some admirable contrivances, now forgotten, before he made the step which created the steam-engine anew-not only the parallel motion, possibly a corollary to the proposition on circular motion in the Principia, but the separate condensation, and above all, the governor, perhaps the most exquisite of mechanical inventions; and now we have those here present who apply the like principle to the diffusion of knowledge, aware, as they must be, that its expansion has the same happy effect, naturally 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 its high 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 prop

erties of an acid (chlorine) is found to have no oxygen at all, while many substances abounding in oxygen, including alkalies themselves, have no acid property whatever; and without the access of oxygenous or of other any heat and flame are pro

duced in excess.

gas

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 Biot 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, that in which they stand out prominent among all the other feats of scientific research, stamped with the peculiarity of his intellectual character-is this, that 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 undisputed 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 inhabi tants of the old cast their eyes over lands and seas far distant from those he had traversed; lands and seas of which they could form to themselves no conception, 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 fol lowing 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, determining 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 madehe calculus of variations by Euler and Lagrange, the method of artial differences by d'Alembert-we have every reason to velieve 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 coordinates 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 phenomena, 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 Lagrange and Laplace 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 labors of succeeding geometricians. 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 Lagrange'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 proved both that such substances are carbonaceous, and that the diamond is crystallized carbon; and the foundations of mechanical chemistry were laid by him with the boldest induction and most felicitous anticipations of what has since been effected. The solution of the inverse problem of disturbing forces has led Le Verrier and Adams to the discovery of a new planet, merely by deductions from the manner in which the motions of an old one are affected, and its orbit has been so calculated that observers could find it-nay, its disc as measured by them varies less than a second from the amount given by the theory. Moreover, when Newton gave his estimate of the earth's density, he wrote a century before Maskelyne, who, by measuring the force of gravitation in the Scotch mountains, gave the proportion to water as 4.716 to 1; and, many years after, Cavendish, by experiments with mechanical apparatus, (1798) corrected this to 548, and Baily, more recently (1842) to 5.66, Newton having given the proportion as between five and six times. In these instances he only showed the way and anticipated the result of future inquiry by his followers. But the oblate figure of the earth affords an example of the same kind, with this difference, that here he has himself perfected the discovery and nearly completed the demonstration. From the

SECOND SERIES, VOL. XXVII, No. 79.-JAN., 1859.

mutual gravitation of the particles which form its mass, combined with their motion round its axis, he deduced the proposition that it must be flattened at the poles; and he calculated the proportion of its polar to its equatorial diameter. By a most refined process he gave this proportion upon the supposition of the mass being homogeneous. That the proportion is different in consequence of the mass being heterogeneous does not in the least affect the soundness of his conclusion. Accurate measurements of a degree of latitude in the equatorial and polar regions, with experiments on the force of gravitation in those regions, by the different lengths of a pendulum vibrating seconds, have shown that the excess of the equatorial diameter is about 11 miles less than he had deduced it from the theory; and thus that the globe is not homogeneous. But on the assumption of a fluid mass, the ground of his hydrostatical investigation, his proportion of 229 to 230 remains unshaken, and is precisely the one adopted and reasoned from by Laplace, after all the improvements and all the discoveries of later times. Surely at this we may well stand amazed, if not awe-struck.

A century of study, of improvement, of discovery, has passed away, and we find Laplace master of all the new resources of the calculus, and occupying the heights to which the labors of Euler, Clairaut, D'Alembert and Lagrange have enabled us to ascend, adopting the Newtonian fraction of 1: 230 as the accurate solution of this speculative problem. New admeasurements have been undertaken upon a vast scale, patronised by the munificence of rival governments; new experiments have been performed with approved apparatus of exquisite delicacy; new observations have been accumulated, with glasses far exceeding any powers possessed by the resources of optics in the days of him to whom the science of optics as well as dynamics owes its origin; the theory and the fact have thus been compared and reconciled together in more perfect harmony; but that theory has remained unimproved, and the great principle of gravitation, with its most sublime results, now stands in the attitude, and of the dimensions, and with the symmetry, which both the law and its application received at once from the mighty hand of its immortal author. But the contemplation of Newton's discoveries raises other feelings than wonder at his matchless genius. The light with which it shines is not more dazzling than useful. The difficulties of his course and his expedients, alike copious and refined for surmounting them, exercise the faculties of the wise while commanding their admiration. But the results of his investigations, often abstruse, are truths so grand and comprehensive, yet so plain, that they both captivate and instruct the simple. The gratitude, too, which they inspire, and the veneration with which they encircle his name, far from tending to obstruct future improvement, only proclaim his disciples the