246 



NEW MODE OF REPRESENTING 



Let it be required to determine the equation to 

 the system of lines containing any number of 

 breaks, as in Fig. (4). 



Fig. 4. 



AS Bi Ba 



(10). Put AB = a; AB, = b\ ABj — c, &c. 



Observing the same notation as before, with 

 this difference, that, 



Y, = the ordinate to the system with one break 

 Y2 = Do. Do. two breaks 



Y3 = Do. Do. three breaks 



&c. &c. &c. 



Y„ = Do. Do. n breaks 



Now, if we take for simpHcity 



a — X ^ , a — .V 

 1 + = A and 1 = A, 



' a ^ X a in X 



>+^^' = B 



and 1 - / ~ = B, 



h in X 



