400 MB. A. R. FOBSYTH ON INVARIANTS, COVARIANT3, AND QUOTIENT- 



24. 77ie invariant 6 fi . 



The most general form possible is 



Proceeding as before, it is found that the necessary conditions are 



. _B ___ 3C_.3D^ 14E_ n+1 F n + 1 G re + 1 7J 



= " = ~ ~ ~ 



3 - 5 5 3n + 7 5 ~ 3 + 7 10 ~ 14?i + 31 10 ' 



3K + L = 0, 



. 7n_+_8 

 n + 1 



R _ so A 7n 3 + 28n + 25 

 (n + I) 8 



These conditions leave two constants undetermined ; they may be taken to be A and 

 L. When the values of the others are substituted, it appears that the part of the 

 function involving L can be expressed in the form 



that is, a composite invariant of index 6. As no new function is thereby determined, 

 we omit it ( 18) by making L zero ; and then, taking A to be unity, we have 



-p OB, 104 53 B . go 



~ r ~ * dx ~ 3 <fe* " 8 do* " 14 da* " 7 



25. TAe invariant 7 . 



Proceeding as in the last three cases from the most general form, we are led to a 

 number of relations among the assumed constants which leave two of these constants 

 undetermined. When all the other constants have their values in terms of these two 

 substituted, it is found that the aggregate of the terms involving one of the constants 



