134 



SCIBWCU. 



[Vol. IX., No. 210 



LETTERS TO THE EDITOR. 

 German constructions. 



I DISAGREE toto coclo witli my learned fellow-citizen 

 as to what he is pleased to call ' horrible construc- 

 tion ' in German, but believe, on the contrary, that 

 for one whose ear is trained to it the sentences of 

 qualification are as clear as an assemblage of short 

 phrases, and ever so much more powerfiil. As an 

 example of the involved style (seldom if ever used 

 by the best German writers and speakers, by the way), 

 take this : — 



Dem, der den, der die, das Verbot enthaltende 

 Tafel abgerissen hat, anzeigt, wird hierdurch eine 

 Belohnung zugesichert. 



This is tough for the anti-Teuton, but it says in 

 eighteen words and ninety-five letters what cannot 

 be literally translated into English in less than nine- 

 teen words and one hundred and four letters. 



Peesifok Feazee. 

 Philadelphia, Feb. 8. 



Inertia-force. 



Will you allow me to draw attention to one point 

 in Dr. E. H. Hall's recently published pamphlet on 

 ' Elementary ideas, definitions, and laws in dynam- 

 ics,' which he seems to me to have treated with less 

 success than he has the other points raised ? 



On p. 6 Dr. Hall says, "We have spoken some- 

 times of the force which is applied to a body to 

 change its motion, and sometimes of the resistance 

 or counter-force with which the body meets the 

 applied force. Each is necessary to the other. We 

 could not exert force upon a body if the body offered 

 no resistance. On the other hand, resistance would 

 be impossible if there were no applied force to be 

 met. We shall call the counter-force, which a body 

 in virtue of its inertia exerts to meet a force applied, 

 the inertia-force.'''' On what body this counter-force 

 is supposed to be exerted is not at once clear. At 

 first it seemed to me to be the body by which the 

 applied force was exerted, the applied force and the 

 counter-force being thus the opposite aspects of the 

 same stress. And this seemed especially probable 

 from the fact that on p. 24 the third law of motion 

 (which of course applies only to the two opposite 

 aspects of one stress) is cited to prove the equality 

 of the applied force (there treated as doing work) 

 and the counter-force (there called a resisting force). 

 But the following quotations show that this is 

 not Dr. Hall's meaning : "The force, or resistance, 

 exerted by a body varies greatlj' with the conditions 

 of the experiment, being sometimes large, sometimes 

 small, according to the following general law : 

 When the ball's motion is changed slowly, it offers a 

 slight resistance, — a small force suffices ; when a 

 considerable change is to be effected in a short time, 

 we encounter a large resistance, — a great force is 

 required" (p. 5) ; and, " There is no change of mo- 

 tion, and hence no inertia-force is developed " (pp. 

 6 and 7). The counter-force may thus become zero, 

 though the stress still act ; and hence it cannot be 

 one aspect of that stress. The following qiiotation, 

 however, seems to settle the matter : "If one of the 

 opposing applied forces is greater than the other, 

 the greater will prevail, and a change of motion 

 will occur, occasioning an inertia-force, which will 

 work with the smaller applied force against the 

 greater" (p. 7). The inertia-force, therefore, is 

 supposed to act on the body by which it is exerted. 



The magnitude of this inertia-force is determined, 

 according to Dr. Hall (see above quotation from p. 

 5), by the magnitudes of the forces applied to the 

 body ; and the following quotation — ' ' The working 

 force and the resisting force must also be equal " 

 (p. 24) — shows that just sufficient inertia-force is 

 called into play in any case to satisfy the conditions 

 of equilibrium. 



Now, this sounds very like the old notion of cen- 

 trifugal force. It was formerly held that a body 

 moving with uniform speed in a circular path was 

 acted upon not only by a force directed towards the 

 centre of the path, and applied, say, by means of a 

 string, but also by an equal force directed from the 

 centre, called the centrifugal force, and exerted on 

 the body by the body itself, which was accordingly 

 considered to be in equilibrium. Dr. Hall's inertia- 

 force is thus just a generalization of the old notion 

 of centrifugal force. 



Although Dr. Hall thus proposes to re-introduce 

 what seems to be an old error, the only evidence he 

 brings forward for his inertia-force is the assertion 

 contained in the first of the above quotations, that, 

 of the applied and inertia-forces, each is necessary to 

 the other. Yet he does not leave us without means 

 of judging of his theory of the ' resistance ' which 

 bodies offer to applied forces ; for according to 

 his own account of this inertia-force, as shown above, 

 it both acts on, and is exerted by, the same body. 

 Now, on p. 18 he admits that " every force implies 

 an action between two bodies." Hence the supposed 

 inertia-force cannot be a force at all. And again, as 

 we have seen above, according to Dr. Hall's own ac- 

 count, all bodies must be acted upon by equilibrat- 

 ing systems of forces, if this inertia-force be taken 

 into account ; and therefore, if this inertia-force be a 

 force, a body's motion may be changing though it 

 satisfy the conditions of equilibrium. 



Api^arently Dr. Hall has been led to postulate this 

 inertia-force, because, 1°, he holds that a body re- 

 sists an applied force (he even takes this to be a fact 

 given in consciousness, for he says, p. 3, " One feels 

 that the hand is pulling, that it encounters a resist- 

 ance, which is offered in some way by the ball at the 

 other end of the string " ) ; and, 2*^, he cannot under- 

 stand a force as being resisted in any other way than 

 by the exertion of an opposing force. I agree with 

 him that the term 'resistance' should in dynamics 

 be restricted to the opposition of forces. But the 

 manifest consequence is, that a body ought not to be 

 said to resist a force, and that Maxwell's queries, 

 quoted by Dr. Hall (p. 32) — " Is it a fact that mat- 

 ter has any power, either innate or acquired, of re- 

 sisting external influences ? Does not every force 

 which acts upon a body always produce exactly 

 that change in the motion of the body by which its 

 value as a force is reckoned ? " — are to be answered, 

 as Maxwell evidently intended them to be answered, 

 the former in the negative, the latter in the affirma- 

 tive, though some of his own definitions may be 

 thereby shown to be worded in a faulty manner. 



I hope I have not misrepresented Dr. Hall's posi- 

 tion. I have read his pamphlet carefully several 

 times, and can get only one meaning out of it. Were 

 I reviewing the pamphlet, I would find many points 

 to praise ; and i draw attention to the above apparent 

 error only because the excellence of the pamphlet 

 generally is likely to cause it to take root and spread. 

 Dr. Hall, in his appendix, quotes a passage from 

 Minchin's ' Uniplaner kinematics ' which seems to 



