NA TURE 



[June 27, 1907 



now involves terms linear in the velocity-components 

 as well as quadratic terms. The procedure of 

 Lagrang-e, evolved originally from the side of the 

 Principle of Action, constituted the science of general 

 dynamics by eliminating from the problem all variables 

 the values of which are prescribed in terms of the re- 

 maining ones by relations of permanent constraint, 

 thus reducing the dynamical analysis to ihe discussion 

 of just as many quantities as are required to specify 

 the state of the system. It gives cause for some sur- 

 prise that nearly a century elapsed before the correlative 

 step was taken, namely, the elimination from the ana- 

 lytical specification ot the system of permanently steady 

 or cyclic motions, as well as the permanent geometrical 

 constraints above mentioned. In the hands of the 

 analysts who treated the subject meanwhile, the re- 

 quirements of the actual planetary and lunar theories 

 were perhaps the main aim; it is only recently, and 

 largely in the hands of the English school, notably 

 Lord Kelvin and Clerk Ma.Kwell, in later conjunction 

 with Helmhohz, and building largely on the earlier 

 work of W. Rowan Hamilton, that the subject of 

 general dynamics has been welded into an instrument 

 for the inductive, and in many cases speculative, ex- 

 ploration of physical processes in general. Anyhow, it 

 will be evident how fundamental an advance in the 

 principles of the dynamical interpretation of nature 

 was involved in Routh's formulation of what he called 

 the "modified Lagrangian function." 



The problem thus solved by Routh with remarkable 

 simplicity had already been some time in evidence. 

 In the first edition of Thomson and Tait's " Natural 

 Philosophy " in 1868, the equations of Lagrange had 

 been applied in most eflectivc manner to problems of 

 motions of solids in fluid media, the energy function 

 involved being determined in terms of the motions of 

 the solids alone, and the fluid thus being ignored, in 

 the subsequent work. This procedure was soon chal- 

 lenged by Kirchhoff, as going beyond the existing con- 

 ditions of validity of general dynamical theory; and a 

 special justification for the case of motion in fluids was 

 given by him on the basis of a Least Action analysis. 

 Soon afterwards the same difficulty was pressed on 

 Lord Kelvin independently bv J. Purser, who also 

 published a justification on more physical lines. This 

 was, not unlikely, the origin of Lord Kelvin's general 

 theory of " ignoration of coordinates," first published 

 in 1879 in the second edition of Thomson and Tait's 

 work, but which probably existed in manuscript an- 

 terior to Routh's essay. .\ report was once current 

 that most of it was worked out in the harbour of 

 Cherbourg, while his yacht was refitting, and the car- 

 penters were all the time hammering overhead. This 

 form of the theory, though more expressly suggested 

 by the needs of physical dynamics, was less complete 

 in one respect than Routh's, in that it did not bring 

 the matter into direct relation with a single character- 

 istic function (Lagrangian function of Routh, kinetic 

 potential of Ilelmholtz). but simply obtained and il- 

 lustrated the equations of motion that arose from the 

 elimination of the cyclic coordinates that could be thus 

 ignored. 



Later still. Helmholtz, in his studies on monocyclic 

 and polycyclic kinetic systems, which began in 1884 

 and culminated in the important memoir on the phy- 

 sical meaning of the Principle of Least .\ction in vol. c. 

 (1S86) of CrcUc's Journal, developed the same theory 

 more in Routh's rlianner, and built round it an exten- 

 sive discussion of physical phenomena, so that on the 

 Continent the whole subject is usually coupled with 

 his name. Shortly before, the work 'of Routh and 

 Kelvin had already been coordinated with the Prin- 

 ciple of Action by more than one writer in England. 



The most elaborate published result of Dr. Routh's 

 scientific activity was the " Treatise on the Dynamics 



NO. 1965, VOL. 7 61 



of a System of Rigid Bodies," which began as a 

 thorough, though rather diflicult, handbook in one 

 octavo vohune, but expanded in successive editions in 

 a manner of which other classical instances readily 

 occur to mind, until it became a sort of cyclopedia of 

 the dynamical section of theoretical physics. In the 

 course of an inquiry some ten years ago as to the 

 reason whv English mathematical physicists had so 

 much practical command over the application of their 

 knowledge, the mode of teaching in Cambridge came 

 under review; and in particular this book was dis- 

 covered by Prof. F. Klein, of Gottingen, who made 

 arrangements for its introduction to the Continental 

 public in a German translation, containing some brief 

 valuable annotations such as the wide analytical out- 

 look at Gottingen suggested. Especially was em- 

 phasis given to the great extension of the scope 1 ' 

 abstract dynamics above described, with which Routh 

 name was associated, it is to be hoped permancntl} 

 Somehow the book does not seem to have attracted 

 even yet much sustained attention in France. 



Until lately. Dr. Routh's presence was a faniiliai 

 and welcome one to residents in Cambridge. Though 

 he never sought public positions, his services were in 

 requisition in many ways, as Senator and Fellow of 

 the University of London, as member of the Univer- 

 sity Council at C.unbridge, member of council of Ihi 

 Royal Society, and in other activities; while he de- 

 clined more prominent offices more than once. In 

 society he was bright and attractive though somewhat 

 retiring, simple, and entirely free from any suggestion 

 of superiority. The respect and affection which It 

 inspired in a long succession of disting-uished pupil 

 found expression on the occasion of his partial with- 

 drawal from work in 1888, when at a remarkable 

 gathering of judges, engineers, and men of science, 

 his portrait by Herkomer was presented to Mrs. Routh, 

 with many expressions of warm appreciation. Hi- 

 leisure he employed mainly in mathematical research, 

 and in the preparation of a series of treatises on sub- 

 jects of mathematical physics, of which the only criti- 

 cism to be made is that his wealth of valuable mate- 

 rial tended to convert them into cyclopedias rather 

 than text-books. His last public action was 

 to take the lead in opposition to the proposals for 

 change in the system of the mathemiitical tripos at 

 Cambridge. It is possible that he did not fully 

 reali.se the altered circumstances of the time, and the 

 insistent claims of other studies ; anyhow, it will be 

 matter for congratulation if the new arrangement- 

 work as I'-ell ."ad as smoothly as did the older mathe- 

 matical tripos during the long period when the prac- 

 tical direction was mainlv in his hands. 



J. L. 



PROF. A. S. HERSCHEL. F.R.S. 

 'T'HE death of Prof. Alexander Stewart Herschel, 

 -'■ F.R.S. . on June i8 will be deplored by many 

 astronomers. Prof. Herschel was born in 1836, and 

 was the second son of Sir John Herschel. He was 

 appointed professor of physics at the Durham College 

 of Science, Newcastle-on-Tyne, in 187 1, and was 

 honorary professor and governor of the college at the 

 time of his death, though he left Newcastle about 

 twenty years ago, and resided with his brother. Col. 

 John Herschel, F.R.S., at Observatory House, 

 Slough, which was the home of his renowned 

 grandfather. Sir William Herschel, and of his father. 

 Prof. Herschel was elected a Fellow of the Royal 

 .Astronomical Society in 1867, and of the Royal 

 .Society in 1884. 



Inheriting an illustrious name. Prof. Herschel 

 also inherited the love for astronomy, the 

 indomitable perseverance and capacity for work. 



