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

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 N▲y=5+ (8/N), and for lim N ∞o, lim Ay=0, lim NAy=5. It was stated in my note which Professor Huntington is criticizing 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 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 dr, 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, Ay, Az) pertain to it, and are corresponding increments of the instantaneous state of the variables, also, increments in the 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 increments 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

Herms is Professor S. B. Freeborn, also of the University of California and a small group of students. The present intensive investigation follows a general malara-mosquito survey of California which was completed last summer.

PROFESSOR WARREN D. SMITH, of the University of Oregon, has been given leave of absence to spend a year in geological work for the Philippine government, as chief of the Division of Mines of the Bureau of Science at Manila.

PROFESSOR FRANK T. MCFARLAND, department of botany, University of Kentucky, has been granted a leave of absence for the year 1920-21. He will spend this summer and next year in study at the University of Wisconsin. While on leave, Professor McFarland's place will be filled by Mr. E. D. Hull, a graduate of the University of Chicago.

By action of the convention of the Sigma Xi Society at its meeting in St. Louis, a limited charter was granted to the University of North Dakota. The installation exercises of this chapter were recently held, Dean Lauder W. Jones, of the University of Minnesota, presiding. These exercises consisted in the formal installation of the chapter on the evening of June 2, followed by the initiation of four active members elected from the faculty, and five associate members from the graduates and the senior class. The exercises were followed by a banquet. On the morning of June 3, Dean Jones addressed the university convocation on the subject of "Science and industry." A fuller account of the proceedings will appear later in the Sigma Xi Quarterly.

DR. IRA REMSEN, formerly president of Johns Hopkins University, delivered the commencement address at West Virginia University on June 15. His subject was "This is the Age of Science." After the commencement exercises Dr. Remsen was entertained by the members of the West Virginia Alumni Association of Johns Hopkins, six of whom are heads of departments in the state university.

UNIVERSITY AND EDUCATIONAL
NEWS

CORNELL UNIVERSITY has received an anonymous gift from a professor and his wife of a trust fund for an institute of pure and applied mathematics. The gift amounts to $50,000 and is to be held in trust for a hundred years and allowed to accumulate.

WALLACE W. ATWOOD, professor of physiography at Harvard University, has been appointed President of Clark University, succeeding President G. Stanley Hall, of the university, and President Edmund C. Sanford, of the college. Dr. Hall, who has been president of the University and professor of psychology for thirty-two years reached his seventy-fourth birthday on February 1.

HECTOR JAMES HUGHES, professor of civil engineering and director of the Harvard Engineering Camp, has been chosen dean of the Harvard Engineering School to take the place left vacant by the retirement of Dean Comfort Avery Adams.

W. H. CHANDLER, professor in pomology at the New York State College of Agriculture, has been appointed vice-director of research at the Cornell University Agricultural Experiment Station. Professor Chandler has been at the college as professor in research in pomology since 1913.

DR. NORMAN MCDOWELL GRIER has been appointed professor of biology at Washington and Jefferson College to succeed Dr. Edwin Linton, who has retired under the provisions of the Carnegie Foundation.

DR. ARTHUR W. HAUPT, formerly professor of biology at Carthage College, Carthage, Ill., has been elected to the chair of biology at Saint Lawrence University, Canton, N. Y.

THE following changes have been made in the department of medical zoology of the school of hygiene and public health of the Johns Hopkins University. New appointments: Dr. Chas. E. Simon, lecturer in medical zoology; Mr. D. L. Augustine, assistant in helminthology; Dr. W. H. Taliaferro, from instructor to associate in protozoology; Dr. F. M. Root,

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

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 criticizing 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 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 dr, 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 "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 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

da de subject states www dated in 2. Pianal an. Aarsas by Mr. e large reddishCon dvd abundantly in the Nampak about four Vue *" In his *w* dp av Now the specimens he ***** deve, but in regard to * * * #Aap dis material was collected, interese para paper is in the nature

Apvds ar "a detailed study of the the in Scolopendra heros, Www wwdy for publication." This www poor was published from the UniYogya Kansas, so evidently he used the

material that he did in his first and pers on the subject. In his third poss* of the series, ho identifies his speci

* Maskman, M W., Spermatogenesis of the Mycsapda 1 Notes on the Spermatocytes and Apersualita of Scolopendra," Kans. Univ. Quart., te a cd, pila, & 7, 1901.

•Hankman, W. M., "Spermatogenesis of the Myriapoda 11. On the Chromatin in the Spermafoox.com at Scolopendra heros,'' Biol, Bull., 5: 187217, 29 #gs, 1903,

* Mbackman, W. M.,

Spermatogenesis of the Averopods. 111. The Spermatogenesis of Scolopondra Aeroa, '' Bull, Mus, Comp, Zool, Harvard, 4N. 1 138, pls. 1 9, 1905.

cs as S. heros, and says that most of the vers was done on forms collected in Russell

ny, Kansas, but "later a number of specimens of the same variety of S. heros were received from Beulah, Colorado, through Mr. 3. 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: 138159, pls. 1-2, 1910.

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

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.