Although I have never associated colors with letters or figures, from my earliest recollection I have always thought of letters and of figures arranged in the relative positions shown on page 395. The origin of this I do not know. It might have been something in the presentation of these things by my first teacher, or the manner in which little wooden sticks were laid out on my desk in the first number work. These little sticks, each about 3 mm. in diameter and 20 mm. long, had been split out of pine for me by my father. Occasionally I used to chew up one of them, because it tasted sweet.

EVANSTON, ILL.

ARTHUR B. SMITH

QUOTATIONS

WAR AND ENGINEERING EDUCATION

LAST week some 500 colleges opened their doors to receive some 150,000 students. These young men were inducted into the Students' Army Training Corps and have thus become candidates for commissions in the army. The part of the engineering colleges will be to train men especially for the Engineer Corps, the Signal Corps and the Chemical Warfare Service, and it may be noted with pardonable pride that the training previously given in engineering is considered the best preparation for these branches of the service. Under the new regime, however, the maximum time allowed for the full engineering course is two years, including work in the summer quarters, and the further training of men with advanced standing will be curtailed accordingly. Each college will be expected to outline its courses much on its own initiative, especially for men who have already spent a year or more in that institution.

neering education for war we are reminded of the work done by teachers in the engineering colleges beginning a year ago last May, when they were asked on about two weeks' notice to prepare to receive men for training in military aeronautics. While the lecture material and laboratory apparatus were collected and arranged under difficult circumstances, the officers in responsible charge in Washington were enabled to choose the best methods developed in the six different schools and thus quickly arrange a satisfactory training course. It is to be hoped, however, that the engineering colleges will not follow in the footsteps of the aviation schools in at least two respects. It seems undesirable to put civilian instructors in uniform and certainly a mistake to have them decorated with brevet officers' bars. An instructor with any character should have no trouble in gaining the respect of his classes in this serious undertaking. Again, in the matter of standardization we trust the engineering colleges will not make animated phonographs of their teachers.

It is quite evident that the War Department has outlined an excellent device for producing a high grade of men to lead the army. Those who are left behind in their college work are transferred to army cantonments, while those who complete their college courses with credit are sent to officers' training camps and there must prove their ability to handle men before they receive commissions. Only the most capable men will survive such tests.

While we are thus assured that the primary purpose of developing a high class of officers will be attained, it is interesting to speculate upon the effect of this intensive training on engineering education. Much of the preliminary work in mathematics, languages and science will be eliminated or curtailed, and we shall have an opportunity to view the results of this system of education, provided that the war lasts several years. On the one hand, it is doubtful if these men will have the training which will probably be required for meeting the tremendous problems of reconstruction. It would seem desirable, therefore, to encourage

tion after the war, and the plan of giving credit for the intensive war courses toward a degree in engineering should be adopted. On the other hand, it is reasonably certain that the character of the men who complete the new engineering courses will be excellent, and the colleges should insist upon this high standard of scholarship and character after the war.The Electrical World.

SCIENTIFIC BOOKS

Annals of the Astronomical Observatory of Harvard College. Vol. 79, Part 1. 4°, pp. 86; Vol. 83, Part 2, 4°, pp. 28; Vol. 91, 4o, pp. 290. Edward C. Pickering, Director. Cambridge, Mass. 1918.

The Annals of the Harvard College Observatory occupy a unique position in the literature of astronomy by reason of their great extent and the wide range of subject matter included in them. Collectively they form an impressive memorial to the indefatigable director who has inspired the production and publication of more than three fourths of the four score volumes composing the series. In diversity of subject matter, in successful coordination of effort and in condensed presentation of material the three volumes briefly cited above are typical of the institution from which they come.

The first of the three, prepared by Leon Campbell, contains observations of three hundred and twenty-three variable stars made during the years 1911-16, in continuation of a program commenced twenty-two years earlier. In accordance with the general policy of the observatory its purpose is the accumulation and preservation of reliable data for future study of the changes in the amount of light received from stars of the class designated variables of long period. These changes of brilliancy are notoriously irregular in character and our knowledge of the causes upon which they depend is only fragmentary. The relation between these causes and the data furnished by the present volume is committed to the future investigator.

The second volume cited, prepared under the direction of Alexander McAdie, lies in the very different field of meteorology and con

tains observations made at Blue Hill Observatory (Mass.) in the year 1917. Apart from a brief preface the work is wholly tabular in character and contains both in detail and in summarized form the customary meteorological data.

The last of the volumes named above, prepared jointly by Annie J. Cannon and Edward C. Pickering is an initial installment of the Henry Draper Catalogue of Stellar Spectra, to be completed in seven more similar volumes. For the most part its pages are tabular in character and are intended to place at the disposal of the theorist, data as accurate and as extensive as can be derived from the great store of Harvard photographs of stellar spectra, relative to the spectrum and magnitude of a great number of stars, so chosen as to be typical of every part of the sky. These photographs, taken partly at Harvard and partly in Peru, have been laboriously examined and classified by Miss Cannon and others and the result of four years of such labor is a catalogue showing as its chief data the magnitude and the spectral type for more than 200,000 stars. The classification is naturally upon the system originated at Harvard and now in general use, in which for the most part, stellar spectra constitute a continuous sequence whose chief divisions are represented serially by the letters B, A, F, G, K, M, with subdivisions of these classes upon a decimal system. The physical significance of this series is recognized to be of fundamental importance in every investigation of the larger problems of stellar astronomy. In accordance with its distinctly enunciated plan that we have noted above, the present volume is devoted to the preparation of material out of which the implications of this series may be worked more perfectly than has yet been done. As a contribution to that end the introduction to the volume contains explicit definition and illustration of each spectral class and of many of their subdivisions, presented in brief but very convenient form.

