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which are always a source of admiration to those who belong to less active institutions. There was a special collection of historical photographs arranged for the occasion; and other interesting features selected from the hundreds of thousands of plates now stored and making a permanent record of the sky.

A session was held at the Whitin Observatory, Wellesley College, and also at the Students' Astronomical Laboratory in Cambridge. On the day after the meeting some of the members visited the Massachusetts Institute of Technology, and others made a short cruise on Mr. W. V. Moot's yacht Adventuress, which is being used for instruction in navigation.

The society adopted with practically a unanimous vote a committee's recommendation that the astronomical day begin at midnight, and that after January 1, 1925, all astronomical dates should be reckoned in this way. This change will cause much trouble and confusion in astronomical work, but was recommended for the convenience of mariners.

In view of the uncertainty of what conditions would prevail in another year, the council took no definite action in regard to the time and place of the next meeting.

Officers were elected for the ensuing year:
President-Edward C. Pickering.

First Vice-president—Frank Schlesinger. Second Vice-president-W. W. Campbell. Secretary-Joel Stebbins.

Treasurer-Annie J. Cannon.

Councilors-E. B. Frost, 1918-20; Otto Klotz, 1918-20; E. W. Brown, 1917-19; S. A. Mitchell, 1918-19.

The program of papers was as follows:

C. G. Abbot: The Smithsonian solar constant observatory at Calama, Chile.

W. S. Adams and A. H. Joy: Spectroscopic observations of W Ursa Majoris.

W. S. Adams and C. E. St. John: The green corona line at the 1918 eclipse.

Robert G. Aitken: The orbit of Sirius.

Robert G. Aitken: The spectral classification of 3919 visual binary stars.

Sebastian Albrecht: Personality in the estimation of tenths.

S. I. Bailey: Note on the magnitudes of the variables in Messier 15.

E. E. Barnard: Nova Aquila No. 3.

E. E. Barnard: The prominences of the total solar eclipse of 1918, June 8.

E. E. Barnard: Some remarkable small black spots in the milky way.

Benjamin Boss: Systematic corrections to and weights of stellar parallax.

Benjamin Boss: Real stellar motions.

Benjamin Boss: Stellar luminosities and absolute magnitudes.

Leon Campbell: The light-curve of Nova Aquilæ No. 3.

Annie J. Cannon: The spectrum of Nova Aquila No. 3.

J. B. Cannon: The spectroscopic binary Boss 1275.

Wm. A. Conrad: A short method of mean place reduction with natural numbers.

J. J. Crane: The reduction of Schönfeld's observations to the Harvard photometric standard of magnitudes.

Ralph E. De Lury: Simultaneous variations in solar radiation and spectroscopic determinations of the solar rotation.

Ralph E. De Lury: Spectroscopic measurements of the sun's rotation.

Ralph E. De Lury: The nature of a supposed cyclic variation in the solar rotation.

Ralph E. De Lury: A possible relationship between numbers of meteors and quantities of nitrogen compounds in freshly fallen rain and snow.

A. E. Douglass: The Steward Observatory of the University of Arizona.

A. E. Douglass: Atmospheric haze causing twilight effects.

Alice H. Farnsworth: The color-index of Nova Aquila No. 3.

Edwin B. Frost: Usefulness of "movie" camera for photographing phenomena of solar eclipses.

Edwin B. Frost and J. A. Parkhurst: The spectrum of Nova Aquila on June 8, 9 and 10, 1918.

Asaph Hall: A brief description of the 26-inch equatorial instrument of the Naval Observatory, and accessories, etc.

Asaph Hall: Account of some of the series of satellite observations made with the 26-inch equatorial.

W. E. Harper: The orbit of the spectroscopic binary 19 Lyncis.

W. E. Harper: The orbits of the spectroscopic components of Boss 5173.

W. E. Harper: The spectrum and velocity of Nova Aquila No. 3.

Margaret Harwood: The variability of Eros in 1900-1901.

F. Henroteau: Note on the spectroscopic binary 55 Ursa Majoris.

Frank C. Jordan: Notes on the light curves of XX Cygni and U Pegasi.

Edward S. King: A new method of determining the color of a star.

Jakob Kunz and Joel Stebbins: Photometric results at the eclipse of June 8, 1918.

C. O. Lampland: Variable stars in the Trifid Nebula (N. G. C. 6514) and the Lagoon Nebula (N. G. C. 6523).

C. O. Lampland: Photographic observations of the variable nebula, N. G. C. 2261.

C. O. Lampland and E. C. Slipher: Some photographic results of the Lowell Observatory solar eclipse expedition.

Henrietta S. Leavitt: The light-curves of eleven


W. F. Meggers: Solar and terrestrial absorption in the sun's spectrum from 6400 A to 9400 A.

John A. Miller: The total eclipse of June 8, 1918.

R. M. Motherwell: Nova Aquilœ No. 3.
R. M. Motherwell: 12 Lacertæ.

Margaretta Palmer: The Yale index to star catalogues.

