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metic," in the Encyclopædia Metropolitana, treating of the introduction of the Arabic numerals into England, has quoted Chaucer's poetry, to prove that he had the newe figures," as he denominated them, about 1375; and argues that the phrase, newe figures," does not necessarily imply very recent introduction, as that title might stick by them for a century. Granting this, we are rather inclined to think that the words "newe figures" were either introduced for the sake of the measure, or to avoid scientific terms in poetry, for, in this treatise on the astrolabe, Chaucer speaks of the Arabic numerals as the “numbers of augrime, that deuiden thilke same degrees fro fiue to fiue," and that “the numbers of the signs of the degrees been written in augrime." Augrime is the corruption from the Arabic that we now write algorithm, and all the more ancient books on the Arabic numerals specified those numbers by that title.

Chaucer died in the year 1400, at the age of 72.

V.-Nomenclature of the stars. Up to the time of Bayer, (A.D. 1603,) it is supposed that the stars were never otherwise distinguished in Europe than either by their Arabic names, such as Aldebaran, Rigel, &c., or by their positions with respect to the constellation, such as, "in the head of Andromeda," "the first in the belt of Orion," &c. The maps of the well-known (by name) Bayer have gained him immortality at no great price, simply from his employing the letters of the Greek and Roman alphabets to distinguish the stars. The idea, if original, was improved by himself before the end of his life, as appears from the joint edition by himself and Julius Schiller, in which numbers are substituted. But, in our time, Bayer is only known by his letters, and the numbers employed are those given by Flamsteed, Piazzi, &c.

It has escaped the notice of all the historians of astronomy, that letters had been used to distinguish one star from another, before the time of Bayer, by Alexander Piccolomini, of Siena, who was successively Bishop of Patras, and Archbishop of his native place. This Piccolomini was a very miscellaneous writer. He was reckoned one of the best comedians of his day, and wrote

commentaries on Aristotle, and various other works, besides the one in question. The third edition of his treatise "Della Sfera del Mondo," accompanied by his work "Delle Stelle Fisse," was published at Venice in 1553; and throughout the whole of the latter he employs the italic letters to distinguish the principal stars of each constellation from each other, and has given some rude maps in which they are employed. Neither Bayer nor Piccolomini at all insist upon their use of letters as an improvement, or even make any prominent allusion to it in their introductions; though, as it happens, the name of either would hardly have been mentioned in our day on account of anything else in their writings. The work of Piccolomini alluded to, was sufficiently well-known to be translated into Latin, and published at Basle, (A.D. 1568 or 1588,) so that Bayer may very possibly have seen it. VI.-Treatises on Natural Theology. There have been a great many attempts to apply geometry to the proof of religious assertions. The last we can find, and one of the most absurd, is "Mathematical principles of Theology, or the Existence of God geometrically demonstrated, &c. by Richard Jack, teacher of Mathematics, London, 1747." Mr. Jack lays down his definitions, one of which is, "the evanescent existence of any being is that point of duration in which its existence terminates or ends;" then proceeds to his axioms, the first of which is, "nothing hath no properties," and another of which no being can exert a power which it does not possess;"-and finally establishes his point in a hundred and eleven theorems. The following is a specimen.

is,

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"THEOREM XXXII. A being cannot act after its existence is terminated.

A

+

B

D E

C

Let A be any being; I say it is impossible for the being A to act after its existence is terminated. For let B C represent any portion of time, and D the point of duration, when the existence of A is terminated, and D C that part of duration that immediately succeeds the termination of A's existence. It is impossible for A to act in any one point of the duration

DC: for if it be possible, let it act in the point E. Then because (Ax. 4) any being exists in all the points of duration in which it acts, therefore the being A will exist in the point of duration E, but its existence terminated in the point of duration D; therefore A will both exist and not exist in the same point of duration E, which is absurd. Therefore, a being cannot act after its existence is terminated; which was to be demonstrated."

We shall notice one more treatise on natural theology, because it is the reverse of the preceding. On account of its shortness, and the practical good sense shown in the method of handling the subject, we shall give it entire. It was published the year after the "House that Jack built."

Gowin Knight, M. B. on Attraction and Repulsion, London, 1748, p. 3; "The most general truth that occurs to us, in contemplating the works of the creation is, that there is a Being of infinite wisdom, goodness, and power, the first cause of all things. This is a proposition to which (one would imagine) no one who had ever cast an eye on the works of nature, could deny his assent. But if any such there are, the best advice I can give them is, To look again.'

