9-] MASS. 



j 



6. Thus, a geometrical point endowed with mass is called a 

 material particle. We may regard such a mass-point, or particle, 

 as the limit to which a physical body approaches if its volume 

 be imagined to decrease indefinitely, approaching the limit zero, 

 while its mass may remain a finite quantity. From the physical 

 point of view a particle must be regarded as much an abstraction 

 as a geometrical point, since every finite physical mass occupies 

 a finite space and cannot be identified with a point. We shall 

 see, however, that in dynamics this idea of the mass-point, 

 or particle, is of the greatest importance not only because 

 physical matter is usually considered as made up of an aggre- 

 gation of such points or centres possessing mass (molecules, 

 atoms), but principally because in many cases the motion of a 

 solid body can be fully represented by the motion of a certain 

 point in it, called its centre of mass or centroid, the whole mass 

 being regarded as concentrated at this point. 



7. It is also customary in dynamics to speak of material 

 lines and material surfaces, which may be regarded as the limits 

 of physical bodies in which two dimensions or one dimension 

 have been reduced to zero. Thus a material line represents 

 the limit of a wire, chain, or bar, in which two dimensions are, 

 neglected ; a material surface can be imagined as the limit of 

 a thin shell, or lamina, with one dimension reduced to zero. 



8. A continuous mass of one, two, or three dimensions, is 

 said to be homogeneous if the masses contained in any two equal 

 lengths, areas, or volumes (as the case may be), are equal. The 

 mass is then said to be distributed uniformly. In all other 

 cases the mass is said to be heterogeneous. 



9. The whole mass M of a homogeneous body divided by 

 the space V it fills is called the density of the mass or body ; 

 denoting density by p we have therefore 



M 



*FV 



for homogeneous bodies. 



