NOTE ON THE FUNDAMENTAL BASES OF 

 DYNAMICS. 



By Wm. Cain. 



For some years there has been increasing dissatisfaction with 

 the manner of presentation of the fundamental principles of 

 dynamics, as given by text books, particularly for the use of 

 engineering students. From the time of Newton down, mass 

 of a body has been defined as "the quantity of matter in the 

 body" — an admittedly ambiguous term. 



Mass is likewise said to equal density times volume, or density 

 equals mass divided by volume, which gives no precise concep- 

 tion of density until the idea of mass is made clear and precise. 



Next in order comes the definition, force = mass X accelera- 

 tion, which is likewise obscure until mass is quantitatively 

 defined. 



However, as an illustration, if a body of mass m is supposed 

 to fall in vacuo under the force of the attraction of gravitation, 

 whose measure is the weight W in pounds (say), the accelera- 

 tion being g ft. per second per second, then the above equation 

 takes the well known form, 



W = mg; 

 whence m = W/^ 



so that finally it is seen that mass is directly proportional to 

 weight and inversely proportional to the acceleration of gravity. 

 Also, since W. varies directly as g, the ratio W^g is constant for 

 the same body for all points on or in the earth, and it is now 

 realized clearly that mass is something pertaining to a body that 

 does not alter with its position. 



Now it has always seemed to the writer that it would be more 

 logical to start with this precise conception of mass; in other 

 words, define m as W^g, so that there will be no ambiguity, from 

 the start, in ideas of mass, density and force. If this is done, 

 however, it is very important to explain how W is to be found ; 

 for the weight of a body, as estimated by an equal armed bal- 

 ance is not usually the same as that given by a spring balance, 