VII.-The differential Thermometer. The late Professor Leslie invented this instrument, we suppose, without being indebted to an old book which the chances were much in favour of his never having seen. It is well-known to consist of a curved tube with a bulb at each end; the bottom of the tube, and each side up to a certain height, being filled with spirits of wine; the remainder of each tube and the bulbs being filled with air; thus composing two bodies of air which are prevented from mixing by the interposed spirit. So long as the temperature of the two bulbs of air is the same, the equilibrium is not disturbed; but if the temperature of the air in one bulb be increased, the increased elastic force of the air in that bulb compresses the air in the other bulb by means of the interposed fluid, and the spirit of wine rises in the tube the air of which did not receive accession of heat.

In the Collegium experimentale sive curiosum of J. C. Sturm, published at Nuremburg in 1701, the above apparatus is precisely described, and a double-bulbed thermometer drawn, differing only from that of Sir John Leslie in having the two arms of unequal length. The following is the description, (page 49); A and D being the two bulbs, and B and C letters attached to their tubes.

"The second species of thermoscope was a curved tube, A B C D, through the open orifice of which, D, rectified spirit of wine was poured, tinged of a blue colour, so that (as happened of itself by the narrowness of the tube) the bulb A, remaining full of air as far as B, would not admit the ascent of the fluid. The instrument being thus prepared and the hot hand moved towards the bulb A, the spirit B C ascended step by step from C towards D (by a motion contrary to its first motion); and when it was taken away, or anything cold applied, the fluid not only returned again to C, but even descended, being raised up at the other extremity,B, almost even to the middle of the bulb A."

He then proceeds to describe the process of shutting up the open end by the bulb D, and remarks that the indications of the thermometer then become much less sensible. He notices the use of this thermometer for measuring small variations of temperature, such as, "daily, or even horary variations ;" and instances as one possible application, the regulation of furnaces for hatching eggs after the Egyptian method. Sturm was a native of Hippolstein, and died about 1703; and the first edition of the Collegium, &c. was published as far back as 1672.

VIII. The Book of Knowledge, both necessary and useful for the benefit of all people, printed for the booksellers of London and Westminster, 1729. This publication, which seems to have been a sort of stock book, was, as we see, printed after the death of Newton, nearly a century after the death of Galileo, and nearly two centuries after that of Copernicus. A brief view of its contents will serve to show how much profit had been derived from a century at least of rational investigation. Unfortunately, this class of books is not quite extinct;

we have still treatises of astrology, and all kinds of stupidity besides; but not published in the name of the booksellers of London and Westminster. The Book of Knowledge contains predictions for the year, depending on the day of the week on which the Nativity falls; directions what to undertake, and what to avoid on each day of the moon; the effect of thunder in each month of the year; a great quantity of astrology; some geography, the correctness of the proportions of which may be guessed from the coast of Surrey being called 65 miles long, while the " compass of England round about," is 4390 miles, and Venice is said to be 80 miles from Flanders; —prognostics for the weather, and for husbandry: among which every man is advised in March to "advise with the honest and able astrological physician." Then follows a "brief discourse of the celestial part of the world,” in which the motion of the earth is not considered, but the heaven is violently turned about once in 24 hours by the motion of the primum mobile. Here followeth the manner of making all manner of Bonds, Bills, Leases, &c. very necessary for those who live in the country. Then follow some 66 pleasant questions in arithmetic," one of which is so very pleasant and curious a puzzle, that we shall give it.

"A certain man having three daughters, to the eldest he gave twenty-two apples, the second he gave sixteen apples, and to the third he gave ten apples, and sent them to the market to sell them, and gave them command to sell one as many for a penny as the other, namely, seven a penny, and every one to bring him home so much money as the other, and neither change either apples or moneys one with another. How could that be done? This to many seems impossible, but to the arithmetician very easie." The resources of the arithmetician were greater then than now the matter is managed in the following way-1. By sending a lady's steward to market, who buys twenty-one of the first, fourteen of the second, and seven of the third, at three-pence, two-pence, and a penny, leaving the sisters with one, two, and three apples. 2. By making the lady, who was a perfect Eve in the matter