse
Steele Peterhouse
...

He was also the first Smith's prizeman. He spent another two years at Cambridge and he made an attempt to challenge Hopkins as a coach for the Mathematical Tripos. In this he met with limited success: only one student employed him as a coach but that student was more successful than any of Hopkins' students. Tait remarked:-
Oh, that's nothing - I could coach a coal scuttle to be senior wrangler.
Of the Mathematical Tripos he also commented:-
... coaches spend their lives in discovering which pages of a textbook a man ought to read.
Also during these years he collaborated with William John Steele on writing A Treatise on Dynamics of a Particle intended as a text for Cambridge students. Steele was a friend who after being a pupil of Professor William Thomson at Glasgow University was at Peterhouse and graduated second to Tait in the Tripos. He died before the text was completed.

In September 1854 Tait took up the professorship of mathematics at Queen's College Belfast. There is no doubt that up to this time Tait was a mathematician but he became interested in conducting experiments with Thomas Andrews, a chemist at Queen's College. He wrote later of Andrews:-
I have always regarded it as one of the most important determining factors in my own life (private as well as scientific) and one for which I cannot be sufficiently thankful, that my appointment to the Queen's College at the age of twenty-three brought me for six years into almost daily association with such a friend.
Another important friendship that evolved from this time was with his engineering colleague James Thomson (brother of William, later Lord Kelvin). Tait began to correspond with William Rowan Hamilton about quaternions in August 1858 and, in reply to Hamilton's question as to how he had stated to work with quaternions, Tait wrote on 7 December 1858:-
... it was only in August last that I suddenly bethought me of certain formulas I had admired years ago on page 610 of your Lectures - and I thought (and still think) likely to serve my purpose exactly. (The matter which more immediately suggested this to me was a paper by Helmholtz in Crelle's Journal (Vol. LX) which I was reading in July last as soon as we received it ... The title (in German) I forget - but a manuscript translation of my own which I now have beside me is headed "Vortex motion" ... ).
If Tait's friendship with Hamilton was to prove important for his future research, other friendships Tait formed were important in his family life. Two of his friends at Peterhouse were sons of the Rev James Porter and through them Tait met their sister, Margaret Archer Porter, whom he married in Belfast on 13 October 1857.

The Chair of Natural Philosophy at the University of Edinburgh became vacant in 1859, J D Forbes having moved to the University of St Andrews to become Principal. Tait was a candidate for the chair but so was Maxwell who had been forced to seek another post when Marischal College and King's College in Aberdeen combined. Routh, who had been First Wrangler at Cambridge in Maxwell's year, was also a candidate but the real competition was always going to be between Tait and Maxwell. Tait won despite Maxwell's outstanding scientific achievements. When the Edinburgh paper, the Courant, reported the result it noted that Tait had been chosen in preference to Maxwell since:-
... there is another quality which is desirable in a Professor in a University like ours and that is the power of oral exposition proceeding on the supposition of imperfect knowledge or even total ignorance on the part of pupils.
5. The Edinburgh professor

The Committee that chose Tait for his lecturing skills were absolutely correct. He was an outstanding lecturer and the following two extracts from the Scrapbook illustrate this. The first extract is from an article about Tait in the student newspaper of the University of Edinburgh:-

The Student
20 March 1888 Twopence

Professor Tait

Did one wish to give a stranger a good impression of the style and quality of the lectures which are delivered to Edinburgh students, without a doubt he would take him some forenoon to hear Professor Tait.
Two of us a few days ago freshened old memories by a visit to the Natural Philosophy Classroom. ... We were not long seated before the door leading to the Physical Laboratory opened, and the tall figure of the Professor slipped round it. The noises, more pronounced than formerly we thought, soon ceased under the steady gaze which followed the peculiar and well-remembered bow. This seems to be made when the motion towards the audience is combined with that in a direction parallel to it; but the full resolution into its components still remains for some bright young student.
The old gown was yet extant, and the dark jacket, fastened by a single button at the neck, still seemed as far as ever from the toga virilis.
The lecturer has lost nothing of his ancient power of graphic illustration and charming style. The conclusions are obtained from various trains of reasoning, and apt reference to everyday commonplaces clinches the argument, while the subtle humour of the man is every now and then revealed, and serves to keep his audience in good fettle. Details are skilfully subordinated, and the principles stand out in bold relief. The brilliant experiments are all necessary, and none are shown for effect. Performed at the right moment, they never fail, and make all seem clear as at noon.

