rEBEUART 23, 1917] 



SCIENCE 



189 



the fact that the so-called ' centrifugal ' and 

 ' centripetal ' forces acting upon the particle 

 are equal and oppositely directed." I am 

 afraid the reviewer has overlooked the fact 

 that a particle is in static equilibrium vehen 

 and only when the sum of the forces due to 

 other material bodies acting upon the particle 

 equals zero. When this condition is not satis- 

 fied the particle is accelerated and by virtue 

 of the acceleration the kinetic reaction comes 

 into play. , This kinetic reaction is equal and 

 opposite to the resultant of the forces due to 

 the material bodies. If it were not for the 

 kinetic reaction a finite force would have given 

 a body an infinite velocity in a finite time. 



The kinetic reaction is of the same nature 

 as a force and miglit be called a force, but that 

 would tend to confound the cause with the 

 effect. It would further necessitate changing 

 the statement of the conditions of equilibrium 

 as well as of motion. It was in order to keep 

 the old concept of force as an action which 

 causes acceleration and to distinguish between 

 cause and effect that I refrained from applying 

 the term force to kinetic reactions. 



The concept of kinetic reaction is not new. 

 It has been known to other authors of text- 

 books of mechanic as centrifugal force, inertia 

 force, or inertia reaction. The thing that is 

 new about kinetic reaction in my book is the 

 full recognition it receives and the clear cut 

 treatment which differentiates it from ac- 

 celerating forces. I have preferred the name 

 kinetic reaction to inertia reaction because it 

 is just as much an acceleration-reaction as an 

 inertia-reaction. 



I claim that the point of view which I 

 have adopted in my book has important philo- 

 sophical and pedagogical advantages over the 

 common point of view. The former has en- 

 abled me to differentiate between purely 

 geometrical laws and dynamical principles, be- 

 tween kinematical relations and dynamical 

 equations, between what is fundamental and 

 what is derived in mechanics. I have postu- 

 lated a single dynamical principle which is 

 not only simple and sound, but is correlated 

 with the equally fundamental principles of 

 electrodynamics. Upon this single principle 



I have based the entire subject, deriving from 

 it all the other dynamical laws and principles 

 used in elementary mechanics, such as !New- 

 ton's three laws of motion, the principles of 

 the conservation of energy, of linear momen- 

 tum and of angular momentum. 



Before closing this communication I would 

 like to call the attention of teachers of mechan- 

 ics to the following principle which I have 

 introduced in the second edition of my book 

 and have called it the angular action principle. 



The vector sum of all the external angular 

 action to which a system of particles or any 

 part of it is subject at any instant vanishes: 



2Aa = 0, 



or 



2(G-|-qa)=0, 



where G denotes the moment of force about a 

 given axis and Qo denotes the moment of the 

 kinetic reaction of a particle about the same 

 axis, the latter I have called the angular 

 hinetic reaction. This principle, which is di- 

 rectly applicable to rotating systems, is equiv- 

 alent to and derived from the action principle. 

 It can be easily shovm from the angular 

 action principle that the torque equation 

 da 



holds good only when the center of mass of 

 the moving system remains at a constant dis- 

 tance from the axis of rotation, a point which 

 has eluded most authors of textbooks of 

 mechanics. 



In conclusion I would state that the two 

 action principles are simple statements of the 

 following two sets of equations used in gen- 

 eral dynamics. 



S(X — mx) =0, 



2(r — mii)=0, 



2 (^ — me) = 0, 



j:[y(Z — mz) —ziY — my)] =0, 



2[a(X — mic) —x(Z — mg)] =0, 



2[a;(r — mi/) — i/(Z — mi)] =0. 



H. M. Dadourian 

 Yale TJniveesitt 



the synchronic behavior of phalangid.a; 



Professor H. H. !N'ewman's note in a recent 



nimiber of Science reminds me that in 1901 I 