The three volumes are worthy additions to long line of predecessors whose characteris

tics have become so well determined and so familiar that if title pages were removed and all reference to the authors deleted, no astronomer could be left in doubt as to the source from which they came.

GEORGE C. COMSTOCK

UNIVERSITY OF WISCONSIN

The Chemistry of Food and Nutrition. By HENRY C. SHERMAN. Second edition. New York, The Macmillian Co. 1918.

This well-known text-book has been rewritten and presents modern knowledge upon the subject of nutrition in an exceptionally clear and readable form. The chemistry of foods is described, then the digestion and metabolism of the different food-stuffs. The review of the subject of the "vitamines" and of "growth hormones" is excellently handled and nowhere have these "accessory factors" in nutrition been more clearly defined. Sherman's long experimental studies of the salt metabolism and especially the calcium metabolism give authority to his discussion of the inorganic food-stuffs. The chapter on the dietary standards and economic use of food is of an order of excellence which has never been surpassed. Sherman's experience, based upon his own painstaking researches into the dietary habits of the poor classes of New York City, conducted for the New York Association for Improving the Condition of the Poor, leads him to declare that "the most frequent deficiency in American dietaries is inadequacy of the total food or energy value and most dietaries actually observed are of such composition as would furnish enough of each essential element if the total amount of food eaten were sufficient to provide a liberal energy supply."

Sherman clearly sets forth the principles of a sufficient and economical dietary in such a manner as to bring to mind the really great progress in the science of dietetics which has taken place in the last decade. This excellent and thoroughly scientific treatise upon nutrition should be in the hands of all who are interested in the food question, both as it appears now and as it will shape itself after

the war. It is a pleasure to note that the author has been unusually conscientious and generous in giving credit to the work of others. GRAHAM LUSK

SPECIAL ARTICLES

THE FORMATION OF THE FAT DROPLETS IN THE CELLS OF TISSUE CULTURES EXPERIMENTS of Daddi (1896)1 and more particularly those of Riddle (1910) 2 show that Sudan III., fed to animals, is taken up by fat in the intestine, passes through the intestinal wall in combination with fat, and is deposited in the body cells in the form of red fat globules. These observations suggested a method for testing out the question as to whether or not the mitochondria form the fat droplets. If Sudan III. remains attached to the fat, as Riddle seems convinced it does, and the cells store up this Sudan III. fat, the question arises, is the Sudan III. fat deposited in the mitochrondria before appearing as red fat globules in the cytoplasm? If such were the case, we should be able to find traces of the Sudan III. in the mitochondrium, at least during the final stages in the formation of the fat droplet, but this could not be done, and as will be seen below, the mitochondria take no part in the formation of the fat droplet under such conditions.

The yolk of a hen egg was mixed with Sudan III. until it became red. A small quantity of this red yolk was then diluted with Locke-Lewis solution and placed on a number of twenty-four-hour cultures of 6-9-day chick embryos (Lewis and Lewis method). Certain of the cells were then selected and their unstained fat droplets noted and drawn. Each of these cells was carefully followed for the next few hours, or until a number of fat droplets had appeared in the cytoplasm. These took the form of exceedingly small, reddishyellow droplets, often far removed from any

1 Daddi, L., "Nouvelle méthode pour colorer la graisse dans les tissues,'' Arch. Ital. de Biol., 26, 1896.

2 Riddle, O., "Studies with Sudan III. in Metabolism and Inheritance," Jour. Exper. Zool., 8, 1910.

mitochondrium. The mitochondria at no time contained any orange-colored droplets or any droplets at all. Neither did they become rounded, loop- or ring-shaped. As a matter of fact, they behaved in a manner quite like what has been described as normal for the cells of tissue cultures (Lewis and Lewis, 1915). Once a loop-shaped mitochondrium was seen, but this unbent and became a thread again without the formation of any globule. The very small orange-colored droplets unite into larger ones, others appear in the cell, and thus in the course of five or six hours several additional fat droplets of different sizes can be seen. While this process is going on, the fat droplets previously noted and drawn take on a bright orange stain, so that in a very short time it is impossible to distinguish by means of color those droplets which were present in the cell before the addition of the Sudan III. yolk. The color exhibited by the fat droplet in the living cell, while a bright yellowish-red, was never the same shade as that obtained in a culture fixed and stained with Sudan III. Nile blue sulphate could not be used in these experiments because as has been previously shown, it stains bodies that are not fat in the living cell. The fat droplets of the mesenchyme cells remain distinctly smaller than those of the clasmatocyte. Neither the mesenchyme cell nor the clasmatocyte were ever observed in the process of engulfing a yolk globule. It is doubtful whether either type of cell ingests fat in tissue cultures.

