NA TURE 



[September 12, 1901 



a further condition being that one solution only is given by a 

 group of numbers a, ^, 7 . . . satisfying the equation ; that in 

 fact permutations amongst the quantities o, 6, 7 . . . are not 

 to be taken into account. This further condition is brought in 

 analytically by adding the Diophantine inequalities 



V in number. The importation of this idea leads to valuable 

 results in the theory of the subject which suggested it. A 

 generating function can be formed which involves in its con- 

 struction the Diophantine equation and inequalities, and leads 

 after treatment to a representative as well as enumerative solu- 

 tion of the problem. It enables further the establishment of a 

 group of iundamental parts of the partitions from which all 

 possible partitions of numbers can be formed by addition with 

 repetition. In the case of simple unrestricted partition it gives 

 directly the composition by rows of units which is in fact carried 

 out by the Ferrers-Sylvester graphical representation and has 

 led in the hands of the latter to important results in connection 

 with algebraical series which present themselves in elliptic func- 

 tions and in other departments of mathematics. Other branches 

 of analysis and geometry supply instances of the value of extreme 

 specialisation. 



What we rtquire is not the disparagement of the specialist but 

 the stamping out of narrow-mindedness and of ignorance of the 

 nature ol the scientific spirit and of the life-work of those who 

 devote their lives to scientific research. The specialist who 

 wishes to accomplish work of the highest excellence must be 

 learned in the resources of .science and have constantly in mind 

 its grandeur and its unity. 



SECTION D. 



Oi'EMNG Address by Prof. J. Cossar Ewart, M.D, , 



F.R.S., President of the Section. 



The Experimental Shidy of Variation. 



The study of variation maybe said to consist (i) in noting 

 and classifying the differences between parents and their off- 

 spring ; and (2) in determining by observation and experiment 

 the causes of these differences, especially why only some of them 

 are transmitted to future generations. The facts of variation 

 having been dealt with at considerable length in a recent work 

 by Mr. Bateson, I shall discuss chiefly the causes of variation. 



Though for untold ages parents have doubtless observed 

 differences in the form and temperament of their children, and 

 though breeders have long noted unlooked-for traits in their 

 flocks and herds, the systematic study of variation is of very 

 recent date. This is not surprising, for while the belief in the 

 immutability of species prevailed, there was no special incentive 

 either to collect the facts or inquire into the causes of variation ; 

 and since the appearance in 1S59 of the "Origin of Species" 

 biologists have been mainly occupied in discussing the 

 theory of natural selection. Now that discussions as to 

 the nature and origin of species no longer occupy the 

 chief attention of biologists, variability — the fountain and origin 

 of progressive development— is likely to receive an ever-in- 

 creasing amount of notice. Strange as it may appear, naturalists 

 at the end of the eighteenth century concerned themselves more 

 with the causes of variation than their successors at the end of 

 the nineteenth. BulTon, who discussed at some length nearly 

 all the great problems that interest naturalists to-day, after con- 

 sidering variation arrived at the conclusion that it was due to 

 the direct action of the environment, and even invented a theory 

 (strangely like Darwin's theory of pangenesis) to explain how 

 somatic were converted into germinal variations. Erasmus 

 Darwin and Lamarck also had views as to the causes of variation. 

 Erasmus Darwin believed variability resulted from the efforts of 

 the individual, new structures being gradually evolved by the 

 organisms constantly endeavouring to adapt themselves to their 

 surroundings. Lamarck about the same time endeavoured to 

 prove that changes in the environinent produced new needs, 

 which in turn led to the formation of new organs and the modi- 

 fication of old ones, use being specially potent in perfecting the 

 new, disuse in suppressing the old. Both Erasmus Darwin and 

 Lamarck, without attempting, or apparently even seeing the 

 need of, any such explanation as pangenesis offered, assumed 

 that definite acquired modifications were transmitted to the 

 offspring, and they both further assumed that variations occurred 

 not in many but in a single cle'fifiite direction ; hence they had 



NO. 1663, VOL. 64] 



no need to postulate selection. The speculations of Erasmus 

 Darwin and Lamarck having had little influence, it fell to 

 Charles Darwin to construct new and more lasting foundations 

 for the evolution theory. 



