VI PREFACE. 



derive most of their interest from their bearing on kinetic theories 

 of matter, which seem to lie outside the province of a treatise like 

 the present. 



I have ventured, in one important particular, to make a serious 

 innovation in the established notation of the subject, by reversing 

 the sign of the velocity -potential. This step has been taken not 

 without hesitation, and was only finally decided upon when I found 

 that it had the countenance of friends whose judgment I could 

 trust; but the physical interpretation of the function, and the 

 far-reaching analogy with the magnetic potential, are both so much 

 improved by the change that its adoption appeared to be, sooner 

 or later, inevitable. 



I have endeavoured, throughout the book, to attribute to their 

 proper authors the more important steps in the development of 

 the subject. That this is not always an easy matter is shewn by 

 the fact that it has occasionally been found necessary to modify 

 references given in the former treatise, and generally accepted as 

 correct. I trust, therefore, that any errors of ascription which 

 remain will be viewed with indulgence. It may be well, 

 moreover, to warn the reader, once for all, that I have allowed 

 myself a free hand in dealing with the materials at my disposal, 

 and that the reference in the footnote must not always be taken 

 to imply that the method of the original author has been 

 closely followed in the text. I will confess, indeed, that my 

 ambition has been not merely to produce a text-book giving a 

 faithful record of the present state of the science, with its 

 achievements and its imperfections, but, if possible, to carry it a 

 step further here and there, and at all events by the due coordina- 

 tion of results already obtained to lighten in some degree the 

 labours of future investigators. I shall be glad if I have at least 

 succeeded in conveying to my readers some of the fascination 

 which the subject has exerted on so long a line of distinguished 

 writers. 



In the present subject, perhaps more than in any other depart- 

 ment of mathematical physics, there is room for Poinsot's warning 



