DISCONTINUOUS FUNCTIONS. 247 



1 + ^—^. = C and 1 - ^-=-^ = C, 



And generally, 



1 +-^ = ^ and ' - ^ = ti 



we shall have from equation (3) Art. 8. 



ii = — 2 + 9 "'^ '•'^^ system containing 



one break. 



^ B-*(a,-) B.faCx) ^ , 



1 2 = 2~~ "I" — 2 — ' system containing 



two breaks. 



C-.I>.(:r) C.-f3(x) , . ,, ^ 



13 = 2 "r 2 lor the system contanmig 



three breaks. 



&c. &c. &c. 



i„ = 2 + — 2 — system containing 



n breaks. Where 



$(2;)= Y,, and *, (a;) = Y2, and ^^{x) = Y3. ..$„., (.r) = Y„ 



Now, if we substitute these values of <?!> (cv) &c. 

 in the above equations we shall obtain the ordinate 

 of the system, parallel to the axis of ^, in functions 

 of the independent variable cV in the following 

 manner : 



