(4) A memoir on the Paleozoic reticulate sponges (with Hall) (1898).

(5) The Naples fauna in western New York (1899, 1904).

(6) Early Devonic history of New York and eastern North America (1908, 1909).

(7) Address of the president of the Paleontological Society (1911).

(8) The Eurypterida of New York (with Ruedemann) (1912).

(9) The philosophy of geology and the order of the state (1917).

(10) James Hall of Albany (1921).

(11) Organic dependence and disease (1908, 1921). (12) L'Île Percée, the finial of the St. Lawrence, or Gaspé Flaneries (1923).

In the early summer of 1900 Clarke was not well, and he needed an outdoor change, and one that would take him away from his scene of action. At that time, he and Schuchert were involved with H. S. Williams in the controversy as to the boundary between Silurian and Devonian, and the New York State Survey and the U. S. National Museum arranged to send both of them to see the most perfect sections of these two periods, those of the eastern Maritime Provinces of Canada. Together they visited the coast of Arisaig, then Dalhousie, Percé and finally Gaspé. Soon Clarke told Schuchert that he had found in Gaspé the hobby that he had long been looking for a land of quaintness that reminded him somewhat of Scotland, the Old Red, and Hugh Miller, the land of fish, both fossil and recent. In the end Clarke got this entire Devonian problem to work out. The geological results, his magnum opus, were published in his two-volume "Early Devonic History of New York and Eastern North America," in 1908-1909. Summer after summer Clarke returned to Gaspé, and in the course of time he became the protector of its seabirds and the historian of this land discovered so early by Jacques Cartier, his affection for it finding expression in "Sketches of Gaspé" (1908), "The Heart of Gaspé" (1913), and “L'Île Percée" (1923). This is a side of Clarke little known to geologists, but one that endeared him to the simple habitants of the peninsula. Gaspé also aroused in Clarke an interest in ceramics, and he published a number of articles on this subject, the most important of which are "English gold lusters" and "The Swiss influence on the early Pennsylvania slip decorated majolica," both privately printed at Albany in 1908.

Clarke's strong historical sense is again seen in his placing of memorial tablets. This began in 1901, when he and a few others placed on the home of Ebenezer Emmons in Albany a tablet commemorating the fact that in this house in 1838-1839 was started

the American Association for the Advancement of Science. In 1908 he placed one in Letchworth Park along the upper Genesee to commemorate the first geologic work done by James Hall in western New York in 1839-1843. Five years later, through his efforts, Logan Park was set aside in Gaspé, and here he unveiled before the geologists of the Twelfth International Geological Congress a bronze tablet memorializing Sir William Logan's first field work in eastern Canada. In 1915, at the meeting of the state geologists, a memorial tablet was placed on Hall's private museum in Beaver Park in Albany. The grandest memorial of all, however, was to be unveiled this coming autumn in front of the old Albany Institutea large bronze statue of Joseph Henry, the first secretary of the Smithsonian Institution, who was a native of Albany. Clarke started the movement for this memorial in 1916, raising $25,000, and he was to have made the unveiling speech; the chairman of the committee which was in charge of the ceremonies has since stated that it had been his intention to make the occasion also the apotheosis of Clarke himself.

Clarke was always much interested in the welfare of the city of Albany. Here he did much to rehabilitate the Albany Institute, one of the oldest scientific societies of the country, and had been its president for many years at the time of his death; helped and cheered on the good work of the ladies of the Dana Natural History Society; had been a trustee of the Dudley Observatory since 1916; and was on the local (and national) council of Boy Scouts, where he arranged for the Mayflower Medal to be awarded each year to the scout having the best knowledge of the local history.

Clarke's championship of the cause of scenic beauty is exemplified in the case of Niagara Falls. The "Menace to Niagara," due to the threat of the power companies to take away, if not all, at least much of the beauty of the falls, was long seen coming, and the fight against it culminated in the New York Assembly in 1904. Clarke stood out against this menace, and in public addresses and otherwise pointed out that "the conservation of Niagara Falls is a question of public morals," since about 800,000 tourists visit the Falls each year and their number demonstrates "how closely the interest of the whole world is focused on Niagara, for these visitors are representatives of every nation. How many hundreds of thousands will seek out Niagara when the world learns that the Delilah of commerce has shorn it of its glory? Will they traverse the seas to behold the wonders of a breakfast-food factory or any other industrial triumph? These are everywhere; Niagara is unique." This battle was won, and a treaty has been made with

Great Britain by which the water of the Falls is kept under reasonable control.

