guage that many of such invaluable treatises are to be found. Those of the Useful Knowledge Society are really what they profess to be, introductions to the various branches of science, adapted merely for the use of the common people. They are written in too diffuse and explanatory a style, in general, to merