An important reference is " The Differential Equations satisfied by Concomitants of Quantics," by A.
A great number of birds' bones have been found in caves, and among them some bearing marks of human workmanship. In France we have a large and extinct crane, Grus primigenia, but more interesting are the numerous relics of two species, the concomitants even now of the reindeer, which were abundant in that country at the period when this beast flourished there,and have followed it in its northward retreat.
The dissolution of feudalism, the development of towns, the growth of scholasticism, all these and much more have been ascribed to the Crusades, when in truth they were concomitants rather than results, or at any rate, if in part the results of the Crusades, were in far larger part the results of other things.
There also exist functions, which involve both sets of variables as well as the coefficients of u, possessing a like property; such have been termed mixed concomitants, and they, like contravariants, may appertain as well to a system of forms as to a single form.
He proves, by means of the six linear partial differential equations satisfied by the concomitants, that, if any concomitant be expanded in powers of xi, x 2, x 3, the point variables-and of u 8, u 2, u3, the contragredient line variables-it is completely determinate if its leading coefficient be known.