1912^ Fundamental Bases of Dynamics 73 



(14) The word "force" may be simply defined as a push or a 

 pull. 



(15) From sq. (3), we have, W = rn^. 

 The fundamental formula of mechanics is, 



Y = m a (4) 



where F is the force acting on the body whose mass is m and 

 acceleration a, the force and acceleration being in the same di- 

 rection. 



In the engineers' system of units, when gravity is the force, 

 acting (of course, vertically) F = W lbs., a = g, giving the 

 previous formula as a special case of (4). 

 (4) can likewise be written, 



W 

 F = — a (5) 



9 

 where F and W are expressed in pounds, a and g, in feet per sec- 

 ond per second. 



(16) From (4) other well known formulas as, 'Ft = mv; 

 Y s=y2mv^, can at once be derived. 



(17) Newton's three laws may be stated and commented on 

 at this stage. Formula (4) is the symbolical expression of one 

 law. Let us make an immediate application of the third law, 

 "to every action, there is always an equal and contrary reaction." 



Thus let a perfectly smooth particle of mass m strike a sec- 

 ond similar particle of mass m, both moving in the same direc- 

 tion along the lines of the centers of the particles. In the infin- 

 itesimal time dt, call the accelerations of the particles a and a^ 

 respectively, since they act in opposite directions, a and aj have 

 opposite signs. When by Newton's law of action and reaction 



m Oj 



— m a = 'm-i^a^', — = 



mj a 



In a recent work on Analytic Mechanics by Barton, p. 196, the 

 author follows Mach in giving the last equation as a definition 

 of mass. It is submitted that it is simpler to define mass as in 

 (12), then force as in (15), whence the above formula is seen 

 to be a derived one. 



