been elected full professor of zoology in the Scientific School.

THE following promotions have been made in the department of zoology at the University of California: Associate Professor S. J. Holmes to a professorship; Assistant Professors J. F. Daniel and Joseph Grinnell to associate professorships.

DR. GEORGE R. WELLS, associate professor of psychology in Oberlin College, has been appointed to a new professorship in psychology in the Ohio Wesleyan University, and will assume his duties in September. A psychological laboratory, housed in a separate building, has been provided and is being equipped at the latter institution.

M. P. MARIE, professor of pathologic anatomy at the University of Paris, has been appointed to the chair of diseases of the nervous system, to succeed the late Professor Dejerine. M. Letulle, hitherto professor of the history of medicine, has been given the chair of pathologic anatomy.

DISCUSSION AND CORRESPONDENCE WANT OF ADAPTATION TO THE TIME OF THE PRINTING PRESS

IF the printing press is recognized as the most important instrument for the diffusion of knowledge, the advancement of science requires that it should be used with a precision like that shown in the use of the microscope or in the application of statistical methods.

It seems that this want of adaptation is shown in lack of adequate provision for, and in the common method of, the publication of scientific literature. Gifts to local establishments, in spite of their great value, seem silly compared with a proper endowment for the publication and distribution of scientific separates.

All scientific articles should be printed and sold separately, so that a student could subscribe for the literature of a certain subject. This would not prevent any one from binding together any papers he wished. Scientific publication is in a bad way, if it must be provided for by requiring one to pay for matter one does

not need, and which, as far as one is concerned, is not worth shelf room. I am interested in literature relating to certain bees, but that does not incline me to pay for descriptions of Sarcophagidae which take up eight pages for one species. In the library of the Missouri Botanical Garden I could not find papers by one author because the transactions in which they were printed did not contain enough botanical literature to justify purchase by that institution.

A magazine publishing transient articles is good enough, but one publishing important contributions to science in a various mixture is more or less of a burial place for such literature, whether one considers the persons the authors are trying to reach or those desiring to see the articles. That his writings should reach every one who is interested in them, or would profit by them, is as important for an author as it is for the student to see the writings in which he is interested-and the interests of both are in line with the advancement of science.

That the publishing of heterogeneous articles in journals is objectionable is shown by the practise of printing author's separates. But these are usually unsatisfactorily distributed and soon exhausted. The printing of separates operates against the interests of the journal when a writer avoids subscribing for it on the expectation of receiving the separates from their authors. For the sake of students a discriminative author may be inclined to publish all of his papers on a given subject in the same journal, but the journal may prefer a variety of papers in order to increase its subscription list. So, also, a paper which has some body to it is broken into monthly parts to make room for articles on different subjects. It is a question whether the magazines do not encourage fragmentary and desultory methods of investigation and publication.

On account of objection to too many, or too long, papers on the same subject, or simply inadequate provisions for publication, descriptions of American insects are often published in foreign journals-a practise clearly opposed to the interests of science. However, some au

thors seem to have a mania for scattering literary fragments and may cultivate foreign journals merely for the sake of personal advertising.

Entomological News, 28: 141, after mentioning four journals which lasted an average of five years each, says:

In general it seems that the number of specialists in any one or two orders of insects is not sufficient to support a special journal, and we know of none such provided with an endowment fund guaranteeing its permanency. In this matter we must still be entomologists, apparently, and yet the record of general entomological journals contains many a short-lived periodical.

The significant point here is that, while we are specialists as regards the literature we desire, we are general entomologists as regards the literature we have to pay for.

As educational institutions the university is local, while the printing press is cosmopolitan, the only cosmopolitan university. The publication of scientific literature should not be supported by requiring specialists to pay for literature they do not need, any more than the university should depend for its entire support upon the tuition of its students.

