from teaching fellow to associate in medical entomology.

DR. LOUIS J. GILLESPIE, professor of physical chemistry at Syracuse University, who was formerly with the Department of Agriculture, Washington, D. C., has resigned to go to the Massachusetts Institute of Technology as assistant professor of physico-chemical research.

DR. ARTHUR F. BUDDINGTON, Ph.D. (Princeton, '16), and Dr. Benjamin F. Howell, Ph.D. (Princeton, '20), have been appointed assistant professors of geology at Princeton University.

DISCUSSION AND CORRESPONDENCE MODERN INTERPRETATION OF DIFFERENTIALS

66

IN an advance copy of a note to SCIENCE, which Professor Huntington has kindly sent to me, he says that some indication as to the manner in which N is to vary" is necessary to define dy = lim NAy. This is not true. Of course, there must be some relation between N and Ay, in order that, for example, lim Nay=5, but the number of such relations is infinite, and it is only necessary to know that they exist. For example, if Ay = (5/N)+(8/N2), then NAy=5+ (8/N), and for lim N= ∞o, lim Ay=0, lim NAy=5. It was stated in my note which Professor Huntington is criticizing1 that N varies from zero to infinity. We are not concerned with the method of approach, but only with the possible value of the limit. The preceding illustration shows that if y be an independent variable, such limit dy exists, and in any value we please to name. It is different if It is different if y be dependent, and my note in SCIENCE of May 7, contained a demonstration that df(x) exists when the graph of f(x) has a tangent, and determines its construction, corresponding to any value of dx, including in particular, dx = Ax, which is, of course, not always true.

The problem of differentiation is larger than that of a single value, since it determines an infinite number of corresponding values. We have the analogy of the infinite number of corresponding values of the derivative variable 1 SCIENCE, February 13.

and its argument x. We justify this variable as a limit on the ground that it is a true limit for each numerical value of x. The example having been set, its extension to differentials can not be denied.

The infinite number of corresponding differentials (dx, dy, dz) pertain to the one set of corresponding variables (x, y, z), just as the increments (Ax, ▲y, Az) pertain to it, and are corresponding increments of the instantaneous state of the variables, also, increments in the first ratio (Newton's " first ratio (Newton's "prime" ratio), etc. This is not a vague idea but one which, in numerical cases, determines numerical values. The source of this terminology is the physical idea that equimultiples of very small simultaneous increments are approximately incre ments of the instantaneous state. The differential analysis of Newton, which carries this idea to its logical conclusion, is therefore the mathematical foundation for such physical idea.

It is easy to make statements appear vague by separating them from the facts on which they are based, and such facts appear in the article from which Professor Huntington quotes, with a figure showing the finite equimultiples which are becoming exact differentials-differentials which his "modern" method can not represent, since they pertain to a system of two independent variables, and of which the derivative calculus can give no adequate idea. although they are of great practical importance.

Such so-called modern method is crude in its limitation dx: = Ax, narrow in its application only to plane curves in rectangular coordinates. A natural extension to space is impossible, but Newtonian differentials are coordinates of tangent planes, from their points of contact as origin. By Newton's method, all kinds of continuously variable quantity, in plane or space, lines, areas, volumes, forces, may have corresponding differentials represented in finite quantities of the same kind, and by the limits of finite and visible values.

ARTHUR S. HATHAWAY
ROSE POLYTECHNIC INSTITUTE

NOTE ON DISTRIBUTION AND SPERMATOGENESIS OF MYRIAPODA

DURING the spring of 1912, while working on the Myriapoda of Kansas at the University of Kansas, the writer had occasion to examine a bottle containing several specimens of Scolopendra, each of which had been dissected and had had the gonads removed. As there was no label with them, the matter was called to the attention of Dr. C. E. McClung, who stated they were some of the specimens used by Dr. Maulsby W. Blackman in his work on the spermatogenesis of the Myriapoda, which he started at the above-named institution and later continued at Harvard University. As a result of his observations, the writer is convinced a mistake was made by Blackman in the identification of the form used.

