12 ELEMENTS OF LABORATORY WORK 



contains, and also the number of units of volume. Then the 

 first number, divided by the second, gives the number expressing 

 the density, or 



D = M 



when D equals numerical value of density 

 ,, M ,, ,, mass 



Y volume 



The unit of volume, however, is derived from the unit of 

 length ; for if I denote the unit of length, I- denotes the unit 



of area, and I 3 that of volume. Hence we may write d 



and perceive that d, the unit of density, is derived from the 

 fundamental units of length and mass. 



If a different system of units is used in measuring density, 

 then the numerical values will be found from the following 

 equation : 



M 



D _ m or D _ 

 " " ~ 



Here D, M, and L stand for the respective concrete quan- 

 tities, and d, m, I for the units adopted. 



8. Relation of Areas to Linear Dimensions. 



A square, the side of which has a units of length, contains 

 a 2 units of area. 



A rectangle, the sides of which have respectively a and b 

 units of length, contains ab units of area. 



A circle, the radius of which has r units of length, contains 

 77 r 2 units of area. 



A cube, the edge of which has a units of length, contains 

 6 2 units of area. 



A sphere, the radius of which has r units of length, contains 

 47rr 2 units of area. 



TT stands for 3' 141 5 9 nearly. 



