I have not seen it noticed by any mathematician that in the theory of Linear Differential Equations there are two important classes of functions of the coefficients which have remarkable analogies to the invariants of Algebraic Binary Quantics; consequently I venture to call attention to their existence and also to give examples of their application in the present paper. For convenience I write the equation with binomial coefficients thus d n y / dx n + n P 1dn -1 y/ dxn -1 + n. n -1./2 P 2dn -2 y/ dxn -2 + . . . + P n y = 0 . . . . . (1) where of course P 1 , P 2 , &c., are functions of x only.