232 PETER GUTHRIE TAIT 



redundant. Among the parts which are particularly characteristic of Tail's 

 methods the following may be mentioned : discussion of Fourier's series, of 

 strains, of Attractions and Potential, of Action (under which is included the 

 flow of electricity in a surface), of the strength of tubes under internal and 

 external pressures, of the bending and vibration of rods, of vortex motion, 

 and of surface waves on fluids. Perhaps the practical nature of the book is 

 best indicated by the way in which Lagrange's generalised coordinates are 

 introduced. Having established in ordinary Cartesian symbolism Hamilton's 

 principle of Varying Action, Tait then uses this principle to deduce the usual 

 Lagrangian equations of motion. The demonstration is not general or 

 exhaustive, but it is sufficient for the kind of problems which most naturally 

 present themselves to a student beginning the study of higher dynamics. 



Tail's demonstrations, whether geometrical or analytical, are characterised 

 by neatness and elegance. He used to say that he could always improve 

 a demonstration given by some one else. When reading a newly published 

 paper he was able very rapidly to come to an opinion as to its originality 

 and accuracy. Thus, as already noticed (p. 1 1 3), he was very critical 

 of certain of the mathematical processes used in investigations regarding 

 the kinetic theory of gases. If a theorem could not be proved without a 

 prodigious array of symbols covering pages, he had a feeling that the theorem 

 was not worth the proving. His attitude of mind towards much of mathe- 

 matical literature is well brought out in the answer he gave to one of his sons 

 about the year 1878. He was turning over the pages of a mathematical 

 journal which had just come by post. When asked if he was going to read the 

 journal right through, he remarked : "Certainly not. I am not such a flat as 

 to read other people's mathematics. I look to see what result the beggar 

 brings out, and then if he's right I can usually find a shorter cut." 



About 1892 Tait formed the project of printing a small pamphlet of 

 concise paragraphs to take the place of lecture notes for his students, who 

 would thus be able to pay undivided attention to the explanations and 

 amplifications given in the lectures. Some twenty or thirty pages were put 

 in type, but pressure of other work, more particularly the editing of the 

 reprint of Scientific Papers, prevented the project being carried to completion. 

 When reminded by the publishers that these pages had been lying in type for 

 nearly six years Tait felt that he was not able to carry out fully the original 

 intention, and compromised the matter by confining these notes to a highly 

 condensed discussion of Newton's Laws of Motion, in other words, the 



