482 



SCIENCE 



[N. S. Vol. L. No. 1299 



DOUBLE USE OF THE TERM ACCELERATION 



To THE Editor of Science: Dr. Hering's 

 letter in the issue of October 24 raises a ques- 

 tion of scientific terminology of a kind not 

 altogether unusual. He contends that the 

 term "acceleration" is used in one sense by 

 the engineer, namely, to signify the rate of 

 change of speed; and indiscriminately, in two 

 different senses by the physicist, one of these 

 meanings coinciding with the engineering 

 usage, and the other conflicting with it. This 

 second use of the word is to denote the vector 

 rate of change of another vector, the velocity. 

 As I understand his letter, he proposes that 

 the physicist abandon this second meaning in 

 favor of the first. 



Dr. Hering is an eminent engineer, and I 

 leave it to other engineers to question, if they 

 choose, his right to speak for them. I must 

 protest however, against his version of the 

 views of physicists. The term acceleration, 

 in its strict sense, is now used by physicists 

 only with the second of the two above mean- 

 ings, and then applies, when used without 

 any qualifying word, only to the motion of a 

 point or particle. The word is sometimes 

 used, in order to avoid circumlocutions, to 

 denote merely the scalar magnitude of the 

 vector. The need of a new word to express 

 this second notion, in the manner in which 

 we now customarily distinguish between 

 velocity and speed, has long been felt. This 

 somewhat loose usage is however quite diiler- 

 ent from the definition recommended by Dr. 

 Hering, which would give it the meaning 

 " tangential component of the acceleration." 

 It would be rash to assert that the term is 

 never used in this sense by physicists, for 

 carelessness of language is hard to avoid, but 

 few would be found to defend the usage. 



Dr. Hering chooses as an illustration of the 

 divergents of physicist and engineer: 



. . . the revolution of a fly-wlieel at a constant 

 speed, the rim of which to the physicist is being 

 constantly accelerated while to the engineer there 

 Is no acceleration, as the speed is constant. 



The physicist argues, and quite correctly, that a 

 moving body represents a vector quantity, as it 

 has both speed and direction. The same external 



force applied to such a moving body will change 

 either the speed or the direction, depending upon 

 the relative directions of that force and of the mov- 

 ing body. But as force is defined as mass X ac- 

 celeration, the physicist, apparently forgetting the 

 difference between pure and applied mathematics, 

 methodically divides this force by the mass and 

 calls the quotient acceleration. It simplifies his 

 mathematics. 



I have quoted these remarkable sentences at 

 length, because I should not dare to attempt 

 any summarizing paraphrase. Assimiing that 

 the physicist is "arguing correctly " when he 

 makes a " moving body represent a vector 

 quantity," the offense seems to consist in 

 " apparently forgetting the difference between 

 pure and applied mathematics." What is 

 this difference ? It is that the " pure " mathe- 

 matics is applicable to dynamical problems, 

 whereas Dr. Hering's " applied " mathematics 

 is not. 



The case of the revolving fly-wheel offers 

 no real difficulty either of treatment or of 

 terminology. The " acceleration " of the fly- 

 wheel as a whole is either a term without 

 meaning, or applies to a translatory move- 

 ment. Any point or particle of the wheel is 

 accelerated toward the axis, from which we 

 infer the existence of a force in this direction 

 acting on the particle. Of the fly-wheel as a 

 whole, we speak of the " angular accelera- 

 tion," which is zero when the angular speed 

 is constant and the direction of the axis in- 

 variable. From the vanishing of this vector 

 we infer, not the absence of an external force, 

 but the absence of an external torque or 

 couple. 



Take the case of a, falling particle, describ- 

 ing a parabolic trajectory, and compare the 

 two statements : 



(a) The acceleration is g, vertically down- 

 ward. 



(6) The acceleration is g cos d, where 6 is 

 the angle between the velocity and the down- 

 ward vertical. 



The second of these statements is in con- 

 formity with engineering usage, if I ujider- 

 stand Dr. Hering correctly. The first state- 

 ment describes the motion in such a way that 

 if we know the velocity at any time we can 



