96 MASS AND FORCE. [CHAP. V. 



Suppose m and m are the masses of the bodies (determined 

 by weighing them), u and u the velocities in 

 the line of centres just before they come into 

 contact, v and v the velocities in the line of 

 centres just after they come into contact. 

 Consider a case where the strings are vertical 

 at the instant of collision, and the bodies re 

 bound after collision. With the velocities u 

 and u the bodies approach each other, with 

 the velocities v and v they separate. Hence 

 the changes of velocity in the line of centres 

 are u 4- v and u + v . 

 Fig 41 Now the velocities u, v, u , v can all be 



determined by observing the heights from 



which the bodies were dropped and the heights to which they 



rise; and it is found that 



m (u + v) = m (u + v ). 

 An instrument for making this experiment is known as a 



Ballistic Balance. It is no part of the plan of this book to 



describe the details of instruments. 



94. Gravitation. We have described methods of determin 

 ing the masses of bodies which can be handled. But these yield 

 no way of assigning masses to the Earth, the Sun, or other celestial 

 bodies. Also we have said that it is not generally possible to assign 

 the component accelerations produced in any one of the particles 

 of which a natural body is regarded as made up by the action of 

 particles of other natural bodies. There is however a class of cases 

 of great generality and importance for which this can be done. 

 We can in fact in the case of particles at a distance apart which 

 can be measured by ordinary means, (by a divided scale,) or at any 

 greater distance, state a rule for the intensity of the field of force 

 due to each particle, and then the masses can be once for all 

 assigned so that the resultant intensity at any point coincides 

 with the result of observation. 



The rule in question is known as the Law of Gravitation : it is 

 that the force between two particles of masses m, m at a distance 



r is of magnitude 7 , where 7 is a constant independent of m, 

 m } r and of the time, and the sense of the force exerted by m on 



