304 



SCIENCE. 



[N. S. Vol. XXI. No. 530. 



Newton's laws have long held their place in 

 the majority of English and American books, 

 and in spite of the fact that the philosophical 

 validity of the Newtonian system has been 

 seriously questioned by able critics, this sys- 

 tem, properly understood, still appears to fur- 

 nish substantially the best foundation. It 

 does not follow, however, that a literal transla- 

 tion of Newton's words is the best formula- 

 tion of the laws of motion for the purpose of 

 elementary instruction. That Newton's for- 

 mulation is not easily understood by the be- 

 ginner is tacitly recognized by most writers, 

 much space being ordinarily devoted to ex- 

 planations of the meaning of Newton's lan- 

 guage. Without here attempting a full an- 

 alysis, it may be profitable to suggest certain 

 points in regard to which students may be 

 aided by a departure from the usual method 

 of stating and explaining the fundamental 

 laws. 



(1) Recognizing force as a fundamental 

 quantity whose nature is known roughly, at 

 least, from ordinary experience, its definition 

 should be so stated as to include the fact that 

 a force is exerted by a body. This should also 

 be embodied in the statement of the first law, 

 which might take the form ' a body uninflu- 

 enced by other bodies would move uniformly 

 in a straight line or remain at rest.' It should 

 also be embodied in the statement of the law 

 of action and reaction : ' When one particle 

 exerts a force upon another the latter exerts 

 one upon the former, and the two forces are 

 equal, collinear and opposite.' 



(2) The full explanation of the second law 

 should be preceded by a clear explanation of 

 the meaning of acceleration as a vector quan- 

 tity. The law itself might be stated as fol- 

 lows : ' A force acting alone upon a particle 

 gives it an acceleration whose direction is that 

 of the force and whose magnitude is propor- 

 tional directly to that of the force and in- 

 versely to the mass of the particle.' 



(3) The parallelogram law should receive 

 explicit statement: 'Two forces acting simul- 

 taneously upon a particle give it an accelera- 

 tion which is the vector sum of the accelera- 

 tions which would be due to the forces acting 

 separately.' ' Two forces acting simultane- 



ously upon a particle are equivalent to a single 

 force equal to their vector sum.' These state- 

 ments are seen to be equivalent by virtue of 

 the second law. An experimental statical 

 proof of the parallelogram law is instructive, 

 but its acceptance as an exact law rests on the 

 same basis as that of the rest of the laws of 

 motion — the apparent exact agreement of these 

 laws with all experience. 



Without entering into a detailed account of 

 the treatment of the laws of motion in each 

 of the three books under review, it is of inter- 

 est to notice the diiferent methods of defining 

 and explaining force. Maurer's treatment is 

 in close agreement with that here suggested; 

 the point emphasized in (1) is explicitly stated 

 at the outset, and the above statement of the 

 law of action and reaction is in Maurer's 

 words. Stephan gives the common but vague 

 definition of force as the cause of a change of 

 motion, the elementary but important fact 

 that a force is always exerted by a body being 

 explicitly stated only at the end of the three 

 pages devoted to the preliminary explanation 

 of force and of the law of action and reaction. 

 In Ziwet's book the treatment of force oscil- 

 lates between two different points of view. 

 Force is defined mathematically as the product 

 of the mass of a particle into its acceleration, 

 and the author evidently agrees with those who 

 regard force as a fiction, while he does not find 

 it easy or advisable to discard the conception 

 of force as a cause of motion in explanations 

 addressed to beginners. The definition of 

 force as the product of mass into acceleration, 

 and the denial of force as a physical reality, 

 are in harmony with what is, perhaps, the 

 prevailing view among philosophical critics. 

 Such a view is, however, wholly meaningless to 

 the beginner, and it must be insisted that the 

 treatment of force in an elementary text-book 

 should build upon common notions and every- 

 day experience. 



Although, in an elementary text-book, log- 

 ical rigor is not to be too strictly insisted upon, 

 it is important to avoid false logic, and espe- 

 cially the appearance of logically proving 

 what is really assumed. At certain points 

 many current expositions of the principles of 



