\v 5. 1892I 



NA TURE 



calculus. The fact is, that nearly all the problems of 

 the numerical calculation of perturbations which were 

 urgent at the beginning of the century, in order to bind 

 the solar system to the scheme of universal gravitation, 

 have now been satisfactorily disposed of There is no 

 longer the same need for the greatest intellectual power to 

 set itself to put right some periodic or secular inequality, 

 which requires all the battery of analysis that is available, j 

 and often more. New ground has been broken since | 

 tlien, and there is the great array of the physical sciences, j 

 all struggling to become purely dynamical, but all ' 

 hampered in this by the fact that the dynamical machinery, 

 the phenomena of matter and motion, on which they J 

 depend, are to a great extent concealed from direct obser- 

 vation or exploration. 'Under such circumstances the 

 method of progress is to carefully cherish, and reduce 

 into a scheme such as will appeal directly to the under- 

 standing, all the general principles which have become 

 evolved in the course of dynamical investigations relat- 

 ing to problems of which the data are thoroughly known; 

 and to use them as a key for the dynamical interpreta- 

 tion of more recondite phenomena by the aid of analogies 

 and the numerical verification of their results. The mode 

 of progress has thus veered from the analytical to the 

 synthetical, from the powerful inverse analysis of 

 Laplace and Lagrange to methods more akin to those 

 which were worked by Newton. 



It may be stated as a general rule that the relations 

 most directly intelligible and most flexible in this kind of 

 application are properties of constancy, or of maximum 

 and minimum, such as belong in fact to the more obvious 

 features of the continuous growth of pure quantity. The 

 conservation of energy, of linear momentum, of angular 

 momentum, the minimum energy criterion of equilibrium, 

 of steady motion, the maximum and minimum energy 

 criteria which determine the motion following the appli- 

 cation of impulses specified either by their actual amounts 

 or by the velocities they produce at their points of appli- 

 cation—these may all be cited in illustration. The crown 

 of the edifice will be Maupertuis's principle of Least 

 Action, whose range of exact application, initiated for 

 dynamics by Lagrange and Hamilton, is now being ex- 

 tended into all departments of physics, thus working out 

 an answer to the question — To what extent can the suc- 

 cession of phenomena in inanimate Nature from instant 

 to instant be treated as governed by a principle analogous 

 to that of minimum expenditure of effort in the sentient 

 world ? 



The phrase from instant to instant is essential, for a 

 path may— as, for example, a great circle on a sphere — be 

 the shortest between two points within a given range of 

 each other, but may cease to have that property when the 

 starting point and the final point are taken too far apart 

 on it. In a similar way, in statics, a certain region of 

 stability is determined around each position of equi- ! 

 librium, such that, if the system is not disturbed beyond j 

 that region, it will not leave the neighbourhood ; while, in 

 dynamics of a particle, such a region is more vaguely 

 determined around each orbit by the nature of the 

 enveloping curves or surfaces of the neighbouring orbits. 

 From the point of view of the direct appreciation of 

 dynamical ideas, the small books at the head of this 

 NO. 1 175, VOL. 46 J 



article form a very welcome addition to the ordinary text- 

 books. The work of Prof Perry, popular lecture though 

 it be— and one feels constrained, from the confident style, 

 to believe that his audience of operatives understood every 

 word of it — leads on the reader by vivid illustration into 

 contact with the boldest flights of dynamical speculation. 

 After the ordinary effects of spin have been copiously 

 illustrated, we are taken into a world in which matter has 

 two kinds of inertia ; and, by aid of a chain of balanced 

 gyrostats, we learn that a cord cannot ever transmit 

 motion straight on without also twiddling about. It is 

 fortunate for those of us who have to follow or teach 

 mechanical pursuits that this new species of matter is not 

 often heard of, and is only called up in relation to such 

 unnoticeable, and practically insignificant, phenomena as 

 rotation of the plane of vibration of light waves. The 

 relations of ordinary mass to gravitation, and such like 

 are sometimes intricate enough things to discuss ; the 

 introduction of a second kind of mass, and that of a 

 vector character, might lead to despair. 



The great pioneer in this field of work, of eliciting the 

 concealed dynamical mechanism of tangible phenomena, 

 is, of course. Lord Kelvin, by whom nearly all our 

 knowledge on the subject has been originated, at any 

 rate in its present exact form. Prof Perry's book is all 

 the more welcome and suggestive, in that it claims to be 

 chiefly a connected account of what he has learned at 

 first hand from the teaching of Lord Kelvin ; an account 

 which has possibly not been published before by anyone, 

 at least in a consecutive form. 



Prof Worthington, after an elementary quantitative 

 introduction to dynamical principles, has gone over the 

 part of dynamics of rotation which relates to a single 

 spinning solid, in the manner of a text-book with numeri- 

 cal illustrations ; and there is no doubt that a mastery of 

 his explanations would be a very valuable part of the 

 outfit of a student of physics. J. L. 



THE MAMMALIA OF BRITISH INDIA. 

 The Fauna of British India, including Ceylon and 

 Burma. Published under the authority of the Secre- 

 tary of State for India in Council. Mammalia. Part II. 

 IJy \V. T. BlanforJ, P\RS. (London: Taylor and 

 Francis, 1891.) 



IN our issue of September 27, 1888, we had the pleasure 

 of bringing before the notice of our readers the first 

 part of Mr. Blanford's valuable monograph on the 

 Mammals of British India. The second part, completing 

 this important work, has lately been published. The 

 delay, as is explained in the preface, has been caused by 

 the necessity Mr. Blanford has been under of spending 

 much time in editing the five volumes of the same series 

 that have appeared since the first part of the present 

 work was issued. His labours in this respect have been 

 increased by two unfortunate and unforeseen circum- 

 stances—the lamented death of Mr. Francis Day, and the 

 expiration of the leave of Mr. E. W. Gates, in both cases 

 before the termination of the portions of the work, on 

 fishes and birds respectively, upon which they were en- 

 gaged, and the completion of which has thus fallen upon 

 Mr. Blanford himself. 



