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(1.) The object of this paper is to show, by the use of a special case as illustration, the true limits within which it is possible to reconstruct the parts of an extinct race from a knowledge of the size of a few organs or bones, when complete measurements have been or can be made for an allied and still extant race. The illustration I have taken is one of considerable interest in itself, and has been considered from a variety of standpoints by a long series of investigators. But I wish it to be considered purely as an illustration of a general method. What is here done for stature from long bones is equally applicable to other organs in Man. We might reconstruct in the same manner the dimensions of the hand from a knowledge of any of the finger bones, or the bones of the upper limbs from a knowledge of the bones of the lower limbs. Further, we need not confine our attention to Man, but can predict, with what often amounts to a remarkable degree of accuracy, the dimensions of the organs of one local race of any species from a knowledge of a considerable number of organs in a second local race, and of only one or two organs of the first. The importance of this result for the reconstruction of fossil or prehistoric races will be obvious. What we need for any such reconstruction are the following data:— (a .) The mean sizes, the variabilities (standard-deviations), and the correlations of as many organs in an extant allied race as it is possible conveniently to measure. When the correlations of the organs under consideration are high (e. g. , the long bones in Man), fifty to a hundred individuals may be sufficient; in other cases it is desirable that several hundred at least should be measured.

IV. Mathematical contributions to the theory of evolution.—V. On the reconstruction of the stature of prehistoric races