THE PRINCIPLES OF ENERGY 35 



plied by their molecular weight. (The molecular weight of the 

 lightest molecule, that of hydrogen, Hg, is taken as the standard 

 to which all other molecular weights are applied.) 



Mass and Inertia. — Mass is, then, the most fundamental thing 

 in our notion of materiality, but it is not an irreducible concep- 

 ' tion, and we must seek for some way of defining and measuring 

 it. Note, first of all, that we have a bodily intuition of mass: 

 let there be two exactly similar stoneware, corked bottles, and 

 let one be filled with water and the other with mercury. We 

 cannot say which is which merely by looking at them, but we can 

 distinguish if we lift them, for a greater degree of effort of our 

 muscles is necessary to lift the mercury than to lift the water, and 

 we have the " feeling " of this effort. 



Nevertheless, such an intuition would be mostly useless to us, 

 for it would not apply to great masses which we cannot lift, nor 

 to very small ones, nor to masses which were nearly the same. 

 We must have some way of measuring mass by taking some 

 dimension of space, or by counting (or numbering) something. 

 Now there is a constant and universal property of masses — that 

 ,of gravitation; all material bodies, whatever their nature, or mass, 

 fall to the surface of the earth when they are free to move. If 

 they are sufiiciently far away they will fall 16 feet in the first 

 second, 64 feet in the first two seconds, 144 feet in the first three 

 seconds, and so on, their rate of fall being accelerated by 32 feet 

 per second per second during the time that they are falling. 

 We do not know in the least what the force of gravitation is, 

 I but we know precisely what it does — it accelerates the rate of 

 motion of a body free to fall. Consider what this means : there 

 are three factors — m^s, space, and time; a mass, when it is 

 attracted by the earth, falls with increasing velocity — that is, it 

 falls through a greater space in the third second than in the 

 second one, and through a greater space in the second one than 

 in the first. This acceleration of the motion of a mass during a 

 certain time we shall call the work done by the force (whatever 

 the latter may be). 



Place a mass of metal (say a pound weight) in a scale pan ; it will 

 fall, and the other scale pan will rise. Now place another pound 

 weight in the other scale pan, and the two will balance each other 

 so that neither falls. The work done by gravity on the one is 

 equal to the work done on the other: neither is accelerated; the 

 space and time factors are the same, and therefore the masses are 