The second extract comes from an article about Tait which appeared in The Evening Dispatch following his death in 1901:-

Professor Tait and his class

Professor Tait was the last of the old school amongst the Edinburgh professoriate, and he always insisted on maintaining its traditional vogue, no matter how quaint these might now be. He was accustomed, therefore, to make his daily entrance to his lecture theatre a procedure of some ceremony. The door would be abruptly opened by the assistant who ushered in the Professor. The Professor himself, invariably appeared clad in his academic robes; first of all, an upright majestic figure was seen in the background, then a trip over the doorway, as he entered the classroom with a magnificent and courtly bow to the class. This, of course, always met with a rapturous applause from the class, which as inevitably brought a smile to the old man's face as he stalked to his desk, and at once began to lecture.

When Tait began to lecture all noise and interruption in the class ceased. It was not the force of discipline, because Tait seemed to ignore that, but the sheer force of interest which the Professor compelled in his hearers as he explained the forces physical which he loved so well. As a lecturer his reputation was so great that he drew students to study his one subject alone from all parts of the civilised world.

Tait was proud of the University of Edinburgh as is clear in his address to graduates in 1888 (taken from the Scrapbook):-

The University of Edinburgh never stood higher, in the estimation of those at least whose judgement is of any value, than on the occasion of its Tercentenary four short years ago. To speak of my own department alone: - what University, home or foreign, has been fortunate enough to see assembled at its celebrations such a collection of the very foremost of the world's mathematicians and physicists as then graced this hall? To name only a very few, we had from the continent Cremona, Helmholtz, Hermite, and Mendeléeff; with Cayley, Salmon, Stokes, Sylvester, and Thomson from our own islands.

I have always held, I think in accordance with all the highest authority, that the great object of a University is to teach what is alike surely known and of value when known, and to add to the utmost of our power to the store of really useful human knowledge. In comparison with these great objects, the conferring of degrees is a secondary and relatively unimportant matter.

6. P G Tait on university education

Tait had strong views on how students should be taught. We present two extracts from the Scrapbook, the first being Tait's own report on a new teaching initiative he had undertaken:-

Professor Tait's Report of the Class in Experimental Physics

I undertook, with considerable hesitation, to give a course of lectures on Experimental Physics, which should be (though elementary) strictly scientific, and not (in the common and degraded sense of the word) popular. In other words, I determined that, if I tried the experiment at all, I should do it with the sole view of imparting accurate information; and all mere sensational displays being sedulously avoided.
I intimated in my opening lecture that I was perfectly ignorant of what might reasonably be expected of my class - so far at least as regarded their fitness by preparation, not by natural capacity, for attacking the subject. I was greatly pleased to find that the want of preliminary training did not interfere, to any serious extent, with their progress. A considerable number passed with great credit, and there were a few whose answers could scarcely have been improved. I look upon the experiment as a very successful one indeed, and have no longer any fears of the effects of defective previous training. I have never had, nor (considering the small number of lectures into which so much had to be compressed) one in which the progress made was more marked.

It had been proposed in a government report that only students with the necessary qualifications be allowed to enter university. Tait replied in vigorous fashion in his address to graduates in 1888 (taken from the Scrapbook) saying that this:-

.... seems to threaten in a direct manner one of the most valuable of a Scotsman's birthrights. The Scottish Universities have hitherto made it their proudest boast that they are the property of the Scottish people, without distinction of rank, age or sect. Anyone who can pay his matriculation fee has at present a right to demand enrolment in my class. Is he now to be deprived of this right, or are obstacles to be gratuitously put in the way of enjoying it? I said "gratuitously", I should rather have said "wantonly". Experience has led me to the deliberate conclusion that the less a man knows of Natural Philosophy when he enters my Ordinary Class, the better his progress in that fascinating subject. ... Again many men who have exceptionally high qualifications for the study of experimental science, men who may, if properly guided, render invaluable service to science and to their country, are hopelessly incapable of mastering elementary mathematics, or even the trivial pedantries of grammar. Are these men to be stopped on the very threshold of the career for which nature has specially qualified them? To them a degree is not an object; they come to the University to obtain from it the information they desire, and which it is the primary duty of a University to give to all comers.

