2 INTRODUCTION TO DYNAMICS. [3. 



therefore, with the distance of the body from the earth's centre, 

 and would vanish completely if the earth were suddenly 

 annihilated ; while the indestructibility of mass is the first 

 fundamental principle of chemistry and physics. 



3. To compare the masses of different bodies, we may adopt 

 any given body as a standard. 



Thus in the F. P. S. system, the standard mass is a certain 

 bar of platinum marked " P. S., 1844, I lb.," and preserved at 

 the Office of the Exchequer, London, England. This is called 

 the " imperial standard pound avoirdupois" ; any mass equal to 

 it is a unit of mass in this system. 



In the C. G. S. system, the standard of mass is the " Kilo- 

 gramme des archives," a bar of platinum kept in the Palais des 

 archives, in Paris, France. A mass equal to one-thousandth of 

 this standard is the unit of mass in this system ; this unit is. 

 called \htgram, 



The numerical relation between the British and metric units- 

 of mass is as follows : 



i lb. =453.59265 gm. 



i gm. =0.002 204 621 2 lb. = 15.432 grains. 



4. The three units of space, time, and mass are called the 

 fundamental units of mechanics, because with the aid of these 

 three, the units of all other quantities occurring in mechanics 

 can be expressed. Thus we have seen how the units of velocity 

 and acceleration are based on those of space and time, and we 

 shall have many more illustrations in what follows. Any unit 

 that can be expressed mathematically by means of one or more 

 of the fundamental units is called a derived unit. 



5. From the mathematical point of view, mass appears in our 

 dynamical equations as a coefficient, generally to be regarded as 

 an absolute, positive constant. It serves to give different values 

 (different valency, or " weight " in the meaning of the theory of 

 least squares) to the moving points, lines, areas, volumes, apart 

 from their geometrical extension. 



