their parallaxes. This of course assumes the truth of Kepler's law; but (as in almost all astronomical reasoning) the approximate values are assumed as a basis on which to obtain the more accurate. Now, when we have given the difference of two quantities and their ratio, it requires only the solution of a simple equation to find the actual quantities themselves. In this way, then, the absolute parallaxes of the sun and Venus may be found, and, consequently, their actual distances: hence those of the other planets follow by means of Kepler's law.

Such was the idea started by Halley. From this one phenomenon he proposed to conclude the dimensions of all the planetary orbits; and the observation in question is of a kind admitting of the highest degree of precision. The phenomenon, indeed, is one of very rare occurrence. Halley, however, earnestly recommended the careful observation of them. The next which could happen was calculated for 1761; and, as he could not expect to live to witness it, he addressed to succeeding astronomers an eloquent and even affecting admonition, not to suffer so precious an occasion to pass unheeded, but to unite all their efforts to make, and procure to be made, observations at remote stations on the earth. We shall afterwards see that his exhortation was not made in vain.*

Both before and after his succession to the observatory, (in the year 1720,) the theory of the moon attracted, in a peculiar degree, the attention of Halley. He introduced several improvements in the details, and made some suggestions for perfecting the lunar tables; into these we cannot here enter, though they were of great importance as affording the practical means for finding the longitude by the lunar motions. will only proceed to describe his important discovery of a fact, in regard to the moon's motion, which no previous astronomer had suspected.

*Phil. Trans. 1691 and 1716.

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It had bitherto been the received doctrine that all the planets were subject to such inequalities only as are renewed within a certain space of time, and which, on that account, are called periodic inequalities. The mean motion is determined by a comparison of the planets' places at very distant times, embracing a great number of the periods within which the inequalities are renewed, so that the result obtained is quite independent of these inequalities. No astronomer had hitherto ventured to doubt the uniformity of these mean motions: and, in fact, this has been found correct for the primary planets. But this is not the case with the moon. The mean motion of this satellite is continually, though very slowly, accelerated; and this, from not being subject to periodical changes, is called the secular acceleration: though, strictly speaking, it has been shown to have a period of great length. It was sufficiently established by Halley, and has been confirmed by subsequent observations. Of his speculations on comets we must speak in a future section.

THE

PART III.

PROGRESS OF PHYSICAL

AND

MATHEMATICAL SCIENCE FROM THE TIME OF NEWTON TO THE PRESENT DAY.

THE period of scientific history, which we have surveyed in the preceding section, has presented us with a varied and busy scene, which, in every department, has exhibited great advances. In the first instance, the master spirits, both of Galileo opening the path of experimental research, and of Bacon indicating the route to be followed; in the next, the increasing phalanx of their disciples, prosecuting, with renewed ardour, the varied objects to which research had been directed: and their labours, whether individual or combined, all, in their several ways, co-operating to the discovery of fresh sources of information, and the opening of new avenues to truth. In the results of their enquiries, we have noticed certain infallible indications, not merely in one, but in several branches of science at the same time, of the approaches which were constantly being made to certain boundaries, which seemed to oppose themselves as barriers to the further prosecution of research, as yet insurmountable, even to those energetic minds and active powers of genius, which characterised so many distinguished philosophers towards the middle of the seventeenth century. Every thing seemed to indicate, either that the human mind had brought its inventions to that point, where, from the finite extent of its powers, they must find an impassable limit, and where a boundary must be placed beyond which the most exalted genius may in vain strive to penetrate, or that science was on the very threshold of those mysteries of nature, into which there only wanted some highly favoured and privileged guide to give her admission.

We have now to contemplate the grateful and cheering spectacle of the fulfilment of the latter anticipation. Our first section will be occupied with the discoveries of Newton, and some general account of his system. We shall proceed in the second to review the labours of his successors, who, by gradual improvements upon his discoveries and extensions of his principles, have brought the physical sciences to their existing state of advancement.

SECTION I.

THE DISCOVERIES OF NEWTON.

His early Progress.

IN the same year as the death of Galileo, the birth of Isaac Newton took place, on December 25th, 1642, in the small manor-house, of which his family were the hereditary owners, though in humble circumstances, at Woolsthorpe, in Lincolnshire. The place is religiously preserved to this day. Every thing relating to the life of so great a man acquires an extraordinary interest, but as our object here is distinct from that of personal biography, we must pass over many points of this nature, which we could willingly enlarge upon, and confine ourselves solely to those which have an immediate reference to his philosophical progress, and to his history as identified with that of science.

In delicate health from his birth, he excelled little in the ordinary sports, or even studies of boyhood, but the bent of his genius showed itself in the pursuits of practical mechanics. While his companions were flying kites, he was occupied in investigating the best forms which could be given them, and the most advantageous point for attaching the string; and his ingenuity was

displayed in a variety of contrivances, such as models of machinery, sun-dials, and a water-clock, constructed at an early age. At a later period, his attention was more absorbed by books, and he is described as a sober, silent, thinking lad:" but he does not seem to have given his mind to mathematical studies till he had commenced his residence at Cambridge, where he was admitted at Trinity College, in 1660, under the tuition of Dr. Barrow.

Commencing his studies with the "Elements of Euclid," he is said to have taken in the whole, as it were, by intuition, and thence proceeded immediately to "Des Cartes' Geometry." This, together with "Wallis's Arithmetic of Infinites," and "Kepler's Optics," formed his earliest mathematical course of study: and no doubt the same powerful mind which could connect, under a single point of view, the theorems of elementary geometry, would soon digest into some uniformity of method the valuable materials supplied by the last-mentioned works; and the germs of his future mathematical discoveries were very probably sown in the perusal of these and other writings of that age, in which so many near approaches had been made, as it were, on every side to the essential principle, of which it was reserved for him to gain possession.

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Analysis of Light.

In 1664, Newton has put it on record that he purchased a prism to try the celebrated phenomenon of colours." But intimately as he was acquainted with Dr. Barrow, and consulted, as we know he was, by that distinguished man, upon the publication of his Theory of Colours" (to which we have already alluded) in his lectures in 1668, Newton could not, at that date, have arrived at any decisive results himself, or he certainly would not have allowed his friend to publish so faulty a theory without remark. But it appears that in the very next year he had performed his