CARLINVILLE, ILLINOIS

CHARLES ROBERTSON

FUNDAMENTAL CONCEPTIONS OF MODERN MATHEMATICS

TO THE EDITOR OF SCIENCE: In your issue of August 4, there appeared a review of the first part of our "Fundamental Conceptions of Modern Mathematics," from the pen of Professor G. A. Miller. Against a hostile criticism, giving a portrayal of at least some of the main theses of our book and attempting to controvert them, we would have no inclination to protest. But all the important issues raised by our treatise are ignored by Professor Miller, who dwells upon features having no bearing upon any of the arguments of our work, or upon any of the doctrines which it is the purpose of the arguments to uphold.

Surely a reviewer can be justly expected to take up at least one or two of the principal doctrines of a treatise of which he disapproves,

and show that these doctrines are erroneous. Our book contains an account of quantities and their classification; an investigation into what the symbols used by mathematicians really stand for. We set forth the classification of quantities into what we call sorts, kinds and varieties, and show the importance of this classification in the subdivision (originally conceived by De Morgan) of algebraic science into single algebra, double algebra, etc. A precise statement is given of what we apprehend to be the nature of the quantities dealt with in quaternions and other systems of vector analysis, and of their relation to the quantities of ordinary algebra. We attempt to show that any really scientific treatment of ordinary imaginary quantities must be based on vector analysis, all imaginary and complex abstract quantities (save those of zero value) being, in fact, relations between vectors. This is, we hold, the only way to ascend, from a blind use of imaginary and complex expressions without any clear apprehension of what they denote, to a rational comprehension of the matter; in other words, from mere computation, and manipulation of symbols, to true science. We show further that the mathematicians who look upon a variable as a quantity and those who regard it as a symbol are equally in the wrong; a variable being represented by a symbol and being composed of quantities. We consider the arrangement of the quantities of a variable, and show the importance of this commonly neglected attribute. We discuss the peculiar arrangements which must be at hand to justify the application of the theory of monogenic functions, and show the relation of these multiplex arrangements (as we call them) to the arrangements of the elements of the aggregates designated by Cantor as mehrfach geordnet. As the simplest of variables we put forward the ordinary progressions of elementary mathematics which are not usually recognized as variables at all. We attempt to show clearly just what distinctions should be drawn between a progression and a series; and, including all progressions and all series under the head of sequences, lay down the conditions under which a variable is to be

classified as a sequence. Passing to the question of functional relation we take up independent and dependent variables, and show that these names correspond to at least three separate distinctions, a fact not ordinarily recognized by mathematicians. We give a somewhat elaborate discussion of functional relations, showing that what is ordinarily put forward as the Dirichlet definition of function does not adequately characterize a functional relation, and moreover is not really the definition given by Dirichlet. We lay down what we deem to be the conditions under which two or more variables may be said to be in functional relation with each other; and show that previous authors, in their treatment of functions, have not attained to a clear and precise view of the essential characteristics of a functional relation.

To these salient features of our work Professor Miller gives no heed whatsoever, though assuredly they comprise topics of fundamental importance in mathematics. He is content to dismiss our inquiries by stigmatizing them as relating chiefly "to definitions and the choice of words." We plead that our work is concerned chiefly with the unfolding of the conceptions which words should awaken in our minds, and not with the words themselves. To purely verbal questions we give scant attention. In our endeavors to attain to distinct and exact conceptions of what is fundamental to the inquiries of mathematics, we have found that the portrayal of these conceptions, as set forth by mathematicians of the highest eminence, are not free from great imperfections. We have spared no labor in obtaining and in stating in full "the definitions given by those who have made important advances in the fields" into which we go; and when unable to assent to these definitions, we have carefully set down our reasons for holding that they do not truly depict the lineaments of the conceptions which they purport to unfold. And Professor Miller, though manifesting his disapproval of our criticisms, makes not the slightest attempt to show that our charges of error are baseless, and that Baire, Pringsheim, Riemann, Russell, Weber, and the other

authorities whom we controvert are not guilty of the errors we ascribe to them.