The State Cabinet of New York had its origin in 1843, but it can not be said to have amounted to much until James Hall was placed in charge of it in 1866. In 1904 Clarke was made director of the science division and of the New York State Museum, the successor to the State Cabinet. Three years later Clarke helped in the planning of the State Education Building, which was completed in 1913. In the autumn of that year the State Museum began to move into its new quarters, the entire upper floor, with 60,000 square feet of space. One half of this is devoted to geology and paleontology, an expansion that brought about an increase in the staff and a modernization of the grand collections. The opening of the building took place on December 29, 1916, before the assembled geologists, who were addressed by Theodore Roosevelt. New York now has the best state museum in America, with the finest array of highly significant Paleozoic fossils. From the paleontological side, in fact, it possesses one of the world's most valuable collections, containing upward of 7,000 type specimens, and constituting a mecca to which all students of the older Paleozoic come for inspiration and interpretation. Here also are to be seen most artistic and lifelike restorations of Ordovician, Silurian and Devonian marine assemblages, and this type of teaching had its culmination last February, when Clarke placed before the public a restoration of the Gilboa Devonian forest, a living picture of the first flora to clothe Mother Earth. The New York State Museum is beyond question Clarke's greatest monument.

The philosophy of Clarke's paleontologic studies is to be found mainly in three of his papers, namely, his address to the Paleontological Society as its first president (1911); "The philosophy of geology and the order of the state," being the presidential address to the Geological Society in 1916; and "Organic dependence and disease," published in 1921. His conception of what the life of the past should mean to the living human world may be summed up as follows: "Paleontology is the most far-reaching of all the sciences. In it lies the root of all truth, out of it must come the solution of the complex enigmas of human society." The great significance of evolving life as seen throughout the geologic ages came to Clarke from his studies of the earliest phases of the parasitic or dependent conditions of life-a study of mutual organic associations that led to commensalism, sessility and finally to parasitism. These modes of life involve "the essential abandonment of normal direct, upright living and the benefactors thereby are types of life which Nature has cast out and aside as

hopeless. . . . Individual and locomotive independence, it would seem, has been the major function and prime determining factor in the progress of life. All progress in life, as reckoned in terms of man, has come through independence and through those lines of animal life in which independence has been maintained at any cost. .. Rescue of dependents is therefore not a part of the scheme of Nature, except through the exercise of intelligence."

On the other hand, the communal life of the social insects shows that "socialism and communism have been tried out and found wanting, and Nature holds conspicuously before the eye of the State the warning that they have nothing either for the growth of the spirit or the progress of the intellect."

"Nature makes for the individual," and this truth "is registered on the tablets of the earth. . . . Over and over again the dominant race has started on its career as an insignificant minority struggling for its existence against an overburden of mechanical and vital obstacles, armed only with specific virtues which have little by little fought their way into the foreground, and by so doing consummated their upward purpose. . . . The majority is purely numerical, while wisdom and truth may rest with the minority. . . . The voice of the people is not the voice of God."

The paleontologist, looking at the record of life on the earth, says to the state: "Be intelligently guided in the treatment of hereditary community parasites, defectives, congenital or confirmed misdemeanants, whatever the form of degeneration may be, by recognition of the presumption that in so far as they can not be physiologically corrected, they are abandoned types in which there lies little hope of repair."

Of "honors which beautify and crown success," Clarke had many: was elected to membership in numerous scientific and historical societies in this country, Canada, England, Germany, France and Russia; made an Immortal in the National Academy of Sciences in 1909; elected vice-president of the Geological Society of America in the same year, and its president in 1916; made first president of the Paleontological Society in 1909; awarded the Prix de Léonide Spindiaroff by the International Geological Congress in 1910 for his geologic work in Gaspé; awarded a gold medal by the Permanent Wild Life Protection Fund (1920), the Hayden Gold medal of the Philadelphia Academy of Natural Sciences (1908), and the Thompson Gold Medal of the National Academy of Sciences (1925); received an honorary Ph.D. degree from the University of Marburg in 1898, that of Sc.D. from Colgate in 1909, Chicago in 1916 and Princeton in 1919, and that of LL.D. from

Amherst in 1902 and from Johns Hopkins in 1915. According to letters from Professor Barrois, of the University of Lille, a further honor was soon to have been his through election to fellowship in the French Academy.

