HELMHOLTZ'S APPRECIATION 169 



the main results, and indicating various lines of investigation and gaps to 

 be filled in by subsequent research. The last connected set of notes on 

 the linear vector function began to appear in May 1896, six years after 

 the publication of the third edition of the Treatise, and continued till 

 May 1899 (Set. Pap. Vol. u, pp. 406, 410, 413, 424). During his last 

 illness Tait spoke several times of the importance of the linear vector 

 function, regarding which he felt that some great advance was still to be 

 made. On July 2, 1901, two days before his death, he was able to put 

 some jottings on a sheet of paper, which he handed to his son asking 

 him to place it in a safe place as it contained the germ of an important 

 development. These notes were published in facsimile by the Royal 

 Society together with a commentary in which I indicate their relation to 

 previous papers. 



The general aim of these later papers is to classify and analyse strains 

 with special reference to related pure strains, those, namely, which are 

 unaccompanied with rotation. One of the most interesting of the results 

 is the theorem that any strain in which there are three directions unaltered 

 can be decomposed into two pure strains ; and, conversely, two pure strains 

 successively applied are equivalent to a strain in which there are three 

 directions unchanged but not in general at right angles to one another. 



It is more particularly in reference to the development of the properties 

 of V that the second and third editions of the Treatise show marked advance 

 upon the first. As regards the extent and variety of the physical applications 

 the second edition is indeed an entirely different book. This was the 

 edition which was translated into German by Dr G. v. Scherff (Leipzig, 

 Teubner, 1880) and into French by Gustave Plarr (Paris, Gauthier- 

 Villars, 1884). 



There was a suggestion as early as 1871 to prepare a German 

 translation to be published by Vieweg. But the project was not carried 

 out. Helmholtz, in a letter to Vieweg of date November 19, 1871, spoke 

 of Tait's Quaternions in these words : 



" As regards Tait's Quaternions, it is indeed an ingenious and interesting 

 mathematical book. But it uses a method of mathematical research which, so far 

 as I know, has hardly been taken up in Germany. When perhaps some enthusiast 

 (Liebhaber) working his way into it, will undertake the translation, the book will, 

 I feel almost certain, find a great sale. It is keen and penetrating, full of new ideas 

 and conceptions, and one can speak of its scientific value only with the highest 

 recognition. But it lies somewhat removed from the usual paths of mathematical 



T. 22 