7. Tait writes letter to newspapers

The Scrapbook contains newspaper cuttings of letters which Tait had sent on a wide variety of topics. In the following exchange he is complaining of sewage problems in St Andrews in 1878. Perhaps it is worth noting that St Andrews still had sewage problems 100 years after that!

The St Andrews Gazette 28 September 1878

SIR, - In the Fifeshire Journal of today I observe a long letter from Professor Tait complaining of a sickening smell arising from some drain or sewer at Pilmour Links, and I had the curiosity to visit the spot and judge for myself how matters really stood; but to my surprise I could find no trace whatever of the sickening smell complained of. I learned, however, that a few days ago a gas pipe had accidentally burst in that locality. from which a very bad small proceeded; but when this was repaired all seemed to be right. If the Professor has any real grievance, I am sure the Drainage Committee, on application, will put matters right. CIVIS

The St Andrews Gazette 5 October 1878

SIR, -One who can think it possible to mistake the smell of coal gas for the stench of sewage is scarcely qualified to speak in the name of the Drainage Committee.
The drainage of St Andrews is about as bad as it could be; and, when this has been pointed out, it is vain to try to trail a red-herring across the scent, as you correspondent "Civis" has done.
Instant and thorough action is necessary if the prosperity of the town is to be maintained.

8. Tait and the 15 puzzle

The Scrapbook contains information about Tait's solution of the 15 puzzle. Tait had solved the puzzle and submitted a paper on the solution when he saw two articles in the American Journal of Mathematics in 1879, one by W W Johnson and one by W E Story. Johnson proved that an odd permutation of the pieces of the puzzle is impossible to obtain, Story proved that every even permutation of the squares is possible. On seeing these two papers, Tait then "cut his paper down to the smallest dimensions consistent with intelligibility". Although it has been claimed that no elementary proof was known until A F Archer gave one in 1999 in the American Mathematical Monthly, it appears to me that Tait's proof is completely elementary. He writes a permutation as the product of disjoint cycles, then notes that a cycle of odd length can be written as the product of an even number of transpositions.

He ends his article with comments which would certainly not be considered politically correct today:-

Dr Crum Brown suggests the term Aryan for the normal arrangement, with the corresponding term Semitic for its perversion. Similarly Chinese would signify the Aryan rotated right-handedly through a quadrant, and Mongol the Semitic rotated left-handedly through a quadrant. Now it is easily seen that Aryan is changed into Semitic, and Chinese into Mongol, or vice versa, by an odd number of interchanges. Similarly Aryan and Mongol, and Semitic and Chinese, differ by an even number of interchanges. Hence any given arrangement must be either Aryan or Semitic. The former can be changed into Mongol, the latter into Chinese.

9. Thomson, Tait and Maxwell

Maxwell, Tait and Thomson were friends who worked together, yet must rank as the three most important Scottish mathematical physicists. It is tempting to think of Tait as a minor figure compared with the other two giants of Scottish science, but this is far from the truth. Maxwell, whom we now rate as the most important of the three, was the most modest and least forceful. We note Maxwell's admiration for the work of Tait expressed in a letter of 1871 to Thomson:-
You should let the world know that the true source of mathematical methods as applicable to physics is to be found in the Proceedings of the Royal Society of Edinburgh. The volume- surface- and line-integrals of vectors and quaternions and their properties as in the course of being worked out by T' (Tait) is worth all that is going on in other seats of learning.
It has been said that everything that William Thomson did in the first half of his career was brilliant, and everything he did in the second half of his career was wrong. This is harsh, but largely based on Thomson's insistence on vortex atoms. However modern physics has shown that Thomson's intuition was rather incredible since string theory bases the understanding of fundamental particles on knot theory. Geniuses are sometimes wrong, but it is always worth looking at their failures for they often contain gems of wisdom that should not be lost.

The Scrapbook contains lots of examples of the correspondence between the three friends. Here is an example of a letter from Maxwell to Tait:-

Glenlair
Dalbeattie

30 Sept 1875

O T'

I sent you a Dissertation by Butcher some days ago, understanding from Cayley that you had agreed to examine the quaternions therein. When examined, forward to Cayley, Garden House, Cambridge.

