It may be written in the form n n-1 2 ax 1 +bx1 x2 +cx 1 x 2 + ...; or in the form n n n=1 n n-2 2 +(1)bx x2+ ?
The two forms ax, bx, or of, 0, may be identical; we then have the kth transvectant of a form over itself which may, or may not, vanish identically; and, in the latter case, is a covariant of the single form.
To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.
The load on an element bx of the beam may be represented by wbx, where - w is in general a function of x.
Consider the general quadratic equation ax 2 + bx + c = 0 where a 0.
