ON GRAPHIC METHODS IN MECHANICAL SCIENCE. 



577 



performing of mnltiplication, the graphical analogue of which is as 

 follows: — 



At any arbitrary angle to the given segment A A, (fig. 3) set off a 

 segment, A B,, of unit length and produce it to B„, so that A B„=n 

 units of length. Join Aj B,, and through B„ draw B„ A„ parallel to 

 A] Bi, meeting A Aj produced in A„. 



Then 



A A„=A Ai x?2=A A, A2 . . . A„. 



Fig. 3. 



This process, it will be noted, necessitates the employment of the two 

 dimensions of a plane surface, but only gives results involving one dimen- 

 sion, as the direction is quite an arbitrary matter. 



Culmann and other writers, however, do not limit the idea of addition 

 to parallel segments, but extend it as follows : 



Let it be required to add the segments A Ai, Ai Aj, . . . fig. 4, 

 now no longer parallel. The process of doing this is shown, and A Ag is 

 said to be the graphical sum or result of the operation. This idea is 



Fig, i. 



extended to three dimensions of space ; thus Culmann says : ' The lines 

 may have any direction whatever in space, and the figure can then he 

 looked upon as a projection upon the paper. If such a combination of 

 1893. p p 