How did Butcher discover the power of the dot?...

I am writing out Thermoelectricity for my small book on electricity. Have you any new matter? or data for the Diagram.
I have been defining the diagram and its use. If you make the density of electricity zero and it velocity infinity in a current keeping the product what it ought to be, you may call "Thermoelectric Power" "Entropy of Electricity. Also the momentum of the current vanishes as compared with its energy.
But it is much more likely that electricity is very dense and very slow so the less said of Entropy the better.

If the Earl of March were created a May-Duke determine the probability of his becoming a Winter-King and if he were elected Emperor would it be right to address him as Semper Augustus.
Tell this to the Septembrists.

Yours dp/dt

William Thomson's and P G Tait's Treatise on Natural Philosophy (1873) was known as T & T. However, the three friends christened Thomson T and Tait T'. Maxwell became dp/dt since there is an equation in the Treatise on Natural Philosophy which reads
$dp/dt = jcm$
Of course James Clerk Maxwell was jcm ( and therefore became dp/dt).

10. Tait and golf

The Scrapbook contains many pages relating to Tait's interest in golf. His son Freddie Tait went on to be the double winner of the amateur golf championship. The 16th hole on the Old Course at St Andrews is named after him. There is an annual competition for the Freddie Tait Medal. Tait was interested in golf as a game to enjoy, but he also studied it in his role as a physics researcher. Here is an extract from the Scrapbook which describes his experiments:-

The Evening Dispatch: Tait and his golf ball

One of Professor Tait's most original and interesting investigations was carried on with the assistance of the ever ready Lindsay, on the trajectory and velocity of a driven golf ball. The many experiments extended over several months, during which the Professor used to "bunker" himself intentionally and drive the ball against a wall of sand in order to obtain a measure of the force employed. On several occasions there were minor accidents in the underground laboratory, in which these energetic experiments were conducted, and Lindsay was several times heard to say that he wished the Professor could drive more accurately. The activity was at last concluded, however, and the results embodied in a paper which was submitted to the Royal Society of Edinburgh. Amongst other interesting results, Professor Tait stated definitely the longest distance to which a golf ball could possibly be driven. Scientifically the statement was accepted, but, unfortunately for its permanent accuracy, the ever jolly "Freddy" proved his father to be quite in the wrong by driving his ball some five yards farther within a fortnight of the announcement of the "maximum possible drive!".

[Note: Tait didn't take spin into account and this has a significant effect as any golfer knows!]

11. Miscellaneous material from the Scrapbook

Here are a small number of further extracts from the Scrapbook.

Letter from Stokes to Crum Brown 31 July 1880

.... Isabelle must feel herself now half a Scotch girl - I beg pardon; I should have said Scottish; at least Tait instructed me that I might speak of scotching a snake, but I was by no means to apply such a term to the inhabitants of that part of the island that lies north of the Tweed.

Tait was extremely patriotic and spent much time arguing the case for British scientists about Continental scientists. In many ways this was an unfortunate side to his character since it somewhat distorted his views on certain scientific theories. Here is just a small flavour of this aspect of Tait contained in an extract from the Scrapbook:-

Clausius ingeniously endeavours to put me out of court by calling me 'der englische Mathematiker, Tait.' Of course, if I were merely a mathematician, and had never made physical investigations, I should have no title to write on such matters at all.
Still, I have preferred to retain the discussion of these so-called claim, inasmuch as I may thus be spared the necessity for farther discussion of a subject on which my opponents will at least not allow that they are and have been hopelessly in error. More probably, however, as they have failed to see that Mayer's real claims do not depend upon his first, but upon his latter papers, they will now shift their ground; and finding Mohr a better card to play than Mayer, insist upon his having all the credit which I have shown to be due to Colding and Joule.

To call a Scotsman "English" is, of course, one of the greatest insults possible!

Finally let us record that the Scrapbook contains an invitation to Tait to attend the degree ceremony where he is to be awarded an honorary degree by the University of Edinbirgh. The University of Edinburgh conferred "the honorary degree of Doctor of Laws on Professor P. G. Tait M.A. D.Sc. on Saturday 27 July 1901."

Written by J J O'Connor and E F Robertson
Last Update April 2006