March 3, 1916] 



SCIENCE 



315 



unscientific. On this point I heartily endorse 

 Mr. Kent's somewhat pungent criticisms, which 

 are entirely in accord with previous expres- 

 sions of my own. 



in. Finally, let us examine Mr. Kent's 

 method. Like Professor Hoskins, Mr. Kent 

 introduces mass, or quantity of matter, at the 

 outset, but unlike Professor Hoskins, he 

 frankly defines what he means by this term — 

 namely, the result of weighing on a beam bal- 

 ance. This same plan is followed by several 

 of the writers who have taken part in this dis- 

 cussion, notably by Franldin and MacNutt.' 

 There is no logical objection to this procedure; 

 but — cui hono? The result of weighing a body 

 on a beam balance gives primarily the stand- 

 ard weight of the body as we have seen in (10), 

 above ; if the standard weight of a body, which 

 is simply a force, and which everybody under- 

 stands, is all that is needed, why rename this 

 familiar concept by a less familiar term, like 

 " quantity of matter " ? Further, what are the 

 " dimensions " of " quantity of matter " ?° Is 

 it of the nature of a force, or, like inertia, of 

 the nature of a force divided by an accelera- 

 tion? Or is it wholly independent of force, 

 length and time (in which case it is wholly 

 superfluous) ? Without doubt, later in the 

 course any terms of this sort may be intro- 

 duced at pleasure; but why confuse the iegin- 

 ner with any concepts that are not really 

 needed? The elimination of this one term, 

 quantity of matter, would bring Mr. Kent's 

 method almost exactly into line with my own, 

 except for one point. 



This remaining point of difference, though 



8 Franklin and MaeNutt, Science, July 9 and 

 September 24, 1915. In regard to the supposedly 

 contrasted statements (o) and (6) on page 423 

 of their second article, it may be remarked that 

 these authors have apparently overlooked the 

 fact that each of these statements is a direct 

 mathematical consequence of the other, as one 

 may readily see by an inspection of their diagram 

 on page 422. 



9 Mr. Kent is apparently quite oblivious of the 

 value of the theory of dimensions, as he uses the 

 same letter {g) quite indiscriminately to denote 

 a length, a velocity, an acceleration, or a pure 

 number I 



slight, is, at least from the point of view of 

 the teacher, an important one. My method 

 begins frankly with the idea of acceleration as 

 a fundamental concept — not an easy idea, but 

 one which is so essential that the student does 

 best who faces its difficulty squarely at the 

 outset. Mr. Kent's method, on the other hand, 

 begins with the comparatively simple special 

 case in which the acceleration is constant, and 

 introduces the real thing only later on, as a 

 sort of afterthought. For a student who is 

 never to go further than the special case, the 

 method based on Mr. Kent's equation 

 y = FTg/'W is well enough; and this is what 

 I had in mind when I said that " the method 

 was not without interest on the pedagogic 

 side." But for the student who pursues the 

 subject seriously, the plan of spending so much 

 time on the simple special case is too apt to 

 have only one result, namely that the devel- 

 opment of an umerring, instinctive grasp of 

 what acceleration reaUy means is either long 

 delayed or never attained. And this brings 

 me to the question of the error in Mr. Kent's 

 paper. On page 902 he asks the question: 



How can a body at rest on the earth's surface 

 have an acceleration . . . radially toward the 

 earth's center ... if there is no change in the 

 speed of rotation of the earth? 



The old error of supposing that a particle 

 moving with constant velocity in a curved 

 path has no acceleration! 



Now I have no doubt that if the matter were 

 called to his attention, Mr. Kent would at once 

 remember that a particle moving with a con- 

 stant velocity in a circular path certainly does 

 have an " acceleration radially toward the 

 center," the, value of which is v-/r; but the 

 point I am making is that in the rush of the 

 moment he did not remember this most cardi- 

 nal fact about accelerated motion ; and I attrib- 

 ute the possibility of a man of his experience 

 making a slip of this kind entirely to the 

 grudging fashion in which the subject of ac- 

 celeration was probably presented to him in 

 his first course in mechanics — a precedent 

 which my method refuses to follow. 



Edward V. Huntington 



Harvard Universitt 



