4 INTRODUCTION TO DYNAMICS. [10. 



In a heterogeneous body, this quotient is called the average, 

 or mean, density. In this case the density at any point, or the 

 density of any space-element dV, is defined as the derivative 



dM 



10. The unit of density is the density of a substance such 

 that the unit of volume contains the unit of mass. If the units 

 of volume and mass are selected arbitrarily, there need not of 

 course necessarily exist any physical substance having unit 

 density exactly. Thus in the F.P.S. system, unit density is 

 the density of an ideal substance I pound of which would just 

 fill a cubic- foot. As a cubic foot of water has a mass of 62 \ 

 pounds, or 1000 ounces, the density of water is 62 \ times the 

 unit density. 



The specific density, or specific gravity, of a substance, is the 

 ratio of its density to that of water at 4 C. Let p be the 

 density, p' the specific density, M the mass, V the volume of 

 a homogeneous mass, then in British units 



In the C.G.S. system, the unit of mass has been so selected 

 as to make the density of water equal to I very nearly ; in other 

 words, the unit mass (i gramme) of water, at the temperature of 

 4 C., fills one cubic centimetre. 



In the metric system, then, there is no difference between 

 density and specific density or specific gravity. 



r 

 2. MOMENTS AND CENTRES OF MASS. 



11. The product of a mass m, concentrated at a point P, into 

 the distance of the point P from any given point, line, or plane, 

 is called the moment of this mass with respect to the point, line, 

 or plane. 



