13] ACTION AND REACTION. MASS. 23 



Afr 



dt 



Experiment shows that the factors m l and m 2 are constant for a 

 given body that undergoes no changes other than those of position. 

 These factors are called the masses of the hodies. The nature of the 

 actions between the two bodies may be of any sort, and may be 

 transmitted by the help of any number of intervening bodies. For 

 instance , the actions of two heavenly bodies on each other ; trans- 

 mitted we know not how, or the actions of two bodies kept at a 

 fixed distance by means of a rod or string or connected by an 

 elastic spring, or attracting or repelling each other by magnetic or 

 electric agencies, are all illustrations of the third law. It is obvious 

 that if we could observe the motions so as to obtain the coordinates 

 of both bodies as functions of the time, equations 40) would enable 

 us to determine the ratio of the masses. For example, consider 

 the toy consisting of two horse-chestnuts or bullets connected by a 

 string, and suppose this to be whirled about and projected into the 

 air so that the two bodies describe complicated paths, the whole 

 apparatus describing in general a parabolic path. If we take a series 

 of photographs of it in rapid succession, by means of a kinetoscope 

 or similar device, we may by measurement obtain the coordinates of 

 the two bodies as functions of the time. This illustrates perfectly 

 the dynamical measurement of mass and the means of obtaining the 

 relative masses of the heavenly bodies. We have no means of 

 defining the absolute mass of a body. As a further example of the 

 third law, let us suppose the action is transmitted from one body to 

 the other by means of a flexible string passing over frictionless 

 pulleys, as in the case of Atwood's machine. The assumption here 

 made is that the tension of the string is unchanged by passing over 

 the pulleys. 



A more practical means of realizing the dynamical comparison 

 of masses would be by experimentally establishing the equality of 

 both sides of equations 40) with the same quantity. For example 

 let the body be made to describe a horizontal circular path, say by 

 means of a whirling machine. It will be found that it must be 

 retained in this path by external means such as the tension of a 

 string. Let this be passed over a pulley at the center of the path and 

 exactly balance its pull against that of a weight suspended from it. The 



resultant of the components ^ ^' m ~di?' * s ^ v 30) equal to ^-> 



