476 



SCIENCE 



[N. S. Vol. LIV. No. 1403 



gineering teachers do, and it is a thing many 

 of us physics teachers never will do. 



Concerning physics teaching, my own opin- 

 ion is that students dislike physics because 

 they accomplish so little in the study of it in 

 our elementary college courses; and I believe 

 that they accomplish little because the simple, 

 fundamental mathematical ideas and methods 

 which constitute elementary physics are not 

 sufficiently stressed in the class room and not 

 set forth with clearness and brevity in our 

 text-books. 



" The instantaneous acceleration of a body 

 is the limit of the ratio Av/Ai as At ap- 

 proaches zero, where Av is the change of 

 velocity in time At " ; but the limit of Av/At 

 is unthinkable unless one knows the manner 

 in which Av and At approach zero. Advanced 

 students supply this deficiency, as they look 

 backwards at such a definition, by thinking 

 that they think of the so-called principle 

 of continuity! But what is the principle of 

 continuity to a beginner? And what is the 

 beginner to do? The definition of instantane- 

 ous acceleration can not be given either logi- 

 cally or intelligibly except in terms of a spe- 

 cific algebraic example where the manner in 

 which Av and A^ approach zero is clearly 

 evident. I mention this definition of instan- 

 taneous acceleration because it is given as 

 stated in nearly every physics text known to 

 me; and yet we ask why students dislike 

 physics. Many physics teachers maintain 

 that it is the business of our mathematics 

 teachers to clear up all mathematical difficul- 

 ties; but I believe, most decidedly, that the 

 main business of the physics teacher is to 

 cooperate with mathematics teachers in this 

 extremely important matter. I am here con- 

 sidering mathematics largely as a method of 

 thinking, and, surely, if all the difficulties 

 in this method of thinking were cleared up 

 by our mathematics teachers there would be 

 but little left for us physics teachers to do. 



Let us consider another example. A fluid 

 at rest pushes normally on an exposed sur- 

 face, or the exposed surface pushes normally 

 against the fluid. Most of our physics text- 

 books attempt to explain this fact by stating 



that the shear modulus of a fluid is zero! 

 Or by the following pseudo argument : " If 

 the force exerted on the fluid by an element 

 of the surface were inclined to the surface it 

 would have a component parallel to the siir- 

 face, and this tangential force would set the 

 fluid in motion; therefore, etc., etc." Now 

 it is absurd to say what this tangential force 

 will do to the small adjacent portion of the 

 fluid without considering the forces exerted 

 on the portion by the surrounding fluid. 

 Many such pseudo arguments may be found 

 in almost any of our physics texts, and I be- 

 lieve they account in large part for the dif- 

 flculties our mathematics teachers have in 

 the teaching of mathematics. Our physics 

 teachers not only do not help in the imxwr- 

 tant matter of mathematical training but they 

 sometimes hinder this highly important busi- 

 ness. 



But slovenliness in mathematics is not the 

 only fault in our physics texts. Many a 

 student comes from his boarding house to 

 the class room to hear his physics teacher 

 formalize about position and displacement, 

 although not one of the formalities needs to 

 be used, because the student's already exist- 

 ing knowledge of coming and going is fully 

 sufficient for everything his physics teacher 

 will give him. No wonder that a student 

 never goes from the class-room to his study 

 to read about position and displacement in 

 his physics text, even if there should be the 

 grain of a new idea mixed up with the in- 

 tolerably stupid and immediately purpose- 

 less discussion. 



A young man from the high school is ex- 

 pected to be edified by the study in college 

 of a physics text which discusses levers of 

 the first, second and third classes, which gives 

 all the old stuff about " simple machines " ; 

 and which contains little else that is clear and 

 concise and correct and purposeful! 



In the technical school the student is 

 scheduled to study such things as water 

 wheels, and pumps, and engines, and yet he 

 is expected to study a physics text in which 

 all these things are set forth, but no more 

 completely than in his high-school physics 



