its expansion has the same happy effect naturally of preventing mischief from its excess, which the skill of the great mechanist gave artificially to steam, thus rendering his engine as safe as it is powerful.

The grand difference, then, between one discovery or invention and another, is in degree, rather than in kind; the degree in which a person, while he outstrips those whom he comes after, also lives, as it were, before his age. Nor can any doubt exist that, in this respect, Newton stands at the head of all who have extended the bounds of knowledge. The sciences of dynamics and of optics are especially to be regarded in this point of view; but the former in particular; and the completeness of the system which he unfolded,-its having been at the first elaborated and given in perfection,-its having, however new, stood the test of time, and survived, nay gained by, the most rigorous scrutiny-can be predicated of this system alone, at least in the same degree. That the calculus, and those parts of dynamics which are purely mathematical, should thus endure for ever, is a matter of course. But his system of the universe rests partly upon contingent truths, and might have yielded to new experiments and more extended observation. Nay, at times it has been thought to fail, and further investigation was deemed requisite to ascertain if any error had been introduced-if any circumstance had escaped the notice of the great founder. The most memorable instance of this kind is the discrepancy supposed to have been found between the theory and the fact in the motion of the lunar apsides, which about the middle of the last century occupied the three first analysts of the age. The error was discovered by themselves to have been their own in the process of their investigation; and this, like all the other doubts that were ever momentarily entertained, only led in each instance to new and more brilliant triumphs of the system. The prodigious superiority in this cardinal point of the

Newtonian to other discoveries, appears manifest upon examining almost any of the chapters in the history of science. Successive improvements have, by extending our views, constantly displaced the system that appeared firmly established. To take a familiar instance, how little remains of Lavoisier's doctrine of combustion and acidification, except the negative positions, the subversion of the system of Stahl. The substance having most eminently the properties of an acid (chlorine) is found to have no oxygen at all, while many substances abounding in oxygen, including alkalis themselves, have no acid property whatever; and without the access of oxygenous or of any other gas, heat and flame are produced in excess.

The doctrines of free trade had not long been promulgated by Smith, before Bentham demonstrated that his exception of usury was groundless; and his theory has been repeatedly proved erroneous on colonial establishments, as well as his exception to it on the navigation laws; and the imperfection of his views on the nature of rent is undeniable, as well as on the principle of population. In these, and such instances as these, it would not be easy to find in the original doctrines the means of correcting subsequent errors, or the germs of extended discovery. But even if philosophers finally adopt the undulatory theory of light, instead of the atomic, it must be borne in mind that Newton gave the first elements of it by the well-known proposition in the 8th section of the Second Book of the Principia, the scholium to that section also indicating his expectation that it would be applied to optical science; while M. Brot has shown how the doctrine of fits of reflection and transmission tallies with polarization, if not with undulation also. But the most marvellous attribute of Newton's discoveries, is that in which they stand out prominent among all the other feats of scientific research, stamped with the peculiarity of his intellectual character; they were, their great author lived,

before his age, anticipating in part what was long after wholly accomplished, and thus unfolding some things which at the time could be but imperfectly, others not at all, comprehended; and not rarely pointing out the path and affording the means of treading it, to the ascertainment of truths then veiled in darkness. He not only enlarged the actual dominion of knowledge, penetrating to regions never before explored, and taking with a firm hand indisputable possession; but he showed how the bounds of the visible horizon might be yet further extended, and enabled his successors to occupy what he could only descry; as the illustrious discoverer of the new world made the inhabitants of the old cast their eyes over lands and seas for distant from those he had traversed; lands and seas which they could form to themselves no conception of, any more than they had been able to comprehend the course by which he led them on his grand enterprise. In this achievement, and in the qualities which alone made it possible, inexhaustible fertility of resources, patience unsubdued, close meditation that would suffer no distraction, steady determination to pursue paths that seemed all but hopeless, and unflinching courage to declare the truths they led to, how far soever removed from ordinary apprehension,-in these characteristics of high and original genius, we may be permitted to compare the career of those great men. But Columbus did not invent the mariner's compass, as Newton did the instrument which guided his course and enabled him to make his discoveries, and his successors to extend them by closely following his directions in using it. Nor did the compass suffice to the great navigator without making any observations, though he dared to steer without a chart; while it is certain that by the philosopher's instrument his discoveries were extended over the whole system of the universe, deternining the masses, the forms, and the motions of all its parts, by the mere inspection of abstract calculations and formulas analytically deduced.

The two great improvements in this instrument which have been made-the calculus of variations by Euler and La Grange, the method of partial differences by d'Alembert-we have every reason to believe were known, at least in part, to Newton himself. His having solved an isoperimetrical problem (finding the line whose revolution forms the solid of least resistance), shows clearly that he must have made the co-ordinates of the generating curve vary; and his construction agrees exactly with the equation given by that calculus. That he must have tried the process of integrating by parts in attempting to generalize the inverse problem of central forces, before he had recourse to the geometrical approximation which he has given, and also when he sought the means of ascertaining the comet's path, which he has termed by far the most difficult of problems, is eminently probable, when we consider how naturally that method flows from the ordinary process for differentiating compound quantities, by supposing each variable in succession constant; in short, differentiating by parts. As to the calculus of variations having substantially been known to him, no doubt can be entertained. Again, in estimating the ellipticity of the earth, he proceeded upon the assumption of a proposition of which he gave no demonstration (any more than he had done of the isoperimetrical problem) that the ratio of the centrifugal force to gravitation determines the ellipticity. Half a century later, that which no one before knew to be true, which many probably considered to be erroneous, was examined by one of his most distinguished followers, Maclaurin, and demonstrated most satisfactorily to be true. Newton had not failed to perceive the necessary effects of gravitation in producing other phenomena, beside the regular motion of the planets and their satellites in their course round their several centres of attraction. One of these phenonema, wholly unsuspected before the

discovery of the general law, is the alternate movement to and fro of the earth's axis, in consequence of the solar (and also of the lunar) attraction combined with the earth's motion. This libration, or nutation, distinctly announced by him as the result of the theory, was not found by actual observation to exist till sixty years and upwards had elapsed, when Bradley proved the fact.

The great discoveries which have been made by La Grange and La Place upon the results of disturbing forces, have established the law of periodical variation of orbits, which secures the stability of the system by prescribing a maximum and a minimum amount of deviation; and this is not a contingent, but a necessary truth, by rigorous demonstration, the inevitable result of undoubted data in point of fact, the eccentricities of the orbits, the directions of the motions, and the movement in one plane of a certain position. That wonderful proposition of Newton, which, with its corollaries, may be said to give the whole doctrine of disturbing forces, has been little more than applied and extended by the labours of succeeding geometricans. Indeed, La Place, struck with wonder at one of his comprehensive general statements on disturbing forces, in another proposition, has not hesitated to assert that it contains the germ of La Grange's celebrated inquiry, exactly a century after the Principia was given to the world. The wonderful powers of generalization, combined with the boldness of never shrinking from a conclusion that seemed the legitimate result of his investigations-how new and even startling soever it might appear-was strikingly shown in that memorable inference which he drew from optical phenomena, that the diamond is "an unctuous substance coagulated;" subsequent discoveries having provel both that such substances are carbonaceous, and that the diamond is crystallized carbon; and the foundations of mechanical chymistry were laid by him