reaching notions. Moreover, they suggest many questions as regards subgroups and abstract laws of operation. In particular, this group of order 24 is completely defined by the fact that it contains two operators of orders 2 and 3 respectively whose product is of order 4.

While a group-theory of the third century B. C. is conceivable it could not have been the group-theory of the nineteenth century, since the latter century had a much richer mathematical heritage. The rapid strides of group-theory during the last century were largely due to the utilization of old results as is always the case in generalizations by abstraction. The soil had been prepared by the labors of earlier centuries and it was only necessary to sow on it the new seed to secure the bountiful harvest with which the labors of many workers in this field were rewarded, especially during the last decades of the ninteenth century.

When group-theory appeared explicitly it naturally took a form which was in accord with the spirit of the times. Substitution groups constitute a type of combinatory analysis and arose about the time when the Combinatorial School flourished in Germany under the leadership of C. F. Hindenburg (1741-1808). Abstract group-theory is a type of postulational mathematics and its early development during the middle of the preceding century was in the van of the postulational activity which was so prominent during the second half of the nineteenth century. Continuous and geometric group-theory are mainly applied group-theory and their rapid development during the latter quarter of the preceding century is in accord with the spirit of this age when the fear of mathematical isolation through overspecialization tended to make the study of applications especially popular.

THE OLDEST OF THE FORESTS

By DR. JOHN M. CLARKE

NEW YORK STATE MUSEUM, ALBANY, N. Y.

HE chief signal officer of our army, General Squier, has demon

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strated the reality of what we might well have regarded an almost fanciful conception-one that might have emerged from the rosy mists when fairies had not been reduced to formulas and the notes of Pan were still to be heard in the forest aisles. The trees of the forest, says this distinguished academician, are antennae of the wireless telegraph and conductors of messages which can be interpreted by human ears if they are in human language. Their other messages, untranslatable to our ears, are left to our fancy, but the trees stand reaching their sensitive finger tips out into the sky and it would be strange indeed if they did not catch and draw down other messages which had to do with their own concerns and upbuilding. The picture. is a pretty one and a legitimate fancy indeed if we let the trees in their own silent passages carry on the gossip of the woods, their conversaziones among themselves and the world of life which they shelter.

The fool hath said in his heart that we have passed the age of miracles and that all the phenomena of Nature can be reduced to terms of human understanding. But in the apostolic sense I speak even as a fool in restating so elementary a thought as that the farther we go into the exact interpretation of the facts of Nature, the more deeply the honest mind becomes impressed with the ever enlarging evidence of the miraculous, the processes in Nature which the best of human intellect can not compass or explain. Let the whole organism of the tree be put in terms of chemical and physical reactions, of tissue structure and biological explanation, and the question remains still nakedly unanswered-what is the tree, whence and how has it come, and must remain so until we apprehend the genius and spirit of the tree as well as its substance.

With this short sermon I introduce the brief story I have been asked to tell about the oldest of our forests whose remains are none the less expressive for being turned to stone. The petrified forests of the world have filled museums and homes with fragments of their beautiful woods, often brilliant in the colors of jasper and chalcedony and iridescent with the tints of the opal or their flaming

heart cavities lined with crystals of amethyst, and to a mineralogist all these are only simple evidences of "replacement" by slow process of the woody tissue by silica with various coloring metallic oxides in regions where thermal and alkaline waters abound. It is easy to wave aside such beauties as these with the best explanations we have at hand, but there still remains the greater fact that these objects of our admiration are beautiful and that beauty is not explained by equations. Perhaps among all the worlds of fossil life nothing is quite so impressive to the observer as a petrified tree trunk standing erect in the rocks in the very place where it grew, its roots still running out into the underclays. It conveys a singular conviction of the fact that the embedding rocks about it are after all but the hardened muds in which it grew and which have gradually and quietly overwhelmed it, and there remains no doubt in the observer's mind that he is standing amongst the trees of an earlier order of Nature, amongst the forest groves which in their day must have heard the sound of many voices whose "stilly influences" are still stored away in those very tree trunks. Such an impression is lessened when the stony trunks are in fragments scattered about and prostrated by changes which have befallen since they turned to rock.

In the midst of the vast and brilliant array of disjected timber in the Arizona forests about Adamana and Holbrook and in spite of the profound impression the mind receives.before this unique manifestation of Nature's procedures, the observer has nevertheless the feeling that, as has been often said, he is looking at a great petrified "timberdrive" and a timber-drive is but a raft of chopped down trees. Let the eye catch the marvellous exhibit of the Early Tertiary forests of the Yellowstone National Park, at Junction Butte, at Cache Creek and on the slopes of the Thunderer where the fossil trees stand erect to heights of 20 to 30 feet and the forest bottoms rise from one level to another over not less than fifteen different forest areas which have been buried, each in turn, by the outpourings of volcanic ashes. Here the impression is of so enormous magnitude that the mind can never release itself from the sight enforced; of an earth clothed over all its dry lands with forests giving shelter to hordes of animal life which together were working out the destinies of their evolution untouched and untrammeled by the influence of man.

If such an impression is in any way impaired it may come from the thought that these Yellowstone forests are made up of trees not very unlike those which today help to compose our northern forests. Then, as now, sequoias, other conifers and dicotyledons grew side by side. Even so the much older trees of the Arizona stone timber drives. They are of Triassic age but mostly belong to the race of Araucarian pines, still growing in the mountains of South America