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