Three passages of our work are specifically condemned by Professor Miller. All of these are trivial and could be removed from the work without affecting any of its doctrines or any major or minor argument put forward in defense of them. One fault that is imputed to us is that " on page 177 and elsewhere, the common erroneous assumption according to which the word function was used as synonymous with power is repeated." We merely say that "the word function is said to have been used by the older analysts as synonymous with power." We took care to insert the qualifying phrase is said, and so worded our remark is neither an assumption nor an error. And no reference to this usage occurs elsewhere. We are also rebuked for saying that "The only mathematician that we recall as making a specific distinction between quotient and ratio is Hamilton." We must acknowledge that such a distinction has been made by others, but we deny that the distinction we endeavor to enforce is as common as Professor Miller would have it appear. Finally we are chided for applying to imaginary and complex quantities the distinction between positives and negatives. Yet, if precedent is to be a guide, we can plead that both Gauss and Weierstrass used the two adjectives with respect to imaginary quantities.

ROBERT P. RICHARDSON, EDWARD H. LANDIS

QUOTATIONS

SCIENTIFIC SNOBBERY

ONE reason for the neglect of science is that scientific men themselves frequently misrepresent the objects for which they work. For example, they often pretend that they perform their labors merely for their own amusement. We once heard it wittily said of such a man that he takes out his watch before dinner and exclaims, "Ha! I have half an hour before I must dress for dinner; I will just step over to my laboratory and make a discovery." But the public is not so easily deceived and therefore thinks in its dull way that the man of

science really labors in the hope of making some enormous fortune or obtaining some great honor. On another occasion, we heard it said of a man who has been toiling for years in the tropics for nothing, that "nobody knows why he does it, but we all believe that he wants a knighthood." When we timidly suggested that he was guided merely by a sense of duty, we were met by a stare of astonishment. Certainly this worker has never received a penny for his work as yet and never will, and we fear that not even a knighthood will come his way. No, men of science do not work either for amusement or to make fortunes. Like artists and musicians, they often find their labors fascinating because nature imbues them with an instinct in the directions chosen by them; but they are also conscious that their work will bring them no personal profit-not so much as that which a tithe of the ability shown by them in science would have yielded them in politics, law or grocery. Their ultimate object is to benefit humanity by adding to the store of knowledge which lifts the civilized man so far above the savage of the jungles. And that is the greatest object which any man can keep before his eyes.

Another form of scientific snobbery is the pretense that science has no practical object in view-it is so lofty a pursuit that the man of science should live among the stars and not soil his fingers with the common earth of everyday life. Even Lord Kelvin said "that no great law in natural philosophy has ever been discovered for its practical application" -though no one based more patents on his own researches than did Lord Kelvin. He may have been right in one sense, but certainly not in all (and he can not be accused of any form of snobbery). Thus geometry was really founded for the purposes of architecture and navigation. Mechanics was created to assist the engineer, and the theories of heat and of the conservation of energy were probably generated by the steam-engine; while the entire science of pathology has simply been created for its practical application as regards the prevention and cure of disease. Certainly investigations which were apparently useless at the

outset have often led to valuable practical applications; but they were usually undertaken because the worker knew that he must first solve general problems before applying the solution to specific cases. We believe that all the great theorists had practical applications before them like a distant light even in the greatest darkness of their efforts. Is it likely that Newton, or Harvey, or Faraday did not prophetically see that their work would some day benefit humanity? Nature is infinite, and it is therefore wise to toil in immediate contact with human needs and not to lose oneself entirely far away from the remotest utilitarian objects. In most cases those who lose all touch of the useful in their investigations end by becoming useless themselves. They are above the practical, and therefore become unpractical, and finally impossible.

