278 FROFESSOR M. J. M. HILL ON A SYSTEM OF SURFACES. 
Section VI. (Art. 30 ).—Exceptional Cases. 
Art. page 
30.— I. The Fundamental Equations are satisfied by values of the coordinates which are 
functions of one parameter only. 270 
Example 18. 270 
II. The Fundamental Equations are satisfied by values of the coordinates which are 
independent of the parameters. 271 
Example 19. 271 
III. The Fundamental Equations cannot be satisfied by any values of the coordinates 
which make the Discriminant vanish, the parameters being finite. 272 
Example 20 272 
IV. The Fundamental Equations are equivalent to only two relations between the 
coordinates and parameters. 273 
Example 21 ... , 273 
V. The Fundamental Equations are equivalent to only one relation between the 
coordinates and parameters. 273 