Certain of the cultures, which when living contained no loop- or ring-shaped mitochondria, after the application of different fixatives contained in varying numbers swollen, varicose and ring-shaped mitochondria according to the method of fixation employed. The question of fixation is necessarily quite different in these cultures, since most of the cells are spread out in a thin layer unprotected even by plasma from the direct action of any chemical placed upon them. Nevertheless since certain forms of mitochrondria were shown in

3 Lewis, M. R., and Lewis, W. H., "Mitochondria and other Cytoplasmic Structures in Tissue Cultures,” Amer. Jour. of Anat., 17, 1915.

these cultures to be the result of the method of preservation, it would certainly seem probable that these same shapes observed by other investigators (Dubreuil, 1911 Guilliermond, 1913), were obtained in the same manner.

In the above observations there was no need to resort to fixed preparations, as all the structures of the cell were clearly seen, and the bright orange-colored droplets could be followed without fear of confusing them with the easily distinguishable mitochondria. The fat droplets accumulated in the living cell without being associated at any time with the mitochondria and without any changes taking place in the shape of the mitochondria such as have been claimed by other observers (Dubreuil 1911, Russo 1910, etc.).

MARGARET REED LEWIS

THE AMERICAN MATHEMATICAL

SOCIETY

THE twenty-fifth summer meeting of the society was held, by invitation, at Dartmouth College, Hanover, N. H., on Wednesday, Thursday and Friday, September 4-6, 1918, connecting with the meeting of the Mathematical Association of America, which began on Friday morning. The joint dinner of the two organizations, on Thursday evening, was attended by fifty-six members and friends, who were greeted by Dean Laycock in the name of the College. At the joint session on Friday morning Professor A. G. Webster gave an address on Mathematics of warfare."

The college dormitories were opened for the accommodation of the visitors, and meals were served in the commons. Headquarters and general gathering place between the sessions was provided in College Hall, where an informal reception was held on Wednesday evening. A letter of welcome from Business 4 Dubreuil, G., "Les nitrochondries des cellulesadi peuses, "Compt. rend. Soc. Biol., 1911.

5 Guilliermond, A., "Sur les nitrochrondries des champignons, Compt. rend. Soc. de Biol., 1913. 6 Russo, A., "Sui mutamenti che subiscono i mitochondri ed i materiali dentoplasmici dell oocite di coniglia in diversi periodi di inanizione," Arch. f. Zellf., 4-5, 1910.

Director Keyes tendered the hospitality of the college to the two societies. Excursions into the country about Hanover were arranged for the closing days of the meetings. At the joint session a vote of thanks was extended to the college authorities for their generous cooperation toward a successful occasion.

The meeting of the society included an evening session on Wednesday and the usual morning and afternoon sessions on Thursday, besides the joint session on Friday morning. The attendance included forty-six members. Professor W. W. Johnson presided at the Wednesday session, and Professor H. W. Tyler at the Thursday sessions. The following new members were elected: Professor A. L. Candy, University of Nebraska; Mr. J. R. Carson and Mr. R. S. Hoyt, American Telephone and Telegraph Company; Dr. K. W. Lamson, Columbia University; Professor A. S. Merrill, University of Montana; Mr. F. H. Murray, Harvard University; Mr. H. W. Nichols, Western Electric Company; Professor W. E. Patten, Government Institute of Technology, Shanghai, China. Nine applications for membership were received.

The following papers were read at this meeting:

C. H. Forsyth: "Relative distributions." W. D. Cairns: "A derivation of the equation of the normal probability curve.”

Mary F. Curtis: "Curves invariant under point transformations of special type."

G. D. Birkhoff: "On stability in dynamics." Daniel Buchanan: "Periodic orbits on a surface of revolution."

A. R. Schweitzer: "On the iterative properties of an abstract group (third paper)."

C. N. Haskins: "On the roots of the function P(x) associated with the gamma function" (preliminary communication).

Christine Ladd-Franklin: "Bertrand Russell and symbol logic."

Abstracts of the papers will appear in the secretary's report in the November Bulletin. The next regular meeting of the society will be held at Columbia University on Saturday, October 26.

The society has recently published Part I.

G. A. Miller: "Groups generated by two operators whose relative transforms are equal to each other."

P. J. Daniell: "Differentiation with respect to a function of limited variation."

B. F. Groat: "Models and hydraulic similarity."

L. C. Mathewson: "On the groups of isomorphisms of a system of abelian groups of order pm and type (n, 1, 1, . . ., 1).”

C. N. Reynolds: "On the zeros of solutions of linear differential equations of the fourth order."

J. E. Rowe: "Related invariants of two rational sextics."

W. W. Johnson: "The nature and history of Napier's rules of circular parts."

O. E. Glenn: "On a new treatment of theorems of finiteness."

tures being the lectures given by Griffith C. Evans on "Functionals and their applications: selected topics, including integral equations" at the Cambridge Colloquium, 1916.