ON GRAniTC METHODS IN MECHANICAL SCIENCE. 



377 



Fig. 4. 



C 



? 







For instance, in a paper read by Mr. Price Williams we have the 

 various data about different railways conapared in this way.' 



This method of employing only one dimension of space, or using the 

 scalars of Sir W. R. Hamilton, 

 can only represent a limited 

 number of isolated facts, and, 

 except in the application of scales 

 and for the purposes of slide-rule 

 calculation, has little interest. 



Suppose now a second point 

 be taken 0., ; then the distance 

 of A from it may also represent 

 another numerical quantity, and 

 is quite independent of its dis- 

 tance from Oj. 



Conversely, having two quan- ^ 

 tities to represent a point, A c 

 may be found, which is at dis- 

 tances from 1 and 2 represent- 

 ing respectively these quantities 

 (fig. 5). 



It is clear that by drawing 

 arcs of circles there are two 

 points (A and Aj, fig. 5), and 

 only two, which can be found to 

 correspond with these results — o, O O, oi O^ 



viz., the intersection of the arcs. 



These two points are situated symmetrically on either side of the line 

 through Oi O2. 



So with distances corresponding to OB, OC, . . ., fig. 4, two points 

 being found in each case ; but since the fields separated by Oj O2 are exactly 

 similar to each other and symmetrical in relation to the position of the points 

 A, B, C, D, . . ., only one set of the two situated symmetrically on oppo- 



B 



Fig. 5. 



O, 



.-^-- 



.--p 





\ / 



"^ O, 



site sides of the line joining Oj Oj need be considered. Thus, considering 

 one set of the two symmetrical systems of points, it may be said that each 



' Proceedings of the Institiition 0/ Mechanical Engineert, 1879, p. 96. 



