CYCLOGRAPHIC TRANSFORMATION OF ORDINARY SPACE 43 



In case of a conic the envelope is a curve of the 8th order and 

 4th class. The normals to the conic are the projections of the gen- 

 eratrices of the corresponding developable singular surface of the 

 congruence. The edge of regression of this surface is orthograph- 

 ically projected as the evolute of the conic. All circles tangent to a 

 conic represent a developable surface of the 8th order and 4th class. 



Numerous other applications might be added which would show 

 the usefulness of the method of cyclography for the solution of cer- 

 tain problems of historic interest. Fiedler, for instance, has given a 

 remarkably simple solution of Apollonius' problem by this method. 

 The propositions of this paper concerning orthogonality may also be 

 generalized for isogonality. In a future article the writer intends to 

 continue this subject. 



May 21, 1901. 



