RATES 



131 







FIG. 9. 



H 



The analytical processes, involved in the study of rates, 

 follow from a consideration of this case. 



In Fig. 9 is given the cross section of a road. Axes, 

 OH and OF, permit the expression of the location of 

 any point of the 

 road with reference v 

 to their intersection. 

 For convenience we 

 shall denote dis- 

 tances measured 

 along OH and OF 

 by H and V, respec- 

 tively. Correspond- 

 ing to any chosen 



value of H , or, as we may say, to any value which H 

 may assume, there is a value of F which satisfies the 

 condition that the point determined by these " coor- 

 dinates" lies on the curve representing the road. In 

 other words, as H varies, F also 

 varies, being dependent for its value 

 upon H. It is usual, therefore, to 

 say that H is an independent vari- 

 able and that F, the dependent 

 variable, is a function of H. In 

 the particular case shown in the 

 figure it is evident that the slope 

 varies from point to point, that is, 

 that the slope itself is a function 

 of H. 



Between any two points, as 1 and 2, represented in 

 the enlargement of Fig. 10 by the coordinates HI, Fi, 

 and H 2 , F 2 , respectively, the average slope is the 



', 







FIG. 10. 