Blackman's first paper1 on the subject states that the specimens used were collected in June, 1900, in Russell county, Kansas, by Mr. W. S. Sutton and are "the large reddishbrown Scolopendra, found abundantly in the southwest. It is a large centipede, about four inches long and four lines across." In his second paper, he identifies the specimens he was working on as S. heros, but in regard to the location where his material was collected, simply states that this paper is in the nature of a by-product of "a detailed study of the spermatocyte changes in Scolopendra heros, now practically ready for publication." This second paper was published from the University of Kansas, so evidently he used the same material that he did in his first and third papers on the subject. In his third paper of the series, he identifies his speci

1 Blackman, M. W., "Spermatogenesis of the Myriapods. I. Notes on the Spermatocytes and Spermatids of Scolopendra," Kans. Univ. Quart., 10: 61-76, pls. 5-7, 1901.

2 Blackman, W. M., "Spermatogenesis of the Myriapods. II. On the Chromatin in the Spermatocytes of Scolopendra heros," Biol. Bull., 5: 187217, 22 figs., 1903.

3 Blackman, W. M., "Spermatogenesis of the Myriopods. III. The Spermatogenesis of Scolopendra heros," Bull. Mus. Comp. Zool. Harvard, 48: 1-138, pls. 1-9, 1905.

mens as S. heros, and says that most of the work was done on forms collected in Russell county, Kansas, but "later a number of specimens of the same variety of S. heros were received from Beulah, Colorado, through Mr. R. E. Scammon." The last paper in the series referring to this particular species of centipede was based on the same material "which served as a basis of several previous papers (Blackman :01, :03, :05), the majority of the slides having been mounted nine years."

The specimens seen by the present writer, and which formed part of Blackman's material, were Scolopendra polymorpha and not S. heros, as he designated them. A mistake in the identification of these two forms could easily occur, as each species is very variable not only in color but also in anatomical details, and they have been considered as synonymous by some writers, for example Bollman," whose writings were undoubtedly followed in making the original identification. However, they have been considered as distinct species for some time," the main difference between the two being that S. heros has two fine longitudinal lines or furrows on the cephalic plate which diverge cephalad, while S. polymorpha is without these lines.

The geographical distribution of the two forms also confirms the fact that Blackman was mistaken, as there is no record of S. heros having ever been taken north of the southern tier of counties in Kansas, while S. polymorpha is known to occur throughout the state. Russell county, where Blackman's ♦ Blackman, M. W., "Spermatogenesis of the Myriapods. VI. An Analysis of the Chromosome Group of Scolopendra heros,” Biol. Bull., 19: 138– 159, pls. 1-2, 1910.

5 Bollman, Charles Harvey, "The Myriapoda of North America,'' Bull. U. S. Natl. Mus., No. 46, 1893. (See pg. 175.)

Kraepelin, Karl, "Revision der Scolopendriden," Jahrb. Hamb. Wiss. Anat., 20: 1-276, 1903.

7 Gunthorp, Horace, "Annotated List of the Diplopoda and Chilopoda, with a Key to the Myriapoda of Kansas," Kans. Univ. Sci. Bull., 7: 161-182, pl. 20, 1913.

specimens came from, is some one hundred and twenty-five miles from the southern boundary, in the center of the state. Regarding the specimens from Beulah, Colorado, which Blackman recognized as the same variety of S. heros" as those collected in Kansas, the altitude of this place (over 5,000 feet) would strongly preclude the possibility of S. heros, a sub-tropical form, being found there. Also, the fact that Blackman does not record any difference in the germ cells of these Colorado specimens from those collected in Kansas would prove that they were one and the same species.

WASHBURN COLLEGE, TOPEKA, KANS.

HORACE GUNTHORP

QUOTATIONS

THE ENDOWMENT OF BIOCHEMICAL RE-
SEARCH IN ENGLAND

OUR university correspondent at Cambridge sends us the announcement of a munificent benefaction about to be made for research in biochemistry. A minimum aggregate expenditure of £165,000 is contemplated, and this sum, if necessary, will be supplemented. The scheme includes the erection of buildings on a site to be provided by the university, equipment, provision for maintenance, £25,000 for the endowment of a professorship, and £10,000 for a readership. The money comes from the residuary estate of the late Sir William Dunn, banker and merchant, and Liberal member for Paisley. The testator died in 1912, leaving a fortune valued at a million pounds, and appointing the directors of the Commercial Union Assurance Company as trustees, with some discretionary powers as to the disposal of his residual estate. There were pencil alterations in the text of the will, and it was only after a lawsuit that the trustees were able to act. They appointed an advisory committee under the chairmanship of Sir Jeremiah Colman, and many schemes were considered. Numerous and substantial gifts have been made to well-known philanthropic institutions, but the trustees reserved a large sum to provide a lasting and fitting memorial of Sir

