&UPPLBMENTARY CURVKS. 



197 



For instance, if the given surface be one of the second 

 degree, and if the system of straight lines be drawn parallel 

 to a given line, we should find, as in No. VI., that the 

 supplementary surface is also one of the second degree 

 touching the given surface along the plane curve in which 

 it is cut by the diametral plane which' bisects chords parallel 

 to the given line. And as the preliminary propositions in 

 Section I. can readily be extended to surfaces, the two sup- 

 plementary surfaces will be found to possess properties exactly 

 analogous to those developed in the notes to No. VI. But 

 having extended this paper rather beyond the prescribed 

 limits, I must conclude by merely pointing out to the reader 

 a fertile and interesting field of inquiry, which, as far as I 

 know, has not been hitherto investigated. 



