26 PHYSICAL SCIENCE 



relation to weight ; any discovery of a connection 

 between them must be a matter of experiment. 



Weight is the force which we must apply to 

 a body to prevent it moving in its natural path 

 towards the earth, the product of the mass and 

 acceleration being the same for the earth as for 

 the body. If the forces were equal, the accelera- 

 tions towards the earth of two bodies would, by 

 our definition of mass, be inversely proportional 

 to their masses. By experiments on the accelera- 

 tion, then, the forces may be determined. Now 

 it was shown by Galileo that, if the resistance of 

 the air be eliminated, bodies fall at the same rate 

 to the earth ; that is, that the accelerations of 

 all bodies to the earth are the same. It follows 

 that the forces, that is, the weights of the bodies, 

 must be proportional to the masses. Masses 

 can thus be compared by weighing, and this 

 method is much the most convenient in practice. 

 Nevertheless, it must always be remembered 

 clearly that the proportionality between mass and 

 weight, and the consequent possibility of com- 

 paring masses by means of the balance, is not a 

 relation which could be predicted a priori except 

 by the recent and at present unfamiliar ideas 

 of relativity, but one which historically has been 

 established as the result of careful experimental 

 investigation. 



When we turn from mechanics to the other 

 branches of physics, it is necessary, in the present 

 state of knowledge, to use certain new funda- 

 mental conceptions, such as temperature and 

 quantity of electricity, though it is probable that 

 ultimately these quantities will be connected with 

 the mechanical units. Again, in this place it 



