(4) Aristotle was much struck with certain facts of correlation, of the interdependence of two organs which are not apparently in functional dependence on one another. Such correlation may be positive or negative; the presence of one organ may either entail the presence of the other, or it may entail its absence. Aristotle has various ways of explaining facts of correlation. He observed that no animal has both tusks and horns, but this fact could easily be explained on the principle that Nature never makes anything superfluous or in vain. If an animal is protected by the possession of tusks it does not require horns, and _vice versa_. The correlation of a multiple stomach with deficient development of the teeth (as in Ruminants) is accounted for by saying that the animal needs its complex stomach to make up for the shortcomings of its teeth! (_De Partibus_, iii., 14, 674^b.) Other examples of correlation were not susceptible of this explanation in terms of final causes. He lays stress on the fact, in the main true, of the inverse development of horns and front teeth in the upper jaw, exemplified in Ruminants. He explains the fact in this way. Teeth and horns are formed from earthy matter in the body and there is not enough to form both teeth and horns, so "Nature by subtracting from the teeth adds to the horns; the nutriment which in most animals goes to the former being here spent on the augmentation of the latter" (_De Partibus_, iii., 2, 664^a, trans. Ogle). A similar kind of explanation is offered of the fact that Selachia have cartilage instead of bone, "in these Selachia Nature has used all the earthy matter on the skin [_i.e._, on the placoid scales]; and she is unable to allot to many different parts one and the same superfluity of material" (_De Partibus_, ii., 9, 655^a, trans. Ogle). Speaking generally, "Nature invariably gives to one part what she subtracts from another" (_loc. cit._, ii., 14, 658^a). This thought reappears again in the 19th century in E. Geoffroy St Hilaire's _loi de balancement_ and also in Goethe's writings on morphology. For Aristotle it meant that Nature was limited by the nature of her means, that finality was limited by necessity. Thus in the larger animals there is an excess of earthy matter, as a necessary result of the material nature of the animal; this excess is turned by Nature to good account, but there is not enough to serve both for teeth and for horns (_loc. cit._, iii., 2, 663^b). But there are other instances of correlation which seem to have taxed even Aristotle's ingenuity beyond its powers. Thus he knew that all animals (meaning viviparous quadrupeds) with no front teeth in the upper jaw have cotyledons on their foetal membranes, and that most animals which have front teeth in both jaws and no horns have no cotyledons (_De Generatione_, ii., 7). He offers no explanation of this, but accepts it as a fact.