92 



a tedious process, and will not be indicated here. When performed, how- 

 ever, there results the two differential invariants 



0, = r2 A3 A3 -35 A, Al -7 {a.-Iai}^] ^ (A,)^ 

 ,.= [A.{A._84A.A, + f A^}-12{a,-|a.A3}{a.-1ai} 



+ |{A,-AAi;^]^A^ 

 where A, = 3y'^' y" - 4 {f )\ 



A3 ^ yv (y-)2 _ I5y/V y^// y- + ^ , y-^ S 



A, = 3yv' (y-)3 _24yv Y^' (y-,^ + GOy'^ (y'^^)=' y''-40 y^'OS 

 A5 = 9y^'' (y'O* - 105y^' y'^^ f + 420 y^ (y''^^ ly'';^ — 



70lVv,y.//)3y// + l:^ y-/,5, 



A,, = 27yv^'' (y^^)^ —48 A5 y'" — 810 A, ^Y" r- — 2240 A3 (y"^j^ 



2240 ,,,,6 

 — 2800 A, iY")^ — -q y I • 



