E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
means literally a sediment; that which is on the ground. It is a military term. In battle the Romans drew up their army in three divisions: first, the light-armed troops made the attack, and, if repulsed, the pike-men came up to their aid; if these two were beaten back, the swordsmen (principes) advanced; and if they too were defeated, the reserve went forward. These last were called subsidies because they remained resting on their left knee till their time of action. Metaphorically, money aid is called a subsidy. (Latin, subsideo, to subside.)