362 PROCEEDINGS OF THE AMERICAN ACADEMY. 



the two infinitely near circles which define the direction) such that 

 four infinitely near generators are cut in two poinis by one circle. 



The system U.^can be generated in <:'^^ ways by oc^ circled surfaces 

 having the above property. 



There are oo^ linear series A^ tangent to Ui in a circle C and a cii'cle 

 infinitely near to C. 



17. Three-parameter FAMILIES 17^. There are cc^ linear series As 

 tangent to Ij\ in a given circle C, 



The linear circled swrfaces which have C and three consecutive circles 

 to C in common generate a linear series Ag. 



The circles infinitely near to the first and second order to a given 

 article C of U^ lie in a three-parameter family of order four having five 

 circles of a penticycle for double elements. 



There are cc^ directions such that a linear system A^ will have three- 

 circle contact with 11%. 



Massachusetts Institute of Technology. 



