Apeil 3, 1914] 



SCIENCE 



507 



accepted a professorship of physical chemistry 

 .at Purdue University. 



Dr. L. D. Bristol, now of Syracuse Medical 

 School, has been appointed to succeed Dr. G. 

 F. Euediger as director of the public health 

 laboratory of the University of North Dakota. 

 Dr. E. T. Young has been appointed professor 

 of zoology and succeeds Dean M. A. Brannon 

 as director of the University Biological station 

 at Devil's Lake. 



Dr. Prafulla Chandra Eat has been ap- 

 pointed to the Sir Taraknath Palit professor- 

 ship of chemistry, and Mr. C. V. Eaman to the 

 Sir Taraknath Palit professorship of physics 

 in the Presidency College, Calcutta. 



DISCUSSION AND COEEESPONDENCE 



dadocrian's analytical mechanics and the 

 principles of dynamics 



Professor E. W. Eettger's review of my 

 ■" Analytical Mechanics," which appeared in 

 number 996 issue of Science, gives a wrong 

 impression of my treatment of the principles 

 of dynamics. 



The reviewer's criticisms are directed, 

 mainly, against my claim of having based the 

 science of mechanics upon a single dynamical 

 principle. Starting from certain premises, 

 which can not stand close examination, Pro- 

 fessor Eettger arrives at the conclusion 



He makes more assumptions than are usually 

 made in elementary text -books of mechanics. 



Let us consider the main points of his crit- 

 icisms in detail and see whether the foregoing 

 statement is based upon facts. 



On page 16, he introduces the conception of 

 ' ' force " as an " action " and without hesitation 

 applies vector addition to a system of forces. 

 What is he doing here, but assuming the ' ' parallel- 

 ogram of forces" in its most general form? 



It is intimated here that the " parallelo- 

 gram of forces " is a dynamical law which I 

 have " assumed " without formally introducing 

 it as a new law. It is a fact that I have 

 applied vector addition to forces " without 

 hesitation," but I have shown as little hesita- 

 tion in treating velocities, accelerations, tor- 

 ques, linear momenta and angular momenta as 



vectors. Why did not Professor Eettger ac- 

 cuse me of having assumed the " parallelo- 

 grams " of these magnitudes ? Is the " paral- 

 lelogram of forces " more of a dynamical law 

 than the " parallelogram" of torques, for in- 

 stance ? The " parallelogram " law applies to 

 any vector and is not at all a characteristic of 

 forces, therefore it is not a dynamical law. It 

 does not even deserve being called a " law " 

 when applied to a special type of vectors. In 

 its most general form the " parallelogram law " 

 is the principle of the independence of mutu- 

 ally perpendicular directions in space, a purely 

 geometrical principle. A special case of it is 

 known to students of plane trigonometry as the 

 " law of cosines." In the first chapter of my 

 book this principle is given in its most gen- 

 eral form as well as in its several special 

 forms, and is applied to vector magnitudes of 

 different types. After devoting an entire 

 chapter to vector addition and after defining 

 force as a vector, to introduce the " paralello- 

 gram of forces " as a new law, as Professor 

 Eettger would have it, could serve only to show 

 that the man who did it could not have a clear 

 conception of the meanings of the terms he 

 was using. 



On page 102 he assumes that a force is propor- 

 tional to the acceleration produced. This as- 

 sumes Newton's second law. 



This statement is not quite right. The rela- 

 tion between force and acceleration, which I 

 have called force-equation, is derived on page 

 106 from the fundamental principle which I 

 have postulated. In this derivation I have 

 made use of the definition of kinetic reaction, 

 which is stated and illustrated on pages 102 

 to 105, but this is not equivalent to " assum- 

 ing " a new principle. Will Professor Eettger 

 claim that to define the terms used in a prin- 

 ciple is equivalent to introducing or " assum- 

 ing " new principles ? Suppose I had based 

 my work upon the principles of the conserva- 

 tion of energy and of the conservation of 

 momentum should I have no right to classify 

 and define the different forms of energy and of 

 momentum without being rightly accused of 

 having introduced new principles? Will Pro- 

 fessor Eettger consider the definitions of mo- 

 mentum, of potential energy, and of kinetic 



