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Rh and limited by their past history. Variation, again, as has been shown in this article, is limited by correlation; as any change involves other changes, the possibilities are limited by the organic whole. Finally, it is important to remember that the fundamental characteristic of a living organism is its power of response to environment, a response or series of responses being necessary in a continuous environment for the normal facies of the organism to appear, and necessary in a shifting environment if the organism is to change suitably and not to perish. A continuous environment both from the point of view of production of variation and selection of variation would appear necessarily to result in a series with the appearance of orthogenesis. The past history of the organic world displays many successful series and these, as they have survived, must inevitably display orthogenesis to some extent; but it also displays many failures which indeed may be regarded as showing that the limitation of variation has been such that the organisms have lost the possibility of successful response to a new environment.

Selection and Adaptation.—Although knowledge of variation has become much wider and more definite, the estimation in which natural selection is held has changed very little since Darwin and Wallace first expounded their theories. Variation provides the material for selection, and although opinions may differ as to the nature of that material, the modes by which it comes into existence and their relative values and permanences, there is an increasingly wide consensus of opinion that all such material has to pass through the sieve of natural selection and that the sifted products form new varieties and species, and new adaptations. It appears to be necessary to distinguish between the production of species and the production of adaptation. We have still to admit with Darwin that it is difficult or impossible to assign utility to all the characters that distinguish species, and particularly to those characters by which systematists identify species. The modern tendency for a more complete and detailed separation of individual forms into specific and sub-specific groups, and the immensely larger range of material at the disposal of systematic experts, have combined to make it increasingly difficult to imagine conditions of the environment under which the species of systematists would have been produced by selection. On the other hand, the work of modern systematists shows an extraordinarily exact relation between their species and geographical locality, and the fact of divergent evolution can be almost demonstrated in museum collections when localities have been recorded exactly. The decision as to whether it is the course of variation or the course of selection that has been different in different localities can be made only by the field naturalist and the experimental breeder.

With regard to adaptations, it is becoming more and more apparent, as experimental knowledge advances, that it is a fundamental property of every living organism in every stage of its existence to display adaptive response to its environment. To what extent such responses are transmitted to offspring, and what part they play in the formation of the adaptive characters that are conspicuous in many animals, remain dubious, but it is at least clear that natural selection can favour those individuals and those races which show the greatest power of responsive plasticity in the individual. There remains open a wide field for inquiry as to the precise relations between selection and variation on the one hand, and their products, specific differences and adaptive structures, but the advance of knowledge has supplied no alternative to the Darwinian principles.

In the broadest way variation in organisms is primarily the necessary result of the absence of uniformity in the distribution of physical forces on the globe, in fact is a mere necessary response to the variation of inorganic conditions. So, also, in the broadest way, the result of the existence of variation is equally inevitable. Some individuals happen to fit the environment better, or to respond to the environment better, and these on the average Will survive their less fortunate neighbours. It is plain that whilst the existence of variation can be demonstrated and the occurrence of evolution established by induction and deduction, the part played by selection must remain largely theoretical.

We append, however, again from the late Professor Weldon's article, a summary of the lines on which it seems possible that the actual process of selection may be demonstrated.

Selection and its results can be adequately studied only in those cases which admit of statistical tabulation. In any race of animals, the number of young produced in a season is almost always greater than the number which survives to attain maturity; it is not certain that every one of those which become mature will breed, and not all of those which breed contribute an equal number of offspring to the next generation. At every stage some individuals are prevented from contributing to the next generation, and if the continual process of elimination affects individuals possessing any one character more strongly than it affects others, so that a relation is established between individual character and the chance of producing a certain number of young, selection is said to occur.

We may distinguish broadly two ways by which such selective elimination of individuals from the number of those who contribute to the next generation may occur, viz. a differential destruction, which prevents certain classes of individuals from breeding by killing them, and a series of processes leading to differential fertility among the survivors, without necessarily involving any differential death-rate. A third form of selection, which may affect the composition of the next generation without of necessity involving a differential death-rate or a differential fertility, is assortative mating, or the tendency of those members of one sex which exhibit a particular character to mate only with members of the other sex which exhibit the same or some other definite character.

Differential fertility may be induced in either of two ways. Individuals may not be able to pair unless they possess a character which is absent, or insufficiently developed, in some members of the race. The kind of selection involved may then be measured by comparing those animals which pair with the general body of adults. This is what Darwin especially intended to denote by the term “sexual selection.” Or, again, individuals of certain character may be able to pair, but the fertility of their union may not be the same as that of unions between individuals with other characters. This kind of selection, called by Pearson “reproductive” or “genetic” selection, may be measured by finding the correlation between the characters of the individuals which pair and the number of young produced. For an attempt to treat the whole problem of differential fertility and assortative mating numerically, see Pearson, The Grammar of Science, 2nd edition, London, 1900.

Assortative mating exists when individuals which mate are not paired at random, but a definite correlation is established between the characters of one mate and those of the other. This kind of selection is measured by the correlation between deviation of either mate from the type, and deviation of the other. Pearson has shown that Galton's function has a value of 0.28 for stature of middle-class Englishmen and their wives.

.-W. Bateson, Mendel's Principles of Heredity (Cambridge, 1909); E. Clodd, Pioneers of Evolution (London, 1897); E. D. Cope, Origin of the Fittest (London, 1887); C. Darwin, Origin of Species (London), Variation of Plants and Animals (London); E. Darwin, Zoonomia (London, 1794); J. Cossar Ewart, “Variation, Germinal and Environmental,” in ''Trans. Roy. Dublin Society'' (1901); P. Geddes, “,” Ency. Brit. 9th ed.; G. von Herder, ''Ideen zur Phil. d. Geschichte (1790); R. H. Lock, Recent'' Progress in the Study of Variation, Heredity and Evolution (London, 1906); T. H. Morgan, “Chance or Purpose in the Origin and Evolution of Adaptation,” Science (New York, 1910), p. 201; H. F. Osborn, From the Greeks to Darwin (New York, 1894); E. B. Poulton, Charles Darwin and the Origin of Species (London, 1909); J. H. Stirling, Darwinianism (London, 1894); Sir W. T. Thiselton-Dyer, “The New Origin of Species,” Nature (1910); H. M. Vernon, Variation in Animals and Plants (London, 1903); H. de Vries, Species and Varieties, their Origin by Mutation (Chicago, 1905); The Mutation Theory (London, 1910); A. Russel Wallace, Darwinism (1889); A. Weismann, The Evolution Theory (London, 1904); W. R. F. Weldon, “Variation and Selection,” ''Ency. Brit.'' 10th ed.; Various Authorities in Fifty Years of Darwinism (New York, 1909). (P. C. M.)&emsp;  VARIATIONS, in music, the term given to groups of progressively developed versions of a complete self-contained theme, retaining the form of that theme though not necessarily its melody. This at least is the classical sense of the term, though there are modern developments of the variation form to which this definition is at once too broad and too precise to apply. The aesthetic principle of variations appeared at very early stages of music; and it soon became something far more definite than the use of ornamental versions of a melodic phrase, a use which must have been natural almost as soon as music was articulate at all. During the 16th century