the i t " power of that appertaining to a x and b x multiplied by the j t " power of that appertaining to a x and c x multiplied by &c. If any two of the linear forms, say p x, qx, be supposed identical, any symbolic expression involving the factor (pq) is zero.

00we find that Di must be equal to p x g x for then t x (p x) 3 +, u (g x) 3, Hence, if px, qx be the linear factors of the Hessian 64, the cubic can be put into the form A(p x) 3 +ï¿½(g x) 3 and immediately solved.

00is of the form px 2 + qx -{- r.

00qX +Pu = N.j These equations are applicable to any dynamical system whatever.

00we find that Di must be equal to p x g x for then t x (p x) 3 +, u (g x) 3, Hence, if px, qx be the linear factors of the Hessian 64, the cubic can be put into the form A(p x) 3 +Ã¯¿½(g x) 3 and immediately solved.

00

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