SCIENCE 



[N. S. Vol. XXXI. No. 784 



general review course, I believe the latter 

 should be given. While it may be more 

 interesting and profitable for the professor 

 to teach the advanced subjects, he should 

 subordinate his personal wishes to the effi- 

 ciency of the college. If he be fortunate 

 enough to discover an exceptional man, is 

 it not best for the latter to go to an institu- 

 tion affording larger facilities for his fu- 

 ture work, to an institution where close 

 contact with a number of investigators will 

 stimulate and inspire him? Such a stu- 

 dent will always remain loyal to his old 

 college professor and be proud of being a 

 graduate of an institution which has given 

 him a thorough fundamental training. 



2. As was suggested in the earlier part 

 of the paper, not alone the college curricu- 

 lum of the future high school teacher is 

 being criticized, but also our teaching. We 

 must admit that there is and always will 

 be room for reform. The best we can do 

 is to apply remedies after we have been 

 shown clearly just where the trouble lies. 

 In education we should not apply patent 

 medicine, invented to cure general debility. 

 Therefore we will not talk about methods. 

 It would be an unfortunate condition, end- 

 ing in stagnation, were all university pro- 

 fessors forced to teach according to certain 

 pedagogical rules which suppress individu- 

 ality and kill spontaneous enthusiasm. 



I shall be specific and state my second 

 proposition thus: "We are far from being 

 unanimous in the use of certain terms and 

 frequently employ the same term to desig- 

 nate two entirely different physical quan- 

 tities." This means that we do not pay 

 enough attention to the very things which 

 make physics so valuable as a training of 

 the mind, namely, clearness of thinking 

 and accuracy of expression. 



Let me cite the most flagrant cases : 



a. What is pressure 1 In every-day usage 

 it is a force, pure and simple, as illustrated 



by the classic problem: How large a pres- 

 sure is exerted upon a vertical wall by a 

 beam leaning against it? Leaving this in- 

 terpretation entirely out of consideration, 

 is pressure the force, acting upon unit area, 

 or, the force per unit area, i. e., a force 

 divided by an area ? In other words : Has 

 pressure the dimensions of a force or not? 

 Both definitions are doubtless taught, but 

 if we assume the former to be correct, then 

 in our formula 



F = PA 



A does not represent an area, but the num- 

 her of units of area upon which the force 

 acts. Of course I assume that P stands for 

 pressure. 



But if we do this, we get into trouble 

 when we discuss the work done upon or by 

 a gas. For in the equation 



W = PV 

 the V would no longer represent a volume, 

 but a length. In fact, as soon as we speak 

 of the action of a gas, we discard the force 

 and substitute for it the abstract concept 

 of the proportionality factor P between 

 force and area. This abstract idea, which 

 most of us call pressure, is nevertheless a 

 real physical quantity. 



I believe the greatest difficulty to the 

 beginner in physics arises at the very 

 moment when he is confronted with such 

 an abstract physical quantity, e. g., ac- 

 celeration. He feels suddenly the solid 

 ground slipping away from under his feet 

 and regains confidence only after he has 

 manipulated this quantity again and again 

 in the solution of problems. So it is with 

 pressure ; we can not blame the student for 

 trying to hold on to his old friend, the 

 force, as long as he possibly can. 



Clifford says: "When that which we do 

 not know how to deal with is described as 

 made up of things we do know how to 

 deal with, we have that sense of increased 

 power which is the basis of all higher 