William Dunn's generosity and to carry out his expressed wishes for the alleviation of human suffering and the encouragement of education. The benefaction to Cambridge should serve both these objects. Certainly it represents one of the most munificent and complete gifts ever made to one of the older universities. Only last month we congratulated the University of Oxford on Mr. Edward Whitley's offer of £10,000 towards the endowment of a chair of biochemistry, and on a donation of £5,000 from the British Dyestuffs Corporation to the laboratory of organic chemistry. We may hope that the friends of Oxford and of scientific research will do something to equalize the good fortune that has come to Cambridge. The chemical activities of the living cell and the living tissues provide a limitless field of research. Knowledge of them is only beginning, and until the methods and results of biochemistry have been developed, the practise of medicine will remain empirical, and fashions in drugs will change as quickly as fashions in ladies' hats. The old universities have the tradition of research, and their spirit of detachment supplies an atmosphere suitable to inquiries not too closely bound to immediately utilitarian objects. We rejoice in the great opportunity given to Cambridge, and do not doubt but that she will prove worthy of itThe London Times.

SCIENTIFIC BOOKS

Die Stämme der Wirbelthiere. By OTHENIO ABEL. Publ. 1919 by Verein wiss. Verlegn., W. de Gruyter and Co., Berlin and Leipzig. 914 pages, 669 text figures.

It is to be regretted that there is no good comprehensive modern text-book in English dealing with vertebrate paleontology. The researches of the last twenty years have perhaps made less change in fundamental viewpoints and theories in this than in some other branches of science. But they have added enormously to the data of facts upon which it rests, and knit closer its relationships with the cognate sciences, geology on one side, zoology and comparative anatomy on the other.

Dr. Abel is professor of paleobiology at the University of Vienna, a pupil of the great Belgian scientist Louis Dollo, and a leading authority in his profession. He is the author of two earlier text-books, "Paleobiologie" and "Die vorzeitlichen Säugethiere," the first of which was reviewed in SCIENCE some years ago.

The present volume treats of the origin and evolution of the various phyla ("Stämme ") of vertebrates as shown in the paleontologic record. It is concerned almost wholly with extinct forms; and thanks to this limitation the author has been able to give an unusually full treatment and discussion, especially of the reptiles and Amphibia. The illustrations, while somewhat crude artistically, are excellent for teaching purposes, and its full discussion and fair treatment of recent foreign discoveries are remarkable in a volume prepared and published under war conditions. From first to last Dr. Abel has endeavored to discuss the evidence and give reasons for the conclusions adopted, leaving the way open for difference of opinion on many doubtful problems. A certain unevenness of treatment is manifest, both in the discussion and the taxonomic arrangement, and many details of presentation and classification are open to criticism, as is inevitable in a volume of such wide scope and fundamental treatment. From errors of fact the book is singularly free.

A classified list of the orders and families accepted, with characteristic genera, serves as a preliminary conspectus. To the fishes are allotted 160 pages, partly introductory and dealing chiefly with the early and primitive types. The vast variety of modern bony fishes are treated in a very cursory manner. The Amphibia cover 110 pages, devoted mostly to the Paleozoic types and their relations to the higher vertebrates. The extinct reptiles are quite fully treated, the discussion covering some 355 pages. The most serious criticisms to be made in this section are of the splitting of the pterodactyls into two distinct orders, and the attempt to limit the term dinosaurs to one of the two great orders of gigantic land reptiles that are now under

stood to be included in the old usage of the name. It would be better to retain it with the old scope but in a general unsystematic sense, like "pachyderms among the mammals. On the other hand, the discussion of important researches and discoveries among fossil reptiles and their bearing on the evolution of the vertebrates affords an excellent synthesis of recent progress in the science. Birds are a rather minor group among fossil vertebrates, and 23 pages suffice to cover all the important types in their evolution.

The treatment of the Mammalia is relatively brief, covering 167 pages, passing very briefly and uncritically over some of the orders, and hardly touching upon the Primates, but more extended with other groups, and especially authoritative in the Cetacea, upon which the author has published several very valuable researches.

