mouths of babes and sucklings. Although our seedlings, unlike the sucklings, are dumb, they are by no means speechless. One of the most striking triumphs of modern plant anatomy is to have discovered many examples of recapitulationary confirmation of the principle of evolution. To take a modern and striking instance, let us consider our common and flourishing northern genus, the oak. You are all familiar with the very broad rays which constitute so ornamental a feature of the structure of oak wood. You are likewise doubtless aware that the weight of paleobotanical evidence speaks for the derivation of the oaks from ancestors resembling the chestnuts since the older oaks approach the chestnuts both in their foliage and in their reproductive organs. The wood of the chestnut differs, however, strikingly from that of oaks by the entire absence of large rays. It has been recently discovered that certain oaks of the gold-gravels (Miocene Tertiary) of California have their large rays composed of aggregations of smaller rays. In the seedlings of certain of our existing American oaks this condition, interestingly enough, is a passing phase, which by the loss. of the separating fibers in the congeries of small rays produces the characteristic large rays of the adult. This condition of development in the living oaks is all the more significant because in certain breech-fertilized or chalazogamic amentiferous trees of the present epoch, such as the alder, the hazel and the hornbeam, such aggregated so called false rays are a permanent feature of structure in the adult. From the anatomical side, in the case of the lower Amentiferæ, we have accordingly at the same time an interesting example of the general biological law of recapitulation and a confirmation of the view expressed by Treub and Nawaschin, on evidence from the gametophytic and reproductive side, that the breech-fertilized Amentiferæ Amentiferæ are relatively primitive angiosperms.

Perhaps the most valuable service which anatomy is rendering to phylogeny and evolution is in connection

with the elucidation of the affinities of extinct plants. Certain cryptogamic trees of the Paleozoic, the Lepidodendrids, Sigillarians and Calamites, were, for example, long regarded by competent botanists as seed plants on account of their arboreal habit. The anatomists stoutly maintained, however, that from the structure of their primary wood they must be cryptogams. The subsequent discovery of their reproductive structures entirely confirmed the anatomical view. More recently from the study of the anatomy of certain fern-like plants with secondary growth, from the Paleozoic, English and German anatomists reached the conclusion that they were gymnosperms and allied at once to the ferns and to the cycads. Within the past decade, the brilliant discoveries of Oliver, Scott, Kidston, Grand'Eury and David White in regard to the nature of the reproductive organs of these plants, prophetically dubbed by Potonie, the Cycadofilices, have confirmed the truth of the anatomical view as to their affinities in every particular. Let us take a still more modern instance. There are present in the later Mesozoic strata huge quantities of impressions of the cones and leafy twigs of conifers. These have been referred on features of superficial resemblance to a number of genera of living conifers as well as to others not represented in the existing flora. Since they are very numerous, let us take one typical example, which is at the same time significant. Many species of Sequoia have been described from the upper Jurassic and the Cretaceous beds, on the evidence of the impress upon the stony or argillaceous matrix of their cones and leafy branches. Dr. Arthur Hollick and the present speaker have been fortunate enough to secure by new methods of isolation, material of these cones and twigs, with internal structure preserved. The anatomical features of both reproductive and vegetative organs of the remains in question, show beyond any possible doubt that they belong to a tribe of conifers at present confined to the southern hemisphere, the Norfolk Island and Kauri Pines

or Araucarineæ, and have not even the slightest affinity with the living genus, which externally they so strikingly simulate. The reference of the fossil genus just described to its true affinities as well as similar results in the case of a large number of other Mesozoic conifers, likewise erroneously placed in the system, leads to important general conclusions in regard to the evolutionary history of coniferous gymnosperms, which are too lengthy and too technical even to be mentioned here.