J. A. Parkhurst: The spectrum of the solar corona at the eclipse of June 8, 1918.

C. D. Perrine: Changes in the spectra of some early-type stars showing hydrogen emission.

C. D. Perrine: Announcement concerning the formation of a new catalogue of fundamental star positions.

C. D. Perrine: The early spectrum of Nova Aquila No. 3.

E. Pettit and Hannah B. Steele: Report of the Washburn llege eclipse expedition to Matheson, Colorado.

Edward C. Phillips: On a mechanical method of reducing transit observations.

Edward C. Pickering: Relation of proper motions to spectra.

J. S. Plaskett: The 72-inch reflecting telescope. J. S. Plaskett: Notes on the spectrum of Nova Aquila No. 3.

Susan Raymond: The variability of Antigone (129).

William F. Rigge: The solar eclipse of 1918, June 8, as observed in Omaha.

Luis Rodés: A differential gravimeter and its applications.

Henry Norris Russell: The orbit of Ursæ Majoris.

R. F. Sanford: The spectrum of Bailey's variable star No. 95 in the globular cluster M 3.

R. F. Sanford: The orbit of the spectroscopic binary star p Velorum.

Harlow Shapley and J. C. Duncan: The globular cluster Messier 22 (N. G. C. 6656).

V. M. Slipher: The spectra of two variable nebulæ: a new type of nebular spectrum.

V. M. Slipher: The spectrum of Nova Aquila, No. 3.

V. M. Slipher: Some spectroscopic results of the Lowell Observatory solar eclipse expedition.

C. E. St. John and Louise Ware: Notes on solar rotation.

H. T. Stetson: War-time instruction at the Harvard Astronomical Laboratory.

H. T. Stetson: Preliminary note on the uniformity of film sensitivity of photographic plates from measures with the thermo-electric photometer.

R. M. Stewart: The position of Nova Aquila No. 3.

David Todd: On the construction of high-level laboratories for scientific research.

Robert Trümpler: The position and proper-motion of Nova Aquila No. 3.

Frank W. Very: The luminiferous ether. Its relation to the electron and to a universal atmosphere.

Frank W. Very: What is the bearing of the hypothesis of a gravitational limit on the current relativity discussion?

Frank W. Very: The wasting of stellar substance.

Frank W. Very: Galactic and atomic vortices. Frank W. Very: On Nipher's "gravitational" experiment and the anomalies of the moon's motion.

R. K. Young: The probable error of radical velocities determined with the one prism spectrograph of the Dominion Astrophysical Observatory. Meade L. Zimmer: Preliminary note on an annual term in the right ascensions.




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THE war just and justly closing has many lessons for teachers. One of these is that those who are best prepared intellectually and have a deep interest in their subject will win in the end. Pedagogy like militarism trains directly for the object, but knowledge of the subject like the development of the general resources of a country gives real power and endurance. I fear our schools, especially our universities, have lately tended towards the former type of training for teachers and it is hoped that one of the lessons of this war is that there is danger in this direction. Pedagogy, as far as it enables the teacher to make students study what they do not want to study, is the militarism of the teaching profession. Among the other lessons which this war has taught us as teachers of mathematics is not to lose our confidence in the great usefulness of our subject. If any of us were discouraged during recent years by those who talked thoughtlessly but effectively about the uselessness of algebra and geometry we doubtless have largely recovered from this discouragement. The courses for the Students' Army Training Corps, as well as those given under the auspices of the Y. M. C. A. at the various naval stations, exhibit the extensive mathematical needs of those who aim to render the most efficient service under the most trying circumstances. Our new merchant marine will continue to make large demands for men with considerable mathematical training and will thus tend to emphasize the practical usefulness of our subject.

1 Prepared for the meeting of the Missouri Mathematics Teachers, which was to be held on November 8, 1918, but was postponed on account of the influenza epidemic.

It is still more important to note the value of mathematical training from the point of view of good citizenship. American lower schools devote much more time to mathematics and other sciences than the corresponding schools of Germany and the "German primary and secondary education is more intensely classical and literary than is British."2 Mathematics has for centuries been most highly appreciated in France and it has been most thoroughly mastered in the French schools. The account which the French soldiers have given of themselves during the world war is therefore the more inspiring to us as teachers of this wonderful subject.

The mathematics teachers are the mothers of mathematical progress, while the investigators are its fathers. Our teachers' organizations are thus a kind of mothers' clubs where we are inclined to discuss chiefly matters relating to the interests of those committed to our care. The highest devotion implies however, more than self sacrifice. It implies also thoughtful and arduous preparation. In fact, such preparation tends to make our tasks much easier and the things that we can do easily are usually done most efficiently. Hard intellectual work should be done only privately. All such public service should be easy as a result of thorough preparation.

