118 



Dr. L. Silberstein : Farther Contributions 



vectors on the lines of a. b, etc. Any vector OA = A can be- 

 written A = cra, where a is a scalar number which can always- 

 be made positive (by choosing appropriately between a and) 



its negative a'). With this understanding we will denote a? 

 by I A |, so that 



A= A) a, 



and we will call j A| the tensor of A, always of course witta 

 respect to the chosen k and T. Sometimes A (where it 

 cannot be confounded with "the point A") will be used as a 

 short for [A|. With this notation the equation of the- 

 standard conic will be 



r =1, (*> 



where r is any vector drawn from to the conic tc. 



Having thus fixed upon every line through the origin the 

 points 0, 1 and co (T- point), we can construct upon it in 

 the well-known way (P.V.A., 6, 7) the points 2, 3, etc.. ^, £, 

 etc. in fact, the whole projective scale. The locus of the 

 end-points of all vectors such as 2a, 2b, etc. will again be a 

 conic, k 2 say, whose equation will be 



an 



d so on, in general. 



— 9 



r I =r = const. 



