79-] THE LAWS OF MOTION. 



43 



76. With this definition of force the first law, at least in the ordinary 

 form of statement, for a single particle, merely states that where there is 

 no cause there is no eifect. While this law may appear superfluous to us, 

 it was not so in the time of Newton. Kepler and Galilei, less than a 

 century before Newton, were the first to insist more or less clearly on 

 this so-called law of inertia, viz. that there is no intrinsic power or 

 tendency in moving matter to come to rest or to change its motion in 

 any way. 



77. The second law gives as the measure of a constant force the 

 amount of momentum generated in a given time (see Art. 60) ; it can 

 be called the law of force. If force be defined as the cause of any 

 change of momentum, the .second law follows naturally by assuming, as 

 is always done, that the effect is proportional to the cause. 



The first two laws may thus be regarded from the mathematical point 

 of view as nothing but a definition of force ; but they are certainly 

 meant to emphasize the physical fact that the assumed definition of 

 force is not arbitrary, but based on the characteristics of motion as 

 observed in nature. 



In the corollaries to his laws Newton shows how the composition and 

 resolution of forces by the parallelogram rule follows from his definition. 

 In deriving this result he tacitly assumes that the action of any force on 

 a particle takes place independently of the action of any other forces that 

 may be acting on the particle at the same time, a principle that would 

 seem to deserve explicit statement. Some writers on mechanics, in 

 particular French authors, prefer to replace Newton's second law by this 

 principle of the independence of the action of forces. 



78. The third law expresses the physical fact that in nature all forces 

 occur in pairs of equal and opposite forces. In modern phraseology, 

 two such equal and opposite forces in the same line are said to consti- 

 tute a stress. Newton's third law is therefore called the law of stress. 



This law, which was first clearly conceived in Newton's time, involves 

 what may be regarded as the second fundamental property of matter or 

 mass (the first being its indestructibility); viz. that any two particles of 

 matter determine in each other oppositely directed accelerations along the 

 line joining them. 



79. For a more complete discussion of the physical laws underlying 

 the applications of theoretical mechanics, the student is referred to 

 THOMSON and TAIT, Natural philosophy, London, Macmillan, 1879, 