Perhaps the worst form of scientific snobbery is the pretense that the man of science is absolutely above cash in any form. Let us distinguish. To effect discovery, a man must concentrate all his energies upon a single point; he has no time to watch the share market, or to promote companies in connection with his findings; and it will be lucky if he succeeds in making any advance at all even with all his energies bent upon the point of issue. In that sense, therefore, he must ignore cash. But even here various circumstances should influence him. If he is a bachelor, he may do as he pleases, and may live as a recluse upon brown bread and water in a monk's cell if he wish. But if he has children or other dependants, is he justified in allowing them to be brought up uneducated in poverty? Such a thing would not be meritorious in him but a crime; for we have our duties not only to science but to our families. The scientist who pretends his indifference to money is, therefore, often only a snob. Moreover, although he himself may have no children, or may possess independent means, this need not necessarily be the case with others. His quixotic attitude merely lowers the price of science in the world and causes other and probably better men to suffer. Still further, for the most obvious economical reasons, it causes science

in general to suffer, because when young men see the poverty of the most successful investigators they hesitate to enter such fields of labor and the recruiting of the voluntary army of science is naturally reduced. Certainly no scientific man has the smallest desire to be a millionaire; but moderate competence is useful to him as to others. A certain amount of money gives him a proper influence for good in society, and enables him to devote himself to those investigations which his nature tells him he is most capable of conducting. On the other hand, keep him in poverty and he soon loses his enthusiasm; he becomes a fakir sitting in rags by the roadside, and the ripest years of his life are often wasted. Is there any intrinsic reason why the greatest efforts of the best minds in the most fertile of fields should lead to poverty? Yet the history of the world proves that they generally do so -to the loss not only of science but of the world. And why, pray? Because when science asks for her dole, the world replies, "But those great men, Smith and Jones, are proud to labor for nothing; why then should I pay you?" Alas, poor ignorant world does not know that if Smith and Jones are genuine workers they are probably too much engrossed in their toil to bestir themselves for payment; while if, as more often happens, they are merely purveyors of others' labors, then their lofty and popular pose is adopted for a purpose. And, indeed, snobbery is often a paying cult, and those who labor for nothing do little but frequently get much!

In science as in other things, the proper and honest procedure is to pay for work done; and, to be frank, the encouragement of science, of which we hear so much nowadays, must in the end come to this or to nothing. And in science as in other things snobbery is a false pose which brings only contempt upon those who adopt it.-Science Progress.

PROCEEDINGS OF THE NATIONAL

ACADEMY OF SCIENCES

THE third number of Volume 3 of the Proceedings of the National Academy of Sciences contains the following articles:

The Condensation and Evaporation of Gas Molecules: Irving Langmuir, research laboratory, General Electric Company, Schenectady, N. Y. A discussion of the evaporation vs. the reflection theory with conclusions favoring the former.

The Ninth Satellite of Jupiter: Seth B. Nicholson, Mount Wilson Solar Observatory, Carnegie Institution of Washington. Comparison of the orbits of the Eighth and Ninth Satellites. The mean period of the Ninth is 745 days and its diameter is probably about 15 miles.

Aortic Cell Clusters in Vertebrate Embryos: H. E. Jordan, department of anatomy, University of Virginia. The hemogenic activity of embryonic endothelium is a normal function at a certain stage of embryonic development.

Rheotropism of Epinephelus Striatus Bloch: Hovey Jordan, Bermuda Biological Station for Research, Agar's Island, Bermuda. The lip region is the most sensitive part of the body surface. The end organs of tactile sensitivity serve also as organs of rheotropic sensitivity.

Studies of the Genus Phytophthora: J. Rosenbaum, Bureau of Plant Industry, Washington, D. C. A search for determining characters of diagnostic values in testing the different species.

A Possible Function of the Ions in the Electric Conductivity of Metals: Edwin H. Hall, Jefferson Physical Laboratory, Harvard University. A discussion of the number of ions necessary to maintain currents of great density, and of the temperature relations of conductivity if due to ions.

The Gravimetric Survey of the United States: William Bowie, Division of Geodesy, U. S. Coast and Geodetic Survey. A summary of the present status of the subject.

The Magnetization of Iron, Nickel, and Cobalt by Rotation and the Nature of the Magnetic Molecule: S. J. Barnett, department of physics, Ohio State University. A confirmation of the assumption that only electrons are in orbital revolution in all the substances investigated.