I»2 



NATURE 



[May 3, 191 7 



of words are often of great value; but a writer 

 may bring- his own qualities of judgment ard 

 understanding into discredit by erroneously sup- 

 posing that a misuse requires correction where no 

 such misuse exists. 



We are also unable to admit the validity of 

 Prof. Morgan's assimilation of the "artificiality" 

 of the conditions under which humanly selected 

 breeds are produced and studied to the "arti- 

 ficiality " of a spectroscope or a galvanometer 

 (p. 84). The justification for reserv-e and caution 

 in generalising in the former case is not that these 

 breeds are "artificial," but that the essential and 

 significant conditions of the phenomena they pre- 

 sent are not clearly ascertained, whilst in regard to 

 the instruments known as spectroscope and galva- 

 nometer those conditions are accurately estab- 

 lished. 



The point of greatest interest at the present 

 moment in a critique of the theory of organic 

 evolution by a capable and accomplished investi- 

 g;ator of the facts of inheritance — such as Prof. 

 Morgan — is his answer to the question : " Does 

 natural selection influence the course of evolu- 

 tion?" (p. 187). Prof. Morgan gives a very 

 carefully worded answer in the affirmative. He 

 says : " If through a mutation a character appears 

 that has a beneficial influence on the individual, 

 the chance that the individual will surv'ive is 

 increased, not only for itself, but for all of its 

 descendants that come to inherit this character. 

 It is this increase in the number of individuals 

 possessing a particular character that might have 

 an influence on the course of evolution." He goes 

 op to say : " The causes of the mutations 

 that give rise to new characters we do not 

 know, although we have no reason for sup- 

 posing that they are due to other than 

 natural processes. Evolution has taken place 

 by the incorporation into the race of those 

 mutations that are beneficial to the life and 

 reproduction of the organism. Natural selection 

 as here defined means both the increase in the 

 number of individuals that results after a benefi- 

 cial mutation has occurred (owing to the ability 

 of living matter to propagate), and also that this 

 preponderance of certain kinds of individuals in a 

 population makes some further results more prob- 

 able than others. More than this natural selec- 

 tion cannot mean, if characters are fixed and are 

 not changed by selection." 



We do not know of anyone who maintains 

 that factors are changed by selection. Darwin 

 certainly did not make such a misuse of the word 

 "selection." But there is a great field of inquiry 

 still' to be undertaken which is indicated by the 

 words "if factors are fixed." We are a long way 

 from possessing knowledge that would justify the 

 cnnclusion that they are fixed — as Prof. Morgan 

 is careful to point out (p. i66). Darwin held that 

 they are subject to influences which cause them to 

 vary, and it is by research in this area that we 

 may hope for future advance in the understanding 

 of the complex web of the phenomena of heredity. 



E. Ray Lankester. 



NO. 2479, VOL. 99] 



GENERALISED CO-ORDINATES. 

 An Introduction to the Use of Generalised Co- 

 ordinates in Mechanics and Physics. By Prof. 

 W. E. Byerly. Pp. vii+ii8. (Chicago and 

 London: Ginn and Co., 1916.) Price 55. 6d. 

 n HIS work is sure to be welcomed, because 

 -'• Prof. Byerly has undoubtedly the gift of 

 appealing successfully to the average student. 

 More than that : in its small compass it includes 

 a wide scope because, starting with the notion 

 of generalised co-ordinates in its abstract ana- 

 lytical form, it proceeds to the discussion of such 

 things as the Hamiltonian equations, the principle 

 of least action, the ignoration of co-ordinates, and 

 the proper use of the modified kinetic-energy 

 function. For a teacher the book is * cheap, if 

 only for the example (d) on p. 21, and the subse- 

 quent discussion of the same example on pp. 98— 

 103. We have not seen a more illuminating 

 example within the range of an ordinary student ;^ 

 it shows admirably the difi^erence between abstract 

 dynamics, where all necessary data are provided, 

 and practical physics, where the data are experi- 

 mental, and need by no means correspond with 

 the actual elements of the problem. In this case it 

 is a question of guessing at the simplest explana- 

 tion of an unseen "control " of a mechanism on 

 which we can make experiments within a certain 

 range. 



Among the many merits of this book we may 

 signalise the following : the examples are almost 

 all instructive and free from artificiality ; we have 

 some where the same result is obtained by dif- 

 ferent advanced methods — for instance, pure 

 Lagrange, pure Hamilton', and Hamilton phis 

 Routh (with a modified function), and these are 

 compared with previous solutions by elementary 

 methods. As a matter of notation, we may direct 

 attention to the symbol IVI^. ,. for the energy- 

 function modified with respect to the position- 

 co-ordinates q, r. The meaning of partial deriva- 

 tives is so variable in this connection that we 

 should like such symbols as T(g2), T{p^), T{pq) 

 introduced throughout for the velocity-forms, 

 momentum-forms, and "mixed" forms of T 

 whenever there is any risk of confusion. The fact 

 that, in a certain sense, the Lagrangian function 

 L means T - V (strictly T(q2) _ v), and the 

 Hamiltonian function means T + V (strictly 

 T(/>2) + V), is extremely baffling to a beginner. 

 In particular, the "canonical "equations of Hamil- 

 ton imply a special representation of the energy- 

 function. 



Prof. Byerly 's book is so good that it deserves 

 a much more searching criticism than the present 

 reviewer can pretend to give ; but a few remarks 

 may be ventured here. The example (p. 18) about 

 the dog running down a plank is all right as it 

 stands, but it tacitly implies that the dog is re- 

 duced to a mere machine applying a constant 

 frictional force to the plank parallel to the in- 

 clined plane. Students who try to solve "animal"" 

 problems by Lagrange's method may make some 

 fearful howlers. Another point (p. 72) is the 

 question "how far we can treat toj, <i)2» **3 occurring 



