400 APPENDIX - ON THE 



The two preceding equations are the .most general 

 that can be imagined. 



If the known planes I and 2, be parallel to a diago- 

 nal of the terminal plane of the primary form, the 

 plane 5 will be parallel to the same diagonal ; in 

 this case p , =. q l9 and p t q*i and the values of 



^J and i* become equal ; and by reducing the above 

 r 5 r & 



equations, after the necessary substitutions are made, 

 the followin will result. 





(3) & = ! = 



r. r. 



- }+( - 



3 r 4 r 3 qJ Vpj r 4 T 3 p 



The indices of the planes I and 2, it will be re- 

 marked, have disappeared from this formula, since 

 the condition of planes 5 being parallel to a diagonal 

 of the primary form, does not depend upon any 

 secondary plane. 



If we now suppose the planes 1 and 2 parallel to a 

 lateral edge of the primary plane, the plane 5 will 

 be parallel to the same edge ; then r and r a , become 



infinite, and the values of 2|, ?J, become infinite 



r s r s 

 also. But if, instead of substituting the infinite in 



equations 1 and 2, for the indices of planes 1 and 2, 

 we divide the first equation by the second, we shall 

 obtain a new equation which does not contain the 

 indices of planes 1 and 2, and which gives the values 

 of the indices p s and q^ in function of the indices 

 of planes 3 and 4. 



1 1 



PS _ ?7% ^7?4 

 9 5 " L L_ 



Pl JP 4 r 5 