A study of John M. Clarke's works shows clearly that he was one of the greatest paleontologists of his time and one of the geniuses of science, "standing on the mountain-top and catching the first rays of the rising sun," pregnant with new views of nature. But an intimate knowledge of his life also reveals that his path to eminence was hewn out with much labor among his beloved fossils, taxing to the full the manysided equipment that was his from home, college and environment.

CHARLES SCHUCHERT, RUDOLF RUEDEMANN

SOME MATHEMATICAL ASPECTS OF COSMOLOGY

(Continued from page 99)

There are many more postulates that are worthy of discussion, but let us suppose that they have been read by title, and that our system of postulates is complete. Everything else that happens in our cosmology must be in harmony with them, for they are esthetic propositions and are not to be profaned with evidence. Evidence and experience are dealt with by hypotheses, which include all those statements which we usually call the laws of nature. Perhaps the most fundamental and the best verified of all hypotheses is Newton's law of gravitation, and yet the Neumann-Seeliger proposition, which we have already mentioned, shows that our mathematical formulation of it can not be rigorously true, since it conflicts with our system of postulates. The statement that the effects of a displacement of a body are perceived at distances, however remote, instantaneously is quite likely to be in conflict with any serious system of postulates. Newton's formulation is delightfully simple, and its predictions are almost perfect, but I should very much prefer to think that at distances sufficiently great the attraction of any body whatever is rigorously zero, rather than merely very small. However that may be, we must not push Newton's law "to the limit"; nor, indeed, are we justified by evidence in pushing any physical law "to

the limit."

Similarly, the inverse square law enables us to compute in an entirely satisfactory manner the attraction of an electrically charged surface for an oppositely charged particle, provided the particle is not in the surface. If the particle is in the surface

the situation is mathematically indeterminate. We escape this evil consequence by a hypothesis of fine structure, so that what is a mathematical surface for some purposes is not at all a mathematical surface for others. Again we must not push the law of attraction to the limit. Perhaps a theory of fine structure could be made to account for the complete disappearance of gravitation at distances sufficiently great. However fine the structure may be, eventually it becomes too coarse for gravitation to act.

A second conflict with our postulates is found in the law of radiation, which, again, is an inverse square law. We have already seen that if this law were rigorously true the entire sky would be as bright and as hot as the disk of the sun. The evidence is squarely against it. Relative to such a situation the sky is very dark and cold, and we must admit that the law is not rigorously formulated. But radiation is energy, and energy can not disappear into empty nothingness. It was this difficulty which led me some ten years ago to make the hypothesis 38 that radiant energy can and does disappear into the fine structure of space, and that sooner or later this energy reappears as the internal energy of an atom; the birth of an atom with its strange property of mass being a strictly astronomical affair. Indeed, with an infinite sequence of physical units, no smallest one and no largest one, each an organized system of smaller units, and none eternal, one can hardly escape the hypothesis that energy runs up and down the entire sequence, and that on the whole as much energy is ascending as is descending.

The rate at which radiant energy is being absorbed in space, and consequently the rate at which atoms are being formed, must be very small relative to the standards of a physical laboratory. Trigonometric parallaxes show that there are only six or seven thousand stars within 100 light years of the sun, while estimates for the entire galaxy run from one to two billion. The distance of most of the stars must be great as compared with 100 light years. Assuming the rate of loss of energy to be proportional to the distance travelled, we find that the radiant energy decreases according to an exponential law, and since the reliable distances are certainly very great the rate of loss must, with equal certainty, be very low. But if this loss is only one per cent. in one hundred light years, the Andromeda nebula is at a distance of less than 50,000 light years instead of 1,000,000 light years as at present estimated.

