64 



SCIENCE 



[N. S. Vol. XL VI. No. 1177 



points which have been disregarded in our 

 texts. The result has been that in a large 

 number of cases the student did not see how 

 the force was being exerted; he felt that 

 there was an intangible something about force 

 beyond the range of his ability to grasp. It 

 is small wonder that rapidly increasing con- 

 fusion results from this lack of self-confidence. 



Another point can not be too strongly em- 

 phasized. No author of an elementary text 

 seems as yet to have recognized the impor- 

 tance of distinguishing most carefully between 

 forces of action and forces of reaction. It 

 seems to me of prime importance, if the stu- 

 dent's ideas about force are to be sharply out- 

 lined, to make this distinction. I would sug- 

 gest that it lends facility to the treatment to 

 use the terms " applied " force and " reactive " 

 force for forces of action and of reaction, re- 

 spectively. The following treatment may 

 bear out the contention concerning the im- 

 portance of recognizing both. 



Let us first apply Newton's third law of 

 motion to the case of a body A, acting upon 

 a fixed body B. In this ease the student 

 readily understands that B exerts a reactive 

 force equal and opposite to the applied force 

 exerted by A ; for if this were not true, mo- 

 tion should ensue in accordance with the 

 second law. He also readily sees that the 

 reactive force arises and ceases simultaneously 

 with the applied force. Often, however, when 

 the third law is applied to a movable body B, 

 and the student is told that the accelerated B 

 exerts a reactive force upon A, equal and 

 opposite to the applied force exerted by A, he 

 is dubious and asks : " If that is true, how 

 can there be an acceleration? By the first 

 law, B should then remain at rest or in uni- 

 form motion." With the distinction between 

 applied and reactive forces clearly drawn, this 

 question can not arise. In this particular 

 case we may point out that, to be sure, no 

 acceleration of B could occur if the force 

 exerted by A upon 5 were opposed by another 

 applied force, exerted upon B in the opposite 

 direction by a third body, C. However, since 

 there is only the one applied force, that due 

 to A, acceleration must ensue in accordance 



with Newton's second law; and, simultane- 

 ously with this acceleration, ergo, with the 

 applied force, there arises the reactive force 

 of B upon A. We may, to present the case 

 somewhat more tangibly, speak of the applied 

 force as being exerted by that particular body 

 which, so to speak, takes the initiative in the 

 processes. It is well to point out, further, 

 that the reactive force of B upon A arises re- 

 gardless of whether the motion of B is in the 

 direction of the force exerted by A, or whether 

 there is a finite angle between these two direc- 

 tions. If this angle is a right angle, the 

 applied force causes B to move in a circular 

 path, without change in speed; the applied 

 force is then called centripetal. The reactive 

 force exerted by B upon A under these con- 

 ditions is called the centrifugal force, which 

 disappears at exactly that instant which marks 

 the disappearance of the applied force. 

 Numerous examples to illustrate these state- 

 ments will occur to the teacher. 



If the student is familiar with the above 

 principles, the problem of Atwood's ma- 

 chine becomes very simple. For here con- 

 sidering the moving system as a unit, the ap- 

 plied force of A (the earth) upon B (the sys- 

 tem) is obviously {m^ — mjfii; the reactive 

 force of B upon A is {m., + mja. These, by 

 the third law, are equal. The value of a, 

 or of g, immediately follows from the equality. 



I can not quite agree with Dr. Fulcher that 

 the failing of our authors in treating reactive 

 forces, especially centrifugal force, as they do, 

 is because of " their forgetting that these 

 forces are purely imaginary." Is it not rather 

 attributable to their previous neglect in not 

 having emphasized the difference between ap- 

 plied and reactive forces? 



Just an illustration, in conclusion, to show 

 that American writers do not alone fall under 

 the criticism of giving insufficient thought to 

 the presentation of some of the fundamental 

 things. We find, for example, in a German 

 text, widely used in the Eealschulen, by an 

 author reputed to have been one of the fore- 

 most teachers of physics, a treatment as fol- 

 lows : " Upon the liquid particle A there are 

 acting two forces, the force of gravity, ver- 



