HOW TEACHERS OF PHYSICS ARE "MADE IN GERMANY."

BY E. A. STRONG,

Ypsilanti, Michigan.

In the September number of Zeitschrift fuer den Physikalischen und Chemischen Unterricht Professor E. Wiedemann of Erlangen gives, at the request of the management of that journal, his notion of the best university preparation for teachers of physics in the middle schools-gymnasia, real schools, etc. Those who wish to know about the preparation of teachers for the public schools (primary schools), and especially how the law of 1901 affected this matter, will find an admirable French view of the whole subject now running in Revue Pedagogique, beginning with the September number.

Prof. Wiedemann justifies the association of physics with mathematics in the secondary schools, as is done in Germany, instead of the French practice of combining physics and chemistry, or physics with other sciences. He would, however, have intending teachers give some attention to chemical physics and become familiar with precipitation, filtration, crystallization, etc., and with the preparation of oxygen, hydrogen, carbon dioxide, etc. In mathematics he would have the candidate become familiar with analytical geometry; the calculus, especially in its applications to physics; analytical mechanics; differential equations; and the theory of functions. Especially he would have him know elementary mathematics thoroughly and fundamentally, including the beginnings of the non-euclidean geometry.

He also justifies at considerable length the elementary course in descriptive physics given to intending teachers, along with those. looking forward to other professions, at the beginning of their university course. It is true that students coming from the oberrealschulen and realgymnasien can truly say, "We have heard all that before." Well, if they choose let them cut the lectures and have a good time; but those who attend will find that they have added much to their knowledge and understanding of the subject. They will hear to know and not, as previously, to be prepared for examination. They will get a more connected view of the subject, unobstructed by a multitude of applications. Above all they will form physical concepts directly from the physical world without the intervention of mathematical symbols and formula. So their knowledge will be real and not merely formal, as is

likely to be the case if they go forward at once to theoretical physics. Students who are satisfied with purely formal definitions and who lean constantly upon the mathematical expression of physical ideas will, when they come to teach, be satisfied that their pupils have the same hollow semblance of knowledge. There is not time in the schools, often not the opportunity or the incentive to ponder the great things of physics, to let them sink into the mind and be really penetrated with them; so that the impression that physical subjects make is relatively weak and soon forgotten, as every university man knows. The schools all greatly misjudge as to the amount of abiding, well-digested, and utilizable knowledge which their students carry away with them. Especially is this true of the simplest concepts, which, just because they are so simple, are also so difficult.

Following this semester of descriptive and demonstrative physics two semesters of lectures are given upon theoretical physics, in which the chief stress is placed rather upon the physical content than upon the mathematical relations. This should give the students some ability to read original researches, where the mathematical demands are not too great, and some preparation for an "Arbeit" of their own. Lectures are also given upon particular departments of theoretical physics; upon the history of physics; and upon recent developments in the more important branches of the subject. Some practice is had in soldering, glass blowing, etc., and in preparing material for demonstration; though the writer does not think it worth while for the students to make complete pieces of complicated apparatus. The practical work is more exacting than that given to other students. Special attention is given to the experiments of the secondary schools: as-index of refraction, accurate weighing, etc. Great stress is placed upon the density of gases, for its manipulative value; but the densities of solids and liquids by different methods, specific heats, and a number of other problems, are worked hastily and with no very high degree of accuracy, so as to give time for some more advanced measurements:-as, the dielectric constants, polarization angles, heat of neutralization, elevation of boiling point, heat of combustion, etc.

In Bavaria the examination for intending teachers is divided into two parts: one after the fourth and one after the eighth semester. For the second part a scientific arbeit is demanded. Concerning the value of this arbeit to a teacher there has been

much discussion, but the writer thinks it equal in value to a dissertation in mathematics and justified by the fact that skill in using apparatus is always useful to a teacher.

Upon suggestion of the government officials they have hit upon the following scheme:

Themes, mathematical and physical, such as will come up for discussion in the schools, are distributed among the candidates. Those who specialize physics may get mathematical themes, and conversely. The candidate then has to treat the subject in a manner corresponding to the underlying knowledge and the power of comprehension of pupils and with apparatus such as he would use in early experimental work. Some one or other of the candidates will be able to prepare such apparatus, or it may be kept in stock. The point of these expositions does not lie in the correction of much formal awkwardness in presenting the experiment and analyzing it upon the blackboard, but in abundant instances of want of clearness-indeed of gross errors in comprehension-which come to light and may be corrected. They find the criticism of their fellow students useful, while the one who conducts the exercise gets a view of how much physical knowledge, which he had taken for granted, is really a sealed book to many young people.

