252 NEW MODE OF REPRESENTING 



Required to determine the tangent to the system 

 of lines containing any number of breaks, as 

 in Fig. 4. 



(14). If Y' and x represent the co-ordinates of 

 any point in the system of discontinuous curves ; 

 andj/ and ^ represent the rectangular co-ordinates 

 of any point in the tangent to the point Y' x ; 

 and T the tangent of the angle which the tangent 

 to the curve makes with the axis of x, 



Then we shall have, 



H -\' = T {x - x') (I). 



See Gregory's examples on the differential and 

 integral calculus, page 142. 



We have now to determine the value of T for 

 any point in the curve. 



By referring to art (10) we have -^ = T 

 Hence, d T = d ^ A-B-C...i' ^^.^ _^ A.-BC...t . 