There is nothing particularly strange about the idea that atoms, or electrons, are formed from

38 Astrophysical Journal, July, 1918. See, also, Scientia, January-February, 1923.

smaller units by the addition of a suitable quantum of radiant energy. We all agree that the periodically recurring beauties of the springtime are due to a similar process and that the organic molecules, with their host of marvelous properties, are somehow built up by radiant energy from inorganic molecules. The properties of the organic molecules are not less marvelous than the property of mass, but the rate at which these systems come and go enables us to observe many cycles, while the lives of the atoms are in general very long. Possibly a scientifically inclined mosquito might wonder why the process of vegetable growth has not exhausted the carbon dioxide of the atmosphere long ago.

The hypothesis that atoms are generated by the radiant energy of space does much more than merely account for the blackness of the night sky, which suggested it. It accounts for the existence of that nebulosity with which cosmogonists have always started, and which is so striking a feature of the astronomer's photographs. Even in the apparently dense Orion Nebula it is extremely attenuated, the wonder being that it is visible at all. There is nothing, however, to suggest that these nebulae contract into stars, as was taught during the nineteenth century, and is still largely believed to-day. The twenty million years assigned for the life history of the sun by the contraction theory of Helmholtz is absurdly small even for the requirements of the geologists, perhaps not over one or two per cent. of the required amount; and it vanishes almost completely in comparison with the vast stretches of time which are fundamental in the dynamics of the galaxy.

For example, the close approach of two stars is a primary event in the evolution of a cluster of stars, corresponding to collisions in the kinetic theory of gases. The expectancy of any one star for an approach as close as the earth to the sun, that is, one astronomical unit, is of the order of a million billion (1015) years. If we call such an interval of time an eon, then the eon is a convenient unit of time in describing the history of the galaxy. The statistical studies of Charlier and of Jeans have shown that the galaxy has made observable progress towards the steady state which we can regard as the state of maturity.39 The phenomena of star clusters and star clouds, groups of stars possessing common motion, shows that the galaxy is still a youthful aggregate of stars. Quite likely its present age is to be measured by hundreds of eons, and its state of maturity is still distant by thousands of eons, if it ever arrives. Our information is quite inadequate to probe the possibilities of such vast stretches of time. p. 236.

39 See Jean's "Problems of Cosmogony,"

It should be said, however, that smaller aggregates, the globular star clusters, seem to have arrived at the steady state.

Such considerations force the problem of the source of stellar energies vividly upon our attention. But if the atoms are systems containing energy, as we have supposed, then here is a source that, at least, is worthy of investigation. Possibly in the sun these energies are released just as the stored radiant energy of a cord of wood is set free in a fire. The mechanism of that release is to be found in the intense gravitational stresses which exist in the interior of a star. The earth is a small body astronomically, but the pressure at its center is 22,000 tons per square inch, or a hundred times the greatest pressure attainable in our physical laboratories. For bodies of the same density the pressure varies as the square of the radius. For bodies of the same material in the same physical state, increase of pressure results in increased density, and therefore the pressure increases faster than the square of the radius. A body similar to the earth, but of twice its radius, has a central pressure of 100,000 tons per square inch; double it again, and the pressure rises to 500,000 tons, and we have only reached the size of Uranus and Neptune which are still small bodies astronomically.

If we appeal to the postulate that no organized system can withstand an unlimited amount of violence, it is evident that there is an upper limit to the mass of a solid body. The atoms break down and give up their energy. Imagine the earth to be growing by the addition of meteoric material and nebulosity picked up from space, and imagine this material similar to that which the earth already has. The mass begins to get hot. Permanent gases escape from the interior and enlarge the atmosphere. Eventually, even the surface becomes too hot, and the ocean rises in a cloud of steam. The more volatile substances pass over into the atmosphere, and there is a gradual change from the solid state to a gaseous state accompanied by a marked decline in the mean density. The gaseous state having been reached, a further increase in mass results at first in an increase in density due to compression, just as it does in the solid state. Increase in density can not go on indefinitely in the gaseous state, however, any more than it can in the solid state. The expansive effect of the heat which is liberated by the increasing mass gradually overtakes the compressive effects of gravitation, and there is a second maximum in the density mass curve. For still greater masses the density continues ever afterwards to decline, owing to the excessive generation of heat; the curve becoming asymptotic to the axis of zero density. The mass begins

to glow with a dull red heat, becoming brighter as the mass increases until the entire mass is white hot.

