36 



NATURE 



[July 13, 191 1 



Hamilton was a willing and voluminous correspon- 

 dent, and his letters (the first was forty-five pages long, 

 divided into thirty-two paragraphs), here printed, so far 

 as they are quoted, with all the italics, small capitals, 

 &c, which he used, even in his books, to mark different 

 degrees of emphasis, abound in acute and suggestive 

 remarks, which were no doubt due to the inspiration of 

 the moment. The humour which he displays here 

 and there, as in his "mortal leap from Chaucer to 

 Moigno," and his description of the Abbe, is of a 

 truly Irish flavour, and has the merit of unexpected- 

 ness. 



The absence of quaternions from Thomson and 

 Tait's " Natural Philosophy " has been the subject of 

 some remark. It is now well known that the senior 

 author could not be convinced that the quaternion 

 calculus, or indeed any form of vector analysis, was 

 of advantage in physical work. To this conservative 

 view he adhered to the end of his life, and in a 

 private letter of his later years, written, as he de- 

 scribed it, politely and mildly as to a stranger, he 

 states his adverse opinion with remarkable vigour. 

 And there is the letter to Chrystal, quoted by Dr. 

 Knott on p. 185, on the thirty-eight year war over 

 quaternions. 



It is somewhat remarkable that vectors should have 

 led to so much correspondence of an animated sort. 

 The respective merits of quaternions and the systems 

 of Grassmann and others seem not merely to have 

 kindled the intellects, but to have stirred the emotions 

 of the various advocates to a surprising extent. The 

 playful paraphrase by a physicist of the famous say- 

 ing of Tertullian into " Behold, how these vector- 

 analysts love one another ! " suggests with a 

 touch of irony that after all the differences 

 may not be so fundamental as they appear, 

 that perhaps each sees the truth, and may 

 safely be left to fight its battle in his own 

 way. Let each go on using the armour and 

 weapons he has proved; no man can tell to whom 

 the victory may be; perhaps after all to someone 

 whose equipment seems lamentably inadequate. But 

 nobody can help admiring the steadfast fidelity of Tait 

 to the notation of the master, and his chivalrous 

 defence of quaternions against all comers. He 

 had a right to speak with authority: no man with 

 the exception of Hamilton himself did more for quater- 

 nions or with them. And if the linear vector function 

 ever yields its whole secret to the student of vector 

 analysis, it will be because Tait has made the dis- 

 closure possible. Often light suddenly comes to a 

 man who has turned a subject over in his mind for 

 weeks or months or years. It is surely also possible 

 that one explorer may enter into the labours of 

 another, and quickly behold the promised land which 

 the instinct and faith of the first pioneers told them 

 lay beyond the mountains. 



Cambridge had no more systematic student than 

 Tait, and no university had a more faithful and duty- 

 doing professor. The work to hand, the daily task, 

 the common round of teaching, it was his joy to per- 

 form. In the opinion of some it is waste to keep 

 such a man lecturing to elementary students ; but Tait 

 inspired his students, and that was surely a very great 

 NO. 2176, VOL. 87] 



thing. As a lecturer on experimental physics he was 

 well-nigh unapproachable ; and he was well aided by 

 his mechanical assistants, who understood his methods 

 and knew that he could be depended on to take 

 everything in the carefully thought-out and pre- 

 arranged order. Without such order and close ad- 

 herence to it, no man, however eminent, however 

 great his genius even, can teach a university class 

 effectively. 



In his introductory and other occasional addresses, 

 Tait often dealt with more or less controversial sub- 

 jects. The tract which he wrote on "Thermo- 

 dynamics " contains a sketch of the theory of energy, 

 in which questions of priority of complete logical 

 proof, for example, Joule's establishment of the 

 equivalence of heat and work, are discussed with 

 great force and cogency of argument, albeit with 

 a dash of patriotism. Such things he also discussed 

 in his popular lectures and lighter papers. His book 

 on "Recent Advances in Physical Science," was a 

 course of such lectures, taken down by a shorthand 

 writer, and carefully revised. Its title is out of date 

 now, but as a clear statement of the true foundations 

 of the science of heat, and of the work done by Joule, 

 Kelvin, Balfour Stewart, and others in that field, it 

 cannot be excelled. 



In thermodynamics he insisted always on the im- 

 portance of Kelvin's idea of absolute temperature. 

 Kelvin was undoubtedly behind Clausius in accepting 

 the consequences of the equivalence of heat and work ; 

 but when his first scruples had been overcome, and 

 Carnot's function had disappeared in the idea of abso- 

 lute temperature, the scheme of relations of heat and 

 work stood forth in a logical clearness, which no other 

 mode of treatment has ever approached. The im- 

 perfectly specified thing called a "perfect gas," by 

 means of which temperature is defined in many con- 

 tinental treatises, he cordially disliked, and he lost 

 no opportunity of denouncing the treatment founded 

 upon it. In the cause of accuracy Tait was zealous 

 almost to slaying. No one who heard his lecture on 

 " Force," to the British Association at Glasgow in 

 1876, will ever forget his dramatic denunciation of 

 slipshod popular science and its professors. 



Tait's association with Kelvin in the composition of 

 the "Natural Philosophy" has been referred to. Not 

 the least interesting chapter in Dr. Knott's book is 

 the account of this collaboration. The two men had 

 much in common, they were both pupils of Hopkins, 

 their great mathematical power and sure physical 

 instinct well fitted them to work together, but in 

 other respects the combination was not so successful. 

 Tail was orderly and methodical — that can be seen in 

 his neat penmanship and clear and precise composi- 

 tion, which was fit, with scarcely an erasure or sub- 

 stituted word, to be sent to the printer. On the other 

 hand, the perusal of matter in clear print on a proof- 

 sheet, showed Kelvin so many opportunities of exten- 

 sion and amendment, that he immediately overflowed 

 in new sections on the margins, to the dismay of the 

 printers, and the augmentation of the bill of costs. 

 Then Kelvin had so many irons in the fire ; his 

 thoughts were being carried away continually from 

 the " Natural Philosophy," and that, of course, stood 



