# Popular Science Monthly/Volume 61/June 1902/Peter Guthrie Tait

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* PETER GUTHRIE TAIT.
BY C. K. EDMUNDS,
JOHNS HOPKINS UNIVERSITY.
NEXT to Lord Kelvin, perhaps the most notable figure among the physicists of Great Britain during the past forty years has been Peter Guthrie Tait, professor of natural philosophy in the University of Edinburgh since 1860. One of the first to establish laboratory instruction in Great Britain, and beginning his career at a time when the now prevalent ideas of energy were yet unborn, he has had much to do with the shaping of scientific thought and education during the latter half of the nineteenth century.
He was born at Dalkeith (a town of several thousand inhabitants, about six miles southeast of Edinburgh) in 1831. His early education was obtained at the Dalkeith Grammar School and at the Circus Place School in Edinburgh. Tait was a distinguished pupil, and those of his schoolfellows who are still alive speak of him with so much love and respect that he must have been a leader among them. Clerk Maxwell was his most intimate school and college friend, and the friendship thus begun continued till Maxwell's death, undisturbed by the fact that they were rivals for the Edinburgh chair in 1860. 'Both were men of playful disposition and of absolute frankness and sincerity.'
Tait studied at Edinburgh University for one session under Kelland and Forbes, and the promise he then gave was amply fulfilled at St. Peter's College, Cambridge, where he became senior wrangler and first Smith's Prizeman in 1852, being just twenty-one years of age. His private tutor was William Hopkins, to whose tuition Tait attributed much of his mathematical skill. Tait seems to have joined heartily in all phases of undergraduate life at Peterhouse. He was a keen golfer, and for forty years he spent an annual holiday on the links at St. Andrew's. It is said that his son's progress to the championship in golf was dearer to him than his own scientific fame. And some declare that the untimely death of his son, an officer in the Black Watch in the South African War, hastened his father's last illness, to which he succumbed on July 4, 1901, at seventy years of age.
In 1854 Tait was appointed professor of mathematics in Queen's College, Belfast, and became acquainted with Andrews, the chemist, and Rowan Hamilton, the mathematician. Andrews stimulated his love for physical research and helped him to gain the power of apprehending the facts and of plainly formulating the theories of natural ​philosophy. Through the works and the personal influence of Hamilton he was led to the study of quaternions, to which he gave much attention.
In 1860 he was elected to the chair of natural philosophy in Edinburgh, resigning it in February, 1901, on account of a lingering illness, which resulted in his death four months later. It is estimated that about ten thousand students passed through his class-room during those forty years, and few could do so without carrying away some impress from this notable teacher. Among the first of his 'researchers' were a remarkable trio—Robert Louis Stevenson, Wm. Robertson Smith, the distinguished Scottish Biblical scholar and orientalist, and Sir John Murray, the well-known publisher. Great must have been the attraction of Tait's personality to bring together three men so highly distinguished, yet so utterly different.
About the time of his appointment to the Edinburgh chair, Tait became acquainted personally with Lord Kelvin, who, though also a Peterhouse man, had left Cambridge before Tait came up, "and was already independently and in conjunction with Joule, and concurrently with Rankine and Clausius, writing his classical memoirs on the theory of energy. The first edition of Tait and Steele's 'Dynamics of a Particle' published in 1856, does not contain either of the words work or energy. In its original form it was founded on Pratt's 'Mechanical Philosophy' and written on the old-fashioned Cambridge lines, which knew not of Lagrange and Hamilton. Six years later it is on record that in his introductory lecture Tait handled the notions of the energetic school with freedom and laid down the foundations of a thoroughly modern course in physics. Probably, therefore, he had come under the influence of Joule and Kelvin before he met the latter personally." The conjunction with Kelvin produced the famous treatise on 'Natural Philosophy' by Thomson and Tait in 1867, which began a new era in mathematical physics. Dozens of men nourished by the strong meat of its pages have written treatises in continuation of the lines there laid down.
Tait's contributions to text-book literature include, besides the two works just mentioned, 'Elements of Quaternions' 1867; 'Introduction to Quaternions' by Kelland and Tait, 1868; 'Recent Advances in Physical Science' 1876; 'Thermodynamics' 1868; 'Light' 'Heat' 1884; 'Properties of Matter' 1885 (revised to 1899), and 'Dynamics' 1895.
Although Tait rarely spoke on religious topics, and in general avoided theological controversy, his friends were aware that he held decided views on such matters. He was the joint author with Balfour Stewart of the 'Unseen Universe' (first printed privately in 1875), a book showing, to use Tait's own words, how baseless is the common belief that science is incompatible with religion. "It calls attention ​to the simple fact, ignored by too many professed instructors of the public, that human science has its limits, and that there are realities with which it is altogether incompetent to deal."
