ON GRAPHIC METHODS IN MECHANICAL SCIENCE. 

 Fig. 14. 



597 



It is supposed that always a < 1, and the diflPerent values of p are set 

 off from along the axis of?/, positive helow and negative atoue, and lines 

 parallel to the axis of x are drawn through their extremities. If ^^ is 

 plotted off from the origin along a^, the ordinate of the point thus 

 obtained will be fiai, and the vertical distance from the point from the 

 horizontal through j5i_i is 



This value of iji_i is plotted along the ray a^.j, and from point so 

 obtained the value ?/j_i is set off vertically upivards, because ai_i>l, and 

 also because ^i_2 is a negative value, and it is therefore plotted above the 

 origin. The value ^j_2, being already set off from O along Oy, and a 

 horizontal drawn through its extremity, intersects the vertical line 2/j_i 

 produced so as to give 



yi--2=yi-i»i-i+Pi-2 



= (Piai + Pt-i)«i-i+i'i-2- 



Proceeding in this way the required value of y is obtained, which when 

 all the values of a are the same gives 



l/=J)ia* + p,_ia*-'+ . . . +p„. 

 By making a an unknown quantity x and taking y = the equation 



0=p.iX'+Pi_-iX'-^+ . . . +p„ 



can be solved, this being an equation of the ?(th degree with one unknown 

 quantity. 



Centroids and Moments of Inertia (Derived Diagrams). 



The construction for finding continuous products needs further con- 

 sideration, apart from the applications already mentioned, as it is a 

 matter of general importance to have a graphical method for obtaining 



