CIRCULAR MOTION 117

subject in this way after it had been originally given in another,It is not likely that students will make objection to any methodand if they learn some ostensible proof of the equation a == W4they will very likely dislike to study a second one. One mayhave the discouraging experience of hearing a boy. say that heunderstood the subject all right before he heard the new ex-planation of it. It is hard to help anyone over a difficulty whichhe himself has not encountered. However, I can mention onefurther advantage which this method possesses, and with thisI leave it. We define simple harmonic motion as the motionof the projection, on the diameter of a circle, of a point havinguniform motion on the circumference. We use this definitionin order to express displacement, velocity and acceleration interms of time and the constants of the motion, and finally toprove that the acceleration is proportional to the displacementand opposite in sign. The definition must then imply that thedisplacement of the particle’having the S. H. M. is the projec-tion of the displacement of the particle having the U. C. M.,the velocity of one is the projection of the velocity of the other,and the acceleration of one the projection of the acceleration ofthe other. We can project these quantities only if they arevectors. Therefore, to teach uniform circular motion withoutthe use of vectors is to leave the student completely at a losswhen he requires that kind of motion as an introduction to theother.

EDUCATION OPPORTUNITY ALL THE YEAl^ ROUND.The effect of long vacations has begun to excite serious apprehension.

A few cities are solving the vacation problem by running the schoolsthe entire year. Newark, N. J., may be given as an example. In thatcity many of the elementary schools and- one °high school are in session48 weeks in a year.The children who attend all the year like the plan. One boy says:

"Going to school all year keeps you from hanging around the streetsand saves you from trouble." A mother living in a tenement districtsays: "If there were no summer schools I would not know the where-abouts of my children. They would leave home early in the morningand run all over the city."A school physician says: "There is less sickness among the school

children in summer than in winter. The children who attend duringsummer are in better physical condition in September than the childrenwho have not been to school."A few other cities ha^e organized all-year schools. Most cities con-

duct summer schools of 6 weeks, which is a step toward the all-yearschool. The all-year school is coming. Why not? It must, however,not be a school of mere text-books, but a school where children maylive normal lives in working with their hands, in studying, and in playing.