Tait's collected scientific memoirs have been published by the Pitt Press, and embrace between one hundred and two hundred papers relating to a great variety of subjects. It would be out of place in this paper to attempt any detailed examination of these articles. A rapid sketch of the contents of the two volumes already published will however be given.
A large proportion of each volume is given up to quaternion investigations, a subject and method in which Tait remains almost the sole authority. Lord Kelvin has given the following reminiscence of the collaboration in 'Natural Philosophy': "We had a thirty-eight years' war over quaternions. He (Tait) 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 introduced." In a note in his second volume Tait states that Klein's account of quaternions rests on a misapprehension; and remembering that, though 'the grandest characteristic of quaternions is their transparent intelligibility,' men like Cayley and Klein have gone astray, we may be excused from any attempted discussion of them here. Other abstruse papers are those on 'Amphicherial Knots,' and 'Knottedness.' Many addresses and notes of a less technical nature serve, as Lord Rayleigh has remarked concerning his own, 'to relieve the general severity.' Here and there a biographical notice as of Listing, Kirchhoff, Sir Wm. E. Hamilton and Rankine, or the reprint of an encyclopedian article, as on 'Mirage,' 'Force,' etc., gives interest to the miscellany. Tait was a party—and an active party—to many polemical discussions, but very properly all traces of these keen controversies are omitted in his collected papers.
We have yet to notice the best of his researches. The most noteworthy theoretical discussions are those on the kinetic theory of gases (five papers, Trans. Edin. Roy. Soc, 1886-92), on impact (three papers, 1888-92), and on the path of a rotating spherical projectile. These latter were due to his interest in golf, and on this subject he wrote a series of popular articles, which it is said were widely read and appreciated.
His most important theoretical paper is the review of the kinetic theory of gases, in which he analyzed into their logically simplest elements, the first principles of a difficult subject. He gave several new ​view-points from which to examine the foundations of the theory. There are three advances in the details of the theory with which his name is generally mentioned, as follows: (1) He showed that the analogy between the coefficient of diffusion for gases and the conductivity for the propagation of heat can not be pushed to the conclusion that since the conductivity is a constant magnitude, the coefficient of diffusion is a constant also, for experiments with the same pair of gases. Tait showed that this expectation is not justified by the formula in terms of which the coefficient is deduced, showing in fact that it depends at any instant not only on the temperature and on the pressure of the mixture, but also on the ratio in which the two gases have mixed with each other by that time. (2) He showed that in applying Maxwell's law of the distribution of velocities (a law deduced for a gas without total progressive or rotational motion) to the case of a gas the body of which is in rotation, the interval of time within which the mechanical theorems (deduced for the static conditions) remain valid with sufficient exactness for a single layer (the whole body of gas being considered as divided into layers between which the interchange of energy is slow) may be long enough to allow the very rapidly resulting arrangment in the distribution of velocities according to Maxwell's law to occur. In each of these layers, then, Maxwell's law holds good for the distribution of velocities on the condition that the velocity in which a particle shares by the flow or rotation of its layer is to be subtracted from the value which it would have in the state of rest and equilibrium of the gas as a whole. (3) The calculation of the coefficient of viscosity on the assumption of Maxwell's law of distribution of velocities.
In reading Tait's papers on the kinetic theory of gases it is interesting to note the author's frank confession: "I have abstained from reading the details of any investigation (be its author who he may) which seemed to me to be unnecessarily complex. Such a course has, inevitably, certain disadvantages, but its manifest advantages far outweigh them!"
Tait's chief experimental research was that on the compressibility of water, undertaken in connection with an investigation of the errors of the deep-sea thermometers used on the famous voyage of the Challenger. It is an interesting record of a laborious investigation undertaken to decide a very important practical question.
Several earlier investigators had studied the compressibility of liquids, always chiefly of water. Only the chief among them need be mentioned here. Canton, a hundred and twenty-six years before, had not only exhibited the compressibility of water, but had shown that it decreases as the temperature is raised; and Perkins in 1826 showed very clearly that in water at 10° C. the compressibility diminishes as the pressure increases, quickly at first, afterwards more and more slowly; ​but Perkins' estimates of pressure are inaccurate, and no numerical data of any value can be obtained from his results. Regnault in 1847 attempted to take into account the compressibility of the piezometer by applying pressure alternately to the outside and the inside of the piezometer, and then simultaneously to both. But this method gives the elastic constants of the piezometer only when dealing with an absolutely incompressible liquid. Amaury and Deschamps measured the change in external volume of the piezometer, but Tait points out that unless the bulbs are truly spherical or cylindrical, of uniform thickness and homogeneous material, errors due to application of pressure on the outside or inside alone may be introduced of the same order as the quantity to be measured. A very complete series of measurements had been made for water from 0°—100 °C. by the two Italian experimenters, Pagialini and Vincentini, but only for low pressures. Moreover, though they made careful determinations of the change in the glass due to changes of temperature, they failed to eliminate the effect of pressure on the piezometers, applying pressure to the inside only, and so their results are some forty per cent, too great. Lastly, Amagat made very extensive experiments up to 3,000 atmospheres, but he considered the compressibility of the glass to be of small effect and consequently left it out of account, and the first really satisfactory work on this important subject was that accomplished by Tait and his assistants, the full report of which appears in the 'Challenger Reports.'
