42 INTRODUCTION TO DYNAMICS. [74. 



pounded by geometrical addition, as will be explained more fully 

 in Chapter IV. 



On the other hand, kinetic energy and work are not vector- 

 quantities. 



74. The ideas of momentum, force, energy, work, with the funda- 

 mental equations connecting them, as given in the preceding articles, 

 form the groundwork of the whole science of theoretical dynamics. The 

 application of this science to the interpretation of natural phenomena 

 gives results in exact agreement with observation and experiment. It is 

 therefore important to inquire what are the physical assumptions and 

 experimental data on which this application of dynamics is based. 



These assumptions were formulated with remarkable clearness by 

 :Sir Isaac Newton in his Philosophic naturalis principia mathematica, 

 first published in 1687, and have since been known as Newtan's laws 

 of motion. As these three axiomata sive leges mofus, as Newton terms 

 them, are very often referred to and, at least by English writers on 

 dynamics, are usually laid down as the foundation of the science,* they 

 are given here in a literal translation : 



I. Every body persists in its state of rest or of uniform motion along 

 a straight line, except in so far as it is compelled by impressed (i.e. 

 external) forces to change that state. 



II. Change of motion is proportional to the impressed moving force 

 and takes place along the straight line in which that force acts. 



III. To every action there is an equal and contrary reaction; or, 

 the mutual actions of two bodies on one another are always equal and 

 directed in contrary senses. 



75. Some explanation is necessary to correctly understand the mean- 

 ing of these laws ; indeed, Newton's laws should not be studied by 

 themselves. They become intelligible only if taken in connection with 

 the definitions preceding them in the Principia, and with the explana- 

 tions and corollaries that Newton himself has appended to them. 



The word " body " must be taken to mean particle ; the word " motion " 

 in the second law means what is now called momentum. 



All three laws imply the idea of force as the cause of any change of 

 .momentum in a particle. 



* See the Syllabus of elementary dynamics, Part I., London, Macmillan, 1890. 

 p. 13 sq., prepared by the Association for the Improvement of Geometrical leaching. 