Charles Darwin, clearly realising that variation occurs in 

 many different directions, arrived at the far-reaching conclusion 

 that the best adapted varieties are selected by the environment, 

 and thus have a chance of giving rise to new species. Though 

 impressed with the paramount importance of selection, Charles 

 Darwin realised that *'its action absolutely depends on what 

 we in our ignorance call spontaneous or accidental variation."' 

 Darwin, however, concerned himself to the last more with 

 selection than with variation, doubtless because he believed 

 variability sinks to a quite subordinate po.sition when compared 

 with natural selection. As variations stand in very much the 

 same relation to selection as bricks and other formed material 

 stand to the builder, Darwin was perhaps justified in rating so 

 high the importance of the principle with which his name will 

 ever be intimately associated. Though Darwin considered 

 variability of secondary importance, it may be noted that he 

 did more than any other naturalist to collect the facts of 

 variation, and he moreover consideied at some length the 

 causes of variation. He regarded with most favour the view 

 "that variations of all kinds and degrees are directly or 

 indirectly caused by the conditions of life to which each being 

 or more especially its ancestors have been exposed."" Of all 

 the causes which induce variability, he believed excess of 

 food was probably the most powerful.^ In addition to variations 

 which arise spontaneously in obedience to fixed and immutable 

 laws, Darwin believed with Buffbn that variations were pro- 

 duced by the direct action of the environment, and with 

 Lamarck by the use and disuse of parts ; and he accounted for 

 the inheritance of such variations by his theory of pangenesis. 

 Darwin seems alwaj-s to have regarded the direct action of the 

 environment and use and disuse as, at the most, subsidiary 

 causes of variation ; but Mr. Herbert Spencer and his followers 

 regard "use-inheritance" as an all-important factor in evolu- 

 tion ; while Cope and his followers in America, by a mixture 

 of "use-inheritance" (Konetogenesis) and Lamarck's neck- 

 stretching theory (Archoesthetism), apparently see their way to 

 account for the evolution of animals with but little help from 

 natural selection. 



Prof Weismann and others, however, have recently given 

 strong reasons for the belief that all variation is the result of 

 changes in the germ-plasm ultimately due to external stimuli, 

 the environment acting directly on unicellular, indirectly on 

 multicellular organism. It is convenient to speak of biologists 

 who believe with Mr. Herbert Spencer in the law of use and 

 disuse (use-inheritance) as Neo-Lamarckians, and of those who 

 with Weismann refuse to accept the doctrine of the trans- 

 mission of definite acquired characters, and iir the case of 

 multicellular organisms the direct influence of the environment 

 as a cause of variation, as Neo Darwinians. In discussing 

 variability I shall assume that all variations are 

 transmitted by the germ-cells ; that the primary cause of varia- 

 tion is al.vays the effect of external influences, such as food, 

 temperature, moisture, &c. ; and that " the origin of a varia- 

 tion is equally independent of selection and amphimixis " 

 (Weismann, "The Germ-Plasm," p. 431), amphimixis being 

 simply the means by which effect is given to differences inherited, 

 and to the differences acquired by the germ-cells during their 

 growth and maturation. 



Theoretically the offspring should be an equal blend of the 

 parents and (because of the tendency to reversion) of their respec- 

 tive ancestors. In as far as the offspring depart either in an old or 

 in a new direction from this ideal intermediate condition they may 

 be said to have undergone variation. The more obvious varia- 

 tions consist of a difference in form, size and colour, in 

 the rate of growth, in the period at which maturity is 

 reached, in the fertility, in the power to withstand disease 

 and changes in the surroundings, of differences in tempera- 

 ment and instincts, and in the aptitude to learn. In the members 

 of a human family there may be great dissimilarity, and the dis- 

 similarity may be even greater in the members of a single brood 

 or litter of domestic animals, especially if the parents belong to 

 slightly different breeds. 



1 "Animals and Plants," vol. ii, p. 206. 



- Ibid., vol. ii, p. 240. Elsewhere he says we are "driven to the con- 

 clusion that in most cases the conditions of life play a subordinate p.^rt in 

 causing any particular modification." 



3 Ibid., vol. ii, p. 282. 



