Their complaint against him for having interfered, as they termed it, with their recent discovery of iodine, on which, having obtained a specimen, he chose, naturally enough, to make experiments, appears incomparably absurd. He had never complained of their interference, during his illness in 1807, with the process of deoxygenation by means of galvanic action; on the contrary, he had availed himself thankfully of the lights shed by their ingenuity on his process, and had immediately after made new discoveries, at which they had failed to arrive. It may be more true that his manners were unpleasing; and, as ever happens when a great man is also a shy one, he was charged with being supercilious and cold. They who knew him will at once acquit him of any such charge; but he was painfully timid by nature when mixing with society; and hence the mistake of our neighbours, who, though great critics in manner, are far from being infallible, and are exceedingly susceptible-fully as susceptible as he was shy. Possibly they looked down upon him in consequence of a peculiarity which he no doubt had. He was fond of poetry, and an ardent admirer of beauty in natural scenery. But of beauty in the arts he was nearly insensible. They used to say in Paris that on seeing the Louvre, he exclaimed that one of its statues was a beautiful stalactite ;" and it is possible that this callousness, or this jest, whichever it might be, excited the scorn or the humour of men not more sincere lovers of sculpture than himself, or more able judges of its merits, but better disposed to conceal their want of taste or want of skill.

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When Sir Joseph Banks terminated his long and respectable course in 1820, Davy was unanimously chosen to succeed him as President of the Royal Society, and continued to fill that distinguished office until, his health having failed, he resigned it in 1827, and. was succeeded by his early patron Davies Giddy Towards the end of 1825 he had an apoplectic seizure, which, though slight (if any such attack can be so

called), left a paralytic weakness behind, and he was ordered to go abroad in search of a milder and dryer climate. He returned home in the following autumn, not very ill, but not much restored in strength, and unable to continue his scientific labours. The work

on fly-fishing called 'Salmonia' was the amusement of those hours in which, comparatively feeble, his mind yet exerted what energy remained to it, on the favourite pursuit of his leisure. It contains both curious information on natural history, and many passages of lively and even poetical description. The same may be said of many things in his latest work, Last Days of a Philosopher,' which he wrote in the year after, when he again went to the continent in search of health. He wintered at Rome, and in May 1829, on his arrival at Geneva, after passing the day in excellent spirits, and dining heartily on fish, he had a fatal apoplectic attack in the night, and died early in the next morning, 29th May, without a struggle.

There needs no further remark, no general character to present a portrait of this eminent individual. Whoever has perused the history of his great exploits in science, with a due knowledge of the subject, has already discerned his place, highest among all the great discoverers of his time. Even he who has little acquaintance with the subjects of his labours may easily perceive how brilliant a reputation he must have enjoyed, and how justly; while he who can draw no such inference from the facts would fail to obtain any knowledge of Davy's excellence from all the panegyrics with which general description could encircle his name.

*It may not be impertinent to relate here a singular proof of the admiration in which his name was held by his countrymen, and how well it became known even among the common people. Retiring home one evening he observed an ordinary man showing the moon and a planet through a telescope placed upon the pavement. He went up and paid his pence for a look. But no such thing would they permit. "That's Sir Humphry," ran among the people; and the exhibitor, returning his money, said, with an important air which exceedingly delighted him, that he could not think of taking anything from a brother philosopher.

SIMSON.

THE wonderful progress that has been made in the pure mathematics since the application of algebra to geometry, begun by Vieta in the sixteenth, completed by Des Cartes in the seventeenth century, and especially the still more marvellous extension of analytical science by Newton and his followers, since the invention of the Calculus, has, for the last hundred years and more, cast into the shade the methods of investigation which preceded those now in such general use, and so well adapted to afford facilities unknown while mathematicians only possessed a less perfect instrument of investigation. It is nevertheless to be observed that the older method possessed qualities of extraordinary value. It enabled us to investigate some kinds of propositions to which algebraic reasoning is little applicable; it always had an elegance peculiarly its own; it exhibited at each step the course which the reasoning followed, instead of concealing that course till the result came out; it exercised the faculties more severely, because it was less mechanical than the operations of the analyst. That it afforded evidence of a higher character, more rigorous in its nature than that on which algebraic reasoning rests, cannot with any correctness be affirmed; both are equally strict; indeed if each be mathematical in its nature, and consist of a series of identical propositions arising one out of another, neither can be less perfect than the other, for of certainty there can be no degrees. Nevertheless it must be a matter of regret and here the great master and author of modern mathematics has joined

in expressing it-that so much less attention is now paid to the Ancient Geometry than its beauty and clearness deserve; and if he could justly make this complaint a century and a half ago, when the old method had but recently, and only in part, fallen into neglect and disuse, how much more are such regrets natural in our day, when the very name of the Ancient Analysis has almost ceased to be known, and the beauties of the Greek Geometry are entirely veiled from the mathematician's eyes! It becomes, for this reason, necessary that the life of Simson, the great restorer of that geometry, should be prefaced by some remarks upon the nature of the science, in order that, in giving an account of his works, we may say his discoveries, it may not appear that we are recording the services of a great man to some science different from the mathematical.

The analysis of the Greek geometers was a method of investigation of peculiar elegance, and of no inconsiderable power. It consisted in supposing the thing as already done, the problem solved, or the truth of the theorem established; and from thence it reasoned until something was found, some point reached, by pursuing steps each one of which led to the next, and by only assuming things which were already known, having been ascertained by former discoveries. The thing thus found, the point reached, was the discovery of something which could by known methods be performed, or of something which, if not self-evident, was already by former discovery proved to be true; and in the one case a construction was thus found by which the problem was solved, in the other a proof was obtained that the theorem was true, because in both cases the ultimate point had been reached by strictly legitimate reasoning, from the assumption that the problem had been solved, or the assumption that the theorem was true Thus, if it were required from a given point in a straight line given by position, to draw a straight

line which should be cut by a given circle in segments, whose rectangle was equal to that of the segments of the diameter perpendicular to the given line-the thing is supposed to be done; and the equality of the rectangles gives a proportion between the segments of the two lines, such that, joining the point supposed to be found, but not found, with the extremity of the diameter, the angle of that line with the line sought but not found, is shown by similar triangles to be a right angle, i. e., the angle in a semicircle. Therefore the point through which the line must be drawn is the point at which the perpendicular cuts the given circle. Then, suppose the point given through which the line is to be drawn, if we find that the curve in which the other points are situate is a circle, we have a local theorem, affirming that, if lines be drawn through any point to a line perpendicular to the diameter, the rectangle made by the segments of all the lines cutting the perpendicular is constant; and this theorem would be demonstrated by supposing the thing true, and thus reasoning till we find that the angle in a semicircle is a right angle, a known truth. Lastly, suppose we change the hypothesis, and leave out the position of the point as given, and inquire after the point in the given straight line from which a line being drawn through a point to be found in the circle, the segments will contain a rectangle equal to the rectangle under the perpendicular segments-we find that one point answers this condition, but also that the problem becomes indeterminate; for every line drawn through that point to every point in the given straight line has segments, whose rectangle is equal to that under the segments of the perpendicular. The enunciation of this truth, of this possibility of finding such a point in the circle, is a Porism. The Greek geometers of the more modern school, or lower age, defined a Porism to be a proposition differing from a local theorem by a defect or defalcation in the hypothesis;