While by no means endorsing all of the author's views upon problems of evolution and classification, the present reviewer does not hesitate to commend Dr. Abel's work as highly authoritative and up to date, admirably presented as to form and reliable as to fact. The treatment of the subject differs widely from that in the new edition of Zittel's "Grundzüge der Paläontologie," recently revised by Schlosser and Broili, which affords in many ways an excellent supplement for Abel's volume, especially in its more comprehensive treatment of the Mammalia.

W. D. MATTHEW AMERICAN MUSEUM OF NATURAL HISTORY

SPECIAL ARTICLES

AN ULTRAMICROSCOPIC STUDY OF THE TWO STAGES OF BLOOD COAGULATION1

SCHMIDT2 has described carefully the process of coagulation as it may be followed with the naked eye in the cell-free plasma of a slowlyclotting mammalian blood (horse). He drew attention to the fact that the process may be

1 From the Physiological Laboratory of the Johns Hopkins University.

2 Schmidt, "Zur Blutlehre," Leipsig, 1893, p. 262.

separated into two distinct stages from the standpoint of the changing physical properties and macroscopical appearance of the plasma during the progression of clot-formation. First, the fluid plasma is seen to be transformed into a definite but transparent coagulum of which, 66 on pressure between the fingers, almost nothing remains." This delicate coagulum marks the first visible or palpable stage in the development of the clot. On standing, the transparent, almost structureless, yellow coagulum is observed to become gradually more and more turbid; until at length the second stage is reached, in which the coagulum appears quite opaque and whitish, and assumes the typical characteristics of a firm, fibrin clot. By the use of paraffined vessels and low temperature, the coagulation of human or cat's blood may be delayed sufficiently to permit centrifugalization in order to obtain a clear, cell-free plasma for observation; or one may study the coagulation which follows the recalcification of a centrifugalized oxalted plasma. In either of such quickly-clotting plasmas it is, of course, more difficult, but nevertheless quite possible, to divide the progress of coagulation into the two stages described above.

The transparent-stage and the opaque-stage of blood-coagulation are certainly striking physical phenomena. The question accordingly presents itself: Has each of these stages a separate, underlying causal reaction, or do they represent gradations in a continuous transformation of a sol into a gel? Are the two separate stages superimposable upon separate reactions occurring between the coagulation factors, or does the transparency or opacity of the plasma, as well as its consistency, merely reflect the extent of fibrin-formation?

It seemed that this question might find immediate solution if it could be determined at what point fibrin first makes its appearance during the coagulation of a tube of plasma. In comparison with the appearance of the fibrin which we recognize in a firm, opaque clot, certainly the transparent-stage appears to be entirely fibrin-free. Now it is well known that during coagulation, the formation of

fibrin needles can be followed from the beginning with the aid of the ultramicroscope. Howell has described and figured this beautiful phenomena, in which "bright specks appear first as short rods, which exhibit a genuine saltatory movement, jumping abruptly into and out of focus, and quickly fusing to form longer rods and needles" of fibrin. It was at the suggestion of Dr. Howell that it was decided to use the ultramicroscope as a method of approach to the solution of the question outlined above. The Siedentopf and Zsigmondy slit ultramicroscope, with water-immersion objective was the instrument used; illumination was obtained from a carbon arc-light.

Plasma

After trying various methods, the following procedure was found to yield the most satisfactory results: a horse was bled from the external jugular vein through a paraffined needle into a paraffined tube packed in ice. The blood was taken to the laboratory, filtered through a paraffined funnel surrounded by an ice-jacket, and the cell-free plasma caught in a second iced, paraffined tube. was then, by means of a chilled paraffined pipette, introduced in rapid succession into (1) the cell of the ultramicroscope; (2) a control cell of the same size and shape, not attached to the ultramicroscope, and (3) a homeopathic vial (into which c.c. of plasma was placed in each experiment). These three containers could be filled within ten seconds, so that coagulation began in all three practically at the same moment. Το eliminate any error of interpretation which might conceivably arise from the fact that one vessel was filled a few seconds before another, the order in which they were filled was varied in different experiments. There was, however, no evidence indicating that this theoretical source of error had the slightest influence upon the results in any experiment.

The rationale of using three plasma containers in these experiments may be here explained: (1) The cell of the ultramicroscope was observed closely after filling, in order to determine the time of appearance of the earliest visible needles of fibrin; (2) the homeopathic 3 Howell, Am. Jour. Phys., 1914, XXXV., 143.