CALIFORNIA ACADEMY OF SCIENCES. [Proc. 3D Ser. 



the points of these coincident conies are self-correspond- 

 ing. This special case is Dr. Dickson's transformation. 



A and B are vertices of one of the fundamental tri- 

 angles, A' and B' the corresponding vertices of the other. 

 The remaining vertices C and C are readily found by the 

 following construction (see fig. 2) : 



Let A B meet a again in Qi, and B again in P\ ; let A' B 



meet a again in 7? 2 and B again in JR\. Then A 7? 2 and 

 B R\ meet in C, and A' Qi, and B' P\ meet in C. 



It is obvious that C and C will lie on a third conic 7 

 through Di, D 2 , B 3 , D±. In the case of Dr. Dickson's 

 transformation, however, where a and /? coincide, the above 

 construction shows that C and C coincide, being the inter- 

 section of A B and A' B. 



Finally, the transformation is fully determined if the 

 double points D\, D%, D s , Di and the vertices of one of the 

 fundamental triangles, say A, B, C, be given. These 

 points suffice to determine the conies a, 8 and 7. The 

 vertices of the other triangle can be found by the following 



