August 25, 1916] 



SCIENCE 



279 



of the subject." " The historical order of the 

 development of mechanics is followed by dis- 

 cussing equilibrium before motion." 



The author certainly has given considerable 

 thought to the preparation of his book, which 

 contains some very interesting matter. In the 

 large collection of problems he gives, there 

 will be found some very interesting ones. The 

 reviewer himself was sufficiently interested to 

 think out solutions for a number of them. 



The plan of the book is certainly unique in 

 a number of ways. This is not necessarily a 

 criticism. There is a wide feeling that text- 

 books in mechanics written for our engineer- 

 ing students fail to interest the students as 

 they ought to do, and it may be that that book 

 that will be found most satisfactory will be 

 written according to a plan that will be quite 

 unique when compared with the plans in ac- 

 cordance with which our present standard text- 

 books on mechanics are written. The re- 

 viewer of this particular text-book is unable to 

 appreciate, however, the author's point of view 

 of some parts of his book. 



In the first place, the author devotes his 

 first chapter (of 11 pages) to " Addition and 

 Resolution of Vectors." After that he merely 

 states that a quantity has magnitude and 

 direction and that, therefore, it is a vector. 

 In the composition and resolution of such 

 quantities, he then uses the law of addition and 

 resolution of vectors as developed in his first 

 chapter. This makes everything easy, at least 

 as far as the author is concerned. For in- 

 stance, the composition of couples reduces itself 

 to this : " The resultant of two couples is a 

 third couple whose torque is the vector sum of 

 the torques of the given couples." That is all 

 that need be said concerning the composition 

 of couples. Similarly for the composition of 

 the other directed quantities. 



The reviewer does not wish to criticize this 

 mode of procedure but wishes to ask if this 

 mode of procedure is legitimate. "Vector addi- 

 tion is simply one of the operations in an 

 algebra in which the parallelogram law is made 

 one of the fundamental assumptions. Before 

 we apply the law of vector addition to any 

 kind of quantity, ought we not first assure 



ourselves that the parallelogram law holds for 

 these quantities? Since force, for instance, 

 is a directed quantity, does it follow that the 

 parallelogram law holds for forces ? The same 

 may be said of other directed quantities. 

 Vector representation of directed quantities is 

 very important and useful, and vector addi- 

 tion and resolution should be given, but it 

 should be given only after we are assured that 

 the parallelogram law holds with reference to 

 such quantities. Jf the author is correct in 

 reversing this process, then certainly the 

 theory underlying the composition and resolu- 

 tion of directed quantities becomes very 

 simple. 



In the second place, the author's plan is 

 unique in that he takes the following principle 

 as the foundation of his book : " The vector sum 

 of all the external actions to which a system 

 of particles or any part of it is subject at any 

 instant vanishes." This principle he calls the 

 " action principle." To understand what the 

 author means by this principle, we must under- 

 stand what he means by " action." 



On page 15, the author states that " all ac- 

 tions to which a particle is capable of being 

 subject may be divided in two classes, namely, 

 forces and hinetic reactions." He then de- 

 fines force as the action of one particle upon 

 another. On page 17, he states that kinetic re- 

 action represents the action of the ether on a 

 particle and that it equals the product of the 

 mass of the particle by its acceleration. That 

 is, if q is this kinetic reaction then q = — ma. 

 The negative sign is used since the direction 

 of the action of the ether on a particle is oppo- 

 site to the direction the particle is accelerating, 

 If now F is the vector sum of the forces acting 

 on one particle then the above action principle 

 may be stated as follows (page 17) : 



$(F + q)=0. 



The reviewer is not sure that he understands 

 what the author means by kinetic reaction. 

 On page 17 and also on page 150, he states that 

 kinetic reaction is the action of the ether on a 

 particle. . And on page 150 he adds that 

 " kinetic reactions are not aggressive. In this 

 respect they are similar to resisting and fric- 