The great merit of Tait's work was the careful determination of the pressures used, and the preliminary researches on the compressibility of mercury and of glass, so as to apply the proper corrections to his thermometers and piezometers, together with the fact that his investigations extended to sea-water and to solutions of salt of various strengths. A brief summary of his most important results follows:
As an approximation for the compressibility of fresh water through the whole range of the experiments (pressure from 150 to 450 atmospheres and temperatures from 0° to 15°C), he secured the formula:
${\tfrac {0.00186}{36+p}}\left(1-{\tfrac {3t}{400}}+{\tfrac {t^{2}}{10,000}}\right)$
The point of minimum compressibility of fresh water is about 60°C. at atmospheric pressure, but is lowered by increase of pressure.
The average compressibility of sea-water is about .92 of that of fresh water, with a minimum compressibility at about 56°C, lowered by increase of pressure.
${\tfrac {0.00186}{36+p+s}}$
Six miles of sea water, at 10°C. throughout, are reduced in depth 620 feet by compression. Hence the pressure at a depth of six miles is nearly 1,000 atmospheres.
The maximum density-point of water is lowered about 3°C. by 150 atmospheres of additional pressure.
As to the proper correction to apply to the Challenger thermometers, Tait showed that that previously given by Davis, viz.: .5°F. per ton per square inch, was greatly too large, and that of five sources of error which entered into the test experiments, only one held for the circumstances under which the Challenger thermometers were actually used, that the other four were proper for the experiments in the laboratory, but not for sea-soundings. The only cause of error active in the case of sea-soundings was the direct effect of pressure on the glass and mercury of the thermometer, and the correction due to this was but 0°.14 C. for every mile of depth.
Next to his work on the compressibility of water and the allied investigations, come Tait's experiments in thermo-electricity. He made two contributions in this field.
1. Having supposed that the Thomson effect (the absorption or liberation of heat-energy in a conductor whose temperature varies from point to point when traversed by a current of electricity, the effect being reversible, in any given conductor, with the direction of the current) might, like thermal and electrical resistance, be directly proportional to the absolute temperature, he verified his assumption by experiment, finding that the curves for the e. m. f. in terms of absolute temperature for junctions of any two of iron, cadmium, zinc, copper, silver, gold, lead and some others are parabolas with their axes vertical, if the e. m. f. be taken as ordinates, the apex corresponding to the neutral point, or point of reversal. This amounts to showing that the curve representing the thermo-electric power of any couple in terms of the mean temperature of its junctions is a straight line. We need only draw the diagrams of the thermo-electric powers of all the metals taken separately with one of their number in order to learn the values of the thermo-electric powers of all the metals taken in pairs in any combination. Lead was adopted as the metal of comparison, because as Le Eoux had shown, its specific heat of electricity is zero.
By the 'specific-heat of electricity' is meant the amount of heatenergy developed in the given conductor, according to the Thomson ​effect, between two points whose difference in temperature is 1°C, when a unit quantity of electricity passes between them. And Tait's work amounted to showing experimentally that the 'specific heat of electricity' as defined by Kelvin, was for any given substance directly proportional to the absolute temperature. This is sometimes spoken of as Tait's Law.
From these experimental results Tait suggested the well-known form of the thermo-electric diagrams, the rough preliminary suggestions for which Lord Kelvin had already given. Under Tait's development the diagrams exhibit not merely the relative thermo-electric positions of the metals at various temperatures, with their neutral points, but also the specific heat of electricity in each metal in terms of temperature, the amount of the Peltier effect, and the e. m. f. (and its direction) for a circuit of any two metals with given temperatures of the junctions.
2. Tait also discovered a multiplicity of neutral points for thermo-electric couples of certain substances, such as circuits of iron coupled with various alloys of platinum with iridium, nickel and copper. In each of these cases there are at least two neutral points below the temperature of white heat, and others at still higher temperatures.
Professor Chrystal gives the following vivid picture of Tait:
* ↑ Vol. II., 'Physics and Chemistry,' London, 1889.
* ↑ The 'thermo-electric power' of a couple for a given temperature is the e. m. f. between its junctions when they are kept respectively $^1$⁄$_2$° above and $^1$⁄$_2$° below that temperature.
* ↑ For a discussion of these diagrams see J. J. Thomson's Elec. and Mag., pp. 499-505.
* ↑ Nature, July 25, 1901.