Uniform Motion. 1 7 



3. If the moping forces are equal, the velocities are inversely as 

 (he masses. 



The truth of these propositions is easily shown by put- 

 ting successively the value of m equal to m', that of v equal 

 to T', and that of p equal to / ; the equations thus obtained, reduc- 

 ed and converted into proportions, form the several propositions 

 above stated. 



Remark. 



30. The mass or number of material parts of a body, de- 

 pends upon its bulk or volume, and what is called its density, that 

 is, the greater or less degree of closeness or proximity among 

 its particles. As all bodies have more or less of void space 

 within them, their quantities of matter are not proportional to 

 their bulks ; since, under the same bulk, the quantity of matter 

 is greater according as the parts are more crouded and com- 

 pressed together. A body is said to be more dense than anoth- 

 er, when under the same bulk it has more matter ; and on the 

 other hand to be more rare than another, when under the same 

 bulk it has less matter. 



Accordingly, by means of the density of a body, we are able, 

 when the bulk is known, to judge of the number of material parts 

 which compose it; so that the density may be considered 

 as representing the number of material parts in a given bulk. 

 When we say that gold is 1 9 times as dense as water, we mean 

 that gold contains 1 9 times as many parts in the same space. 



By considering density as expressing the number of material 

 parts of a determinate bulk, taken as the unit of bulk, it is evident 

 that in order to find the mass, or total number of material parts 

 of a body whose bulk is known, we should simply multiply the 

 density by the bulk. If, for example, the density of a cubic 

 inch of gold be represented by 19, the quantity of matter con- 

 tained in 10 cubic inches would be 10 times 19. Thus, designa- 

 ting the mass by m, the bulk by 6, and the density by D, we 

 shall have 



m b X D. 



It will hence be easy to compare together the masses, the bulks, 

 and the densities of bodies. 

 Mech. 3 