My principal object is to inspire some of you to form a new resolution to strive to grow more rapidly along mathematical lines. The scientific development of teachers is not only a state and national question of paramount importance but it is also of international significance. At the outbreak of the world war its instigator Germany offered several prizes for essays relating to the best ways of using the facilities already at hand and of providing additional facilities for advancing the interests of those engaged in teaching.3

The glorious intellectual advances made by American secondary teachers during the last

2 W. J. Pope, "Science and the Nation," 1917,

p. 3.

3 Zeitschrift für naturwissenschaftlichen Unterrecht, Vol. 45, 1914, p. 521.

two or three decades is reflected in the rapid transformations of our universities in favor of teachers. These transformations have been so rapid and extensive as to give us little time to reflect upon their bearing and may have advanced already beyond the danger point.

The summer sessions and the summer quarters of our universities have grown rapidly in importance and influence. The universities are enlisting more and more their best talent for teachers during the summer terms instead of allowing their less progressive members to utilize them to increase their salaries.

Secondary teachers can not be urged too strongly to attend these summer sessions whenever they can do so without endangering their health. Teachers of mathematics in particular should aim to take at least one or two courses in the department of pure mathematics, and should not devote themselves too closely to the study of the methods or the history of teaching. The main element of interest about mathematics is the subject itself and the more advanced subjects throw the clearest light on the more elementary parts. In fact, these advanced subjects are only the elementary subjects grown to manhood and we understand the boy better after we have watched him develop into a man. Methods, on the contrary, are simply the outer garments of our subject and no amount of dress will make a skeleton attractive.

A child once watched a robin bearing a worm to its nest filled with little ones stretching out their necks and widely opened mouths in eager expectancy. The mother robin gave little heed to these gaping mouths, and, after resting a few seconds on the edge of her nest, swallowed the worm herself. The child was exasperated and called the mother robin a horrid old thing, but the father of the child directed attention to the fact that if the mother robin would not preserve her strength the helpless little robins would soon have no one to provide for them.

This simple illustration may serve to emphasize the need of looking after our own intellectual sustenance and growth. The help

we can render our students is a function of many variables but among these variables our own knowledge of the subject which we try to teach is doubtless the most significant. Our enthusiasm for the subject is likely to grow with this knowledge and is another important variable upon which our success will depend. It should also be noted that an enthusiam which is expressed only in words is not likely to reach the student's heart.

It is somewhat like the enthusiasm of our pro-German fellow citizens who had a change of tongue immediately after our entrance into the world war. While we were glad to see these changes we were inclined to await a change of mind and still more a change of heart. The change of tongue is the easiest human transformation, then comes a change of mind and finally a change of heart. The enthusiasm coming from the heart of the teacher is the only one which is apt to reach the heart of the student, and if your heart is in your subject you will want to know more about it.

While the summer sessions of our universities offer important facilities for the scientific development of our teachers there are other facilities which are less expensive and more permanent. Among these the high-school library deserves especial emphasis. Books are the cheapest educational factors in the world and most young teachers do not buy enough books relating to their own fields of work. What is more important they do not provide enough mathematical reading matter for their students.

The number of popular mathematical books is not very large, but this number is increasing fairly rapidly, and all high-school students should have access to at least a few of them. A few books on the history of mathematics, on mathematical recreation and on general mathematical expositions should be in every high school library. Such mathematical journals as School Science and Mathematics and the American Mathematical Monthly should also come regularly to every such library. High school students should be frequently encouraged to read mathematical articles in the genral encyclopedias.

While the books and journals to which we referred should be accessible to the students of every high school, they should especially be used by the teachers, and they afford important facilities for the scientific development of these teachers. Those interested in larger collections and more explicit references should consult A list of mathematical books for schools and colleges," containing titles of 160 books suitable for the school or college library, which was prepared by the library committee of the Mathematical Association of America, and published in the American Mathematical Monthly, volume 24, 1917, page 368.


It should be emphasized that this list of 160 books is for reference and not for intensive study. One of the greatest dangers which beset those of us who are anxious to become strong mathematicians is scientific dissipation. General mathematical reading is extremely useful but the backbone of the equipment of the mathematician is a profound knowledge of a few subjects, and the mastery of a comparatively small number of books. In fact, I believe that if a man would secure a thorough knowledge of certain nine mathematical books beyond a first course in elementary calculus he would be much better informed than the average candidate for the Ph.D. degree.

The mastery of nine volumes does not appear to be an insurmountable barrier between many young teachers of mathematics and the important goal of holding a place in the ranks

of the real mathematicians of our land. I take it that there are many here whose views are in accord with the following words of Bacon, printed for years on the covers of the Mathematical Gazette: "I hold every man a debtor to his profession, from the which as men of course do seek to receive countenance and profit, so ought they of duty to endeavor themselves by way of amends to be a help and an ornament thereunto."

The nine mathematical books whose mastery, together with a fair amount of general mathematical reading, and a development of some of the thoughts contained in these books, would make us an ornament unto our profession could be selected with considerable latitude.

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