VARIABLES AND FUNCTIONS. 



[INT. ii. 



The expression on the left is -^ Hence 



In a similar manner we find 



, _ /(a 3 + .Q(6 8 +>)(<!* + ./) 



V (,,-x) (-,*)- 

 and the parameter of any function F(X, /-t, v) is 



20. Infinitesimal Arc, Area and Volume. If we have 

 any three point- functions q lf q 2) q s forming an orthogonal system 

 of coordinates, since their parameters are 



- -- -&- 





dn 2 



**>% 



FIG. 7. 



the normal distance between two consecutive level surfaces q l and 

 q 1 + dq 1 is ^ = -?p , consequently if we take six surfaces 



q lt q! + q lf q z , q 2 + q 2 , q 3 , 



the edges of the infinitesimal curvilinear rectangular parallelepiped 

 whose edges are the intersections of the surfaces are 



dq 1 dq 2 dq^ 



hi h 2 h s 

 and since the edges are mutually perpendicular, the diagonal, or 



