ON GEAPHIC METHODS IN MECHANICAL SCIENCE. 



605- 



different directions in a plane, and it may not be desirable to commence 

 by making the segments parallel. Let AB, BC, CD, . . . (fig. 17) be 

 segments, the sum of the products of which into the perpendicular 

 distance of their directions from a given point O is required, j 



Fig. 17. 



Draw the equipollent diagram by combining the segments as ali-eady 

 explained. Take any pole P and draw the first derived diagram, and 

 then the second derived diagi-am, and through the point O draw a parallel 

 to the resultant A' 0'. Then the part of it M N intersected between the 

 two extreme lines of the second derived diagram gives the required sum 

 of the products. 



If the point O lies in the resultant which is the line through the point 

 of the intersection of the two extreme lines parallel to the resultant in the 

 first derived diagram, the sum of the products is zero. 



Much more might be written on such subjects as the Sum of Products 

 in Space, the Properties of Reciprocity, and the Null or Focal System, 

 but their treatment would require more space than can be allowed to the 

 report in the present volume. 



Division II. — Summary op Problems for which Graphic 

 Solutions have been Published. 



As already remarked, the limits of the report do not allow a complete 

 statement of the solution of problems in mechanical science to be given. 

 The following is a classified outline of the subject : — 



1. FORCE in its application TO BODIES CONSIDERED AS BEING RIGID. 



(1) General Treatment of External and Internal Forces. — Parallel 

 forces. Centre of gravity of areas and bodies. 



Bending moment and shearing force diagrams for vainous cases of 

 concenti-ated, uniform, and travelling loads. 



Loci of maximum bending moment of a beam for any given system of 

 loads. 