These are consequences which follow from the hypothesis that the atoms are destroyed by sufficiently great gravitational stresses. How does it fit the evidence? Experiment, of course, is out of the question, but we can examine at least some of the astronomical bodies. Commencing with the satellites and planets of our own system, we find that all bodies smaller than the earth are solid and that on the whole the density rises as the mass increases. The next bodies more massive than the earth are Uranus and Neptune, 14 and 16 times the mass of the earth, respectively. Their density is approximately the same, and about one fourth of the density of the earth. The maximum solid body is apparently slightly more massive than the earth, and Uranus and Neptune are in the transitional stage from solids to gases.. Passing next to Saturn, which is 95 times as massive as the earth, we find a density only .6 that of water. Saturn is near the beginning of the dark gaseous state. Jupiter is more than three times as massive as Saturn and its density is nearly twice as great. Jupiter is the largest dark body in our planetary system. There are not enough bodies in our system to locate exactly the second density maximum. There is also a value at which the mass becomes red hot, and is therefore a dull, feeble star. This point is perhaps 100 times the mass of Jupiter, as there is no star whose mass is known to be less than one tenth of the mass of the sun.

One of the fundamental modern contributions to our knowledge of the stars was made by Russell in 1911 in establishing, by statistical methods, the existence of the dwarf and giant series, a classification due originally to Hertzsprung, on the basis of absolute luminosities. Stars of all spectral classes occur in both series. The dull-red, dwarf stars were found to be dense, and to average one half the mass of the sun. As the stars of the dwarf series brightened and became yellow and then white, the average mass increased and the density decreased until for the very white stars the mass was five and one half times the mass of the sun. Passing then to the giant series, as the star's colors passed from the white to the yellow to the red, the mass still further increased to about fifteen times the mass of the sun, while the luminosity increased but slightly, and the density fell to very low figures.

Russell's interpretation40 of these facts was very different from that which I am suggesting, but it can not be doubted that these facts are precisely those which I should anticipate. In the case of the giant 40"The Observatory," 1913, 1914.

red stars with a diameter of two or three hundred millions of miles, the furious radiation near the center must be blue white, but this type of radiation can not penetrate its enormous atmospheric envelope, which is of course relatively much cooler; and the star is red, partially for the same reason that the sunset is red, partially because the radiations from the relatively cool atmosphere also are red.

The energy which a star can draw from its own mass is limited, just as the energy which it can draw from the contraction theory is limited. But as a star moves through space it picks up atoms and molecules or stray meteors or a comet and adds to its mass. Occasionally it enters a distinctly nebulous region, and its mass grows with relative rapidity. We have only to suppose that, on the whole, it picks up as much mass as it loses by radiation to provide for an indefinite duration to its period of luminescence. Its brightness will fluctuate with its mass. At times it will decline to the point of extinction; at other times it will pass over into the giant stage.

Let us see what we might anticipate for the future of our solar system during the next few eons. The mass of the sun will fluctuate, but the planets can scarcely do anything but grow. When the sun declines in mass the planets will recede, the distances of the planets being inversely proportional to the sun's mass. Under these circumstances, the planets become more sensitive to the perturbations of passing stars, and there is greater possibility of the eccentricities being increased. When the mass of the sun is growing, however, as it will when in a densely nebulous region, the planets are growing too. Assuming that the ratios of the masses are maintained, the planets draw closer to the sun, the distances being inversely proportional to the cube of the masses,11 and the eccentricities tending towards zero. If the material is gathered in at random from all directions the planets will grow without substantially altering their distances, or eccentricities. In this manner we see the planets gradually growing towards starhood. Let us suppose that Jupiter has grown to be a dwarf red star, while the sun has just held its own. The distance between them will be reduced, but how much will depend upon the circumstances of growth. Let us suppose it is one half their present distance. Suppose finally they enter a nebulous region, and their masses slowly grow to four times their initial masses. Their distances will be reduced to four million miles and their period to about a day and a half. Jupiter and the sun will form a typical spectroscopic binary star. The earth and the inferior planets will have been

41 See MacMillan, "The growth of the solar system,' American Mathematical Monthly, October, 1919.