236 PETER GUTHRIE TAIT 



I. Some people say this is d'Alembert : 



Let m at x, y, z, be a particle the applied forces being X, Y, Z t and the internal 

 forces f, 17, 



Then mx=X + ^, &c., 



whence 2(w^) = S^", &c., 



f &c. going out. And the same sort of thing when factors &e, &c. are used. 



II. Others say this is d'Alembert : 



Let the notation be as before. Then the statical conditions are 



2(^r+f) = o, &c. 



whence, introducing the reversed effective forces, you get for the kinetical conditions 



2(X-mx + Z) = o, &c. 



And the same sort of thing with any permissible displacements as factors. I is merely 

 Lex III direct. II is amply met by Newton's second interpretation of Lex III, where 

 he points out the Reactiones, "ex acceleratione oriundis," as forces to be taken into 

 account. 



Which is your view of d'Alembert ? 



But there is a point in my paper which may interest you, where I show that the 

 hitherto puzzling Least Action merely expresses the inertia condition, so far as the 

 component motion parallel to an equipotential surface is concerned ...... 



In the winter of 1874, a few months after the delivery by Tyndall of his 

 famous presidential address before the British Association at Belfast, it began 

 to be whispered among the students of Edinburgh University that Tait was 

 engaged on a book which was to overthrow materialism by a purely scientific 

 argument. When, in the succeeding spring, The Unseen Universe* appeared 

 it was at once accepted as the fulfilment of this rumour. The title page 

 of the book contained the words, "THE UNSEEN UNIVERSE, or Physical 

 Speculations on a Future State. The things which are seen are 

 temporal, but the things which are not seen are eternal. London, Macmillan 

 and Co. 1875"; and at the top was a trefoil knot, the symbol of the 

 Vortex Atom imagined by Thomson and discussed at considerable length 

 by the authors of the book. In spite of its anonymous publication it 

 seemed to be known from the beginning that the work was written by 

 Balfour Stewart and P. G. Tait. Anyone at all familiar with Tail's scientific 

 style and with his views of the historic development of the modern theory of 

 energy could not fail to see that his hand must have been mainly responsible 



1 Tait greatly enjoyed Gustav Wiedemann's punning criticism that the book should be 

 called the "Unsinn Univers." 



