572 



SCmNGE. 



[N. S. Vol. XIV. No. 354. 



is concerned with the physical phenomena in- 

 volved in motion " ; while Johnson says, "Me- 

 chanics is the science which treats of the motions 

 oi material bodies, and the causes of these mo- 

 tions. ' ' Definitions of the science, however, are 

 not very important to the elementary student. 

 He must know the subject pretty well before 

 he can appreciate a definition of it. All such 

 definitions as those just cited, need, as their 

 authors doubtless anticipated, much supple- 

 mentary explanation in the light of the student's 

 enlarged expei'ience. 



Professor Hoskins follows the historical de- 

 velopment of the subject and gives to statics 

 first place, passing on thence to kinematics aud 

 kinetics. Professor Slate adopts the modern, 

 more logical, order of presentation beginning 

 with kinematics. Professor Johnson follows 

 more closely the Newtonian method, starting 

 with dynamics and passing on to statics and 

 kinetics, kiuematical principles being explained 

 as needed chiefly. There is much to be said in 

 favor of each of these methods ; and for the be- 

 ginner either method is effective with the aid 

 of a good teacher ; but with proper preliminary 

 training the modern method, introduced by 

 Kelvin and Tait, would seem to be most advan- 

 tageous. 



The theory of dimensions, which helps more 

 than anything else to give clearness to ideas in 

 mechanics, is explained and freely used in the 

 works of Professors Hoskins and Slate, but it is 

 unfortunately omitted from the work of Pro- 

 fessor Johnson. The need of this theory is 

 shown at several points in the latter work ; for 

 example, on p. 126, where the phrase 'inten- 

 sity of pressure ' occurs, and on p. 268, where 

 the equally cumbersome phrase ' intensity of 

 force ' occurs. Both of these phrases, which 

 are now happily obsolescent, are here used by 

 the author in a very puzzling way. Com- 

 monly ' intensity of pressure ' means force di- 

 vided by area, or stress in the more recent 

 use of the latter term. Commonly, also, ' in- 

 tensity of force ' means force divided by mass, 

 or acceleration. But these are not the senses 

 in which Professor Johnson has used these 

 phrases. 



Without constant appeal to the theory of di- 

 mensions it is very difficult for the most careful 



authors to avoid ambiguity of language. Thus, 

 to cite an illustration from the work of Profess- 

 or Hoskins, take his equation (1), p. 194, speci- 

 fying simple harmonic motion, namely, 



wherein the first member means acceleration 

 and a; is a distance. The constant k, then, must 

 be the reciprocal of the square of a time. But 

 Professor Hoskins says that Jc is ' written for the 

 attractive force per unit mass at unit distance 

 from ' (the origin) ; a statement immediately 

 contradicted and corrected by the theory of di- 

 mensions. There is a more refined obscurity in 

 Professor Hoskins' articles 177, 178, wherein 

 the gravitation constant is involved. It appears 

 from these articles that the force of gravitation, 

 like ' electric force ' and ' electromotive force,' 

 may be difi'erent from the force considered else- 

 where in the book. 



Nearly all the older works on mechanics 

 are marred by such obscurities as those noted 

 above. The gravitation constant has been er- 

 roneously defined by many eminent authors, 

 and some of our best works, in the French and 

 German languages especially, are disfigured by 

 the introduction of forces of more than one 

 species. It is high time that all such obscurities 

 and ambiguities, so easily detected by the theory 

 of dimensions, were banished from mechanics. 



In connection with this subject of clear and 

 definite terminology attention should be called 

 to Professor Johnson's revival of the use of the 

 term ' force of inertia ' and to Professor Hos- 

 kins' use of the term ' eflfective forces.' These 

 are properly going, if not wellnigh gone, out 

 of fashion. They seem doomed to be replaced 

 by the more suggestive term 'kinetic reaction,' 

 or 'mass reaction.' The word 'inertia' is re- 

 sponsible for a deal of difficulty in mechanics, 

 and it seems well to follow the example set by 

 Maxwell in his Matter and Motion, and use in- 

 ertia very sparingly, if at all, except in the set 

 phrase ' moment of inertia.' It appears worth 

 while also to note that all the works in ques- 

 tion define the term ' stress ' in its earlier sense, 

 assigned to it by Eankine. The more recent 

 sense of the word, especially appropriate and 

 useful in elasticity and hydromechanics, is 

 force per unit area ; that is, force divided by 