But it is not only in connection with extinct plants that anatomy has shown itself the useful servant of phylogeny. The enforced use of anatomical criteria in the case of fossil forms, where such evidence is absolutely indispensable, has resulted in a new and broader point of view in general botanical morphology. Within the decade we have begun to realize fully the great constancy of fibrovascular structures. This may perhaps be best exemplified by a special case. Superficially there is no organ of the plant more prone to vary extremely, within near lines of affinity, than the leaf. If, however, we look within, it presents anatomical features of great constancy. In the case of the leaf, perhaps the most hopelessly variable feature is its size. Anatomically, however, there are just two sizes of leaves, large leaves (megaphylls) and small leaves (microphylls), which are absolutely characterized by their anatomical relations. The foliar strands of the megaphyll, or large leaf, pass off from the woody cylinder of the stem, leaving corresponding gaps in its wall. Those of the microphyll, or small leaf, equally constantly leave no such gaps in their exit from the woody cylinder. It is even possible to divide the whole vascular series into two clean-cut phyla on the basis of the anatomical features of leaf size, viz., the Pteropsida with, anatomically speaking, large leaves, including the ferns, gymnosperms and angiosperms and the Lycopsida, structurally speaking, small leaved forms including among living plants only the club-mosses and horsetails.

I have tried to show above, with all necessary brevity, that the services of anatomy to phylogeny and the doctrine of descent during the past decade have been neither few nor unimportant. Perhaps the most important general result of recent work in the modern morphological field, not restricting it, of course, to anatomy, may best be expressed in the words of the eloquent and philosophical apostle to the gentiles, viz., that the things seen are temporal, while the things unseen are eternal. You may think that I have too much emphasized the importance of internal morphology. One example will serve to show that I have not. You are all familiar with that great German work on the morphology (or, as its author prefers to call it, the organography) of the higher plants, which not very long ago appeared in a traduction de luxe from the Oxford University Press. If you scan it from cover to cover, I do not believe you will find a single figure of the fibro-vascular structures. Not even the proverbial halfpenny's worth of bread is present to qualify the oceans of sack. It is not surprising that we should hear from such a source a strong note of morphological pessimism. On a recent occasion in our own country, the distinguished author of the work in question compared the task of his science to that of Sysiphus, of classic fable, condemned to roll up the mountainside a stone which continually rebounds. We may confidently expect that the morphology of the future, distrusting the superficial anfracutosities of the steep, will bring the profitless rolling stone to rest in the very heart of the mountain itself.

SHORTER ARTICLES AND CORRESPONDENCE

A NOTE ON THE DEGREE OF ACCURACY OF BIOMETRIC CONSTANTS

The statement is frequently made, either in comment or criticism upon biometric work, that such work is often caused to take on an unwarranted appearance of precision and exactness by the keeping of a larger number of decimal places in the tabled constants than the character of the original data justifies. The contention is made that under no circumstances whatsoever can any statistical constant be more accurate than the data on which it is based. It is held that if one makes a series of measurements accurate to a tenth of a millimeter, it is a logical absurdity to table the mean or standard deviation deduced from these measurements to hundredths of a millimeter. Not only

is this contention made from time to time by biologists, but occasionally even by a mathematician, a fact which of course tends strongly to confirm the biologist in his opinion. Thus Engberg1 specifically says (p. 11) referring to mortality statistics: "The constants can not be more accurate than the data on which they are based."'2

The reply which the statistician makes to the criticism that constants can not be more accurate than the data on which they are based is generally that the accuracy of a statistical constant depends not alone on the accuracy of the original measurements but also upon the number of such measurements. Further it is pointed out that, because of this fact, it is possible to deduce from measurements known to be individually inaccurate constants of a high degree of accuracy, provided that the errors in the measurements are unbiased (that is as often in excess as in defect of the true value) and that there are enough of the data. Finally the statistician contends that the only proper measure of the accuracy of a statistical constant 'Engberg, C. C. The Degree of Accuracy of Statistical Data. Univ. of Nebraska Studies, Vol. III, No. 2, pp. 1-14, 1903.

2

In passing it may be said that any one who is sufficiently interested in the phenomenon of a professional mathematician taking this curious position will find an entirely adequate and satisfactory discussion of the matter in Nature. Vol. 69, p. 93, where Engberg's paper is reviewed.