A COMMUNICATION.

EDITOR SCHOOL SCIENCE AND MATHEMATICS:

In Milne's Plane and Solid Geometry, Book II, Proposition I, Cor. (Section 193), I see this statement: "In the same circle, or in equal

B

B

C

осо

D

circles, arcs whose extremities can be made to coincide are equal." Is this true? In the following figures do not arcs ACB and ADB meet the requirements of the hypothesis? Yet they are evidently unequal.

Yours truly,

O. L. PLUNKETT.

PROBLEM DEPARTMENT.

IRA M. DELONG,

University of Colorado, Boulder, Colo.

Readers of the Magazine are invited to send solutions of the problems in this department and also to propose problems in which they are interested. Solutions and problems will be duly credited to the author. Address all communications to Ira M. DeLong, Boulder, Colo.

ALGEBRA.

36. Proposed by P. G. Agnew, Washington, D. C.

Coal is on the deck and coal is running on the deck from a chute at a uniform rate. Six men can clear the deck in an hour, eleven men can clear it in twenty minutes. How long will it take four men to clear the deck?

Solution by William Bucke Campbell, B.S. in E., Philadelphia, Pa. Let a fraction of quantity on deck originally removed by one man in one hour,

y = fraction added from chute in one hour,

q = quantity on deck originally.

y

11x

3 3

= 0, whence

From the given conditions, q + y − 6x = 0, 9+ x = fq, y = 19. Let z be the number of hours for four men to clear the

37. Proposed by H. C. Whitaker, Ph.D., Philadelphia, Pa.

A man can go to a place by two routes. The shorter route can be made by rail in 6 hours, by boat in 20 hours, and on horseback in 30 hours. In going he takes the shorter route and travels an equal number of hours by each conveyance. He came back by the longer route and traveled as many miles horseback as he had traveled by rail going, as many miles by rail as he went horseback going, and as many miles by steamer as by both rail and horseback. What was the total time consumed in traveling and what is the ratio of the lengths of the routes?

Solution by F. M. Dryzer, B.A., Knoxville, Tenn.

If shorter route, s, can be made by rail in 6 hours, then

can be made in one hour. Similarly, by steamer and by horse. Or, in 3 hours } + 2 + b = can be finished. Hence 12 hours are required for making the trip, and in portions of 4 hours each:

GEOMETRY.

38. Proposed by L. M. Saxton, Edgewater, N. Y.

Given ABCD as any parallelogram, E any point in AB, F any point in DC. Join E with D and C, and F with A and B. Let AF meet DE in Y, and BF meet CE in Z. Let the line YZ produced meet AD in P and BC in Q. Prove that PQ divides ABCD into two equivalent parts.

Solution by I. L. Winckler, Cleveland, O.

Let PQ, produced, meet AB and CD, produced, at K and L respectively. Then in triangle ABF we have ZF. KB. AY BZ. KA. YF......(1), and in triangle CED, YD. LC EZ = EY.LD. ZC......(2),

since a line cutting the sides of a triangle determines upon the sides six segments, such that the product of three non-consecutive segments is equal to the product of the other three.

Also, the triangles BEZ and AEY are similar, respectively to triangles

CZF and DYF.

Therefore, BZ: EZ = ZF : ZC and EY: AY = YD : YF,

From these BZ. ZC = ZF. EZ......

and EY.YFYD. AY..

....

. (3) .(4)

multiplying together (1), (2), (3), (4) and canceling common factors we get KB. LC = KA. LD..........(5), but KB = KA + AB and LD = LC+ CD, substituting these in (5) (KA + AB). LC = (LC + CD) . KA.

Reducing AB. LC = CD. KA and since AB =CD, LC

triangle KAP =

Then area

KA. Therefore,

triangle QLC and AP = QC. Therefore, BQ = PD. trapezoid ABQP = area trapezoid CDPQ.

MISCELLANEOUS.

39. If sin A, sin B, sin C are in harmonical progression, so also will

be 1-cos A, 1

(1)......sin A sin C cos C + cos A sin2 C+ sin2 A cos C + sin A

1- cos A

Expanding

cos A sin C = 2 sin A sin C.

cos B, 1 cos C are in harmonic progression

+

1

cos A one obtains the equation (1).

cos (A+C), clearing of fractions substituting sin2 A = 1 −

CREDIT FOR SOLUTIONS RECEIVED.

Problem 32. John W. Scoville, I. L. Winckler.

Problem 33. I. L. Winckler.

Problem 34. I. L. Winckler.

Problem 35. I. L. Winckler.

Problem 36. T. M. Blakslee, Henry A. Converse, R. S. Pond, S. R.