(34.) Living, then, in a world where such laws obtain, and under their immediate dominion, it is manifestly of the utmost importance to know them, were it for no other reason than to be sure, in all we undertake, to have, at least, the law on our side, so as not to struggle in vain against some insuperable difficulty opposed to us by natural causes. What pains and expense would not the alchemists, for instance, have been spared by a knowledge of those simple laws of composition and decomposition, which now preclude all idea of the attainment of their declared object! what an amount of ingenuity, thrown away on the pursuit of the perpetual motion, might have been turned to better use, if the simplest laws of mechanics had been known and attended to by the inventors of innumerable contrivances destined to that end! What tortures, inflicted on patients by imaginary cures of incurable diseases, might have been dispensed with, had a few simple principles of physiology been earlier recognised! (35.) But if the laws of nature, on the one hand, are invincible opponents, on the other, they are irresistible auxiliaries; and it will not be amiss if we regard them in each of those characters, and consider the great importance of a knowledge of them to mankind,-- I. _In showing us how to avoid attempting impossibilities._ II. _In securing us from important mistakes in attempting what is, in itself, possible, by means either inadequate, or actually opposed, to the end in view._ III. _In enabling us to accomplish our ends in the easiest, shortest, most economical, and most effectual manner._ IV. _In inducing us to attempt, and enabling us to accomplish, objects which, but for such knowledge, we should never have thought of undertaking._ We shall therefore proceed to illustrate by examples the effect of physical knowledge under each of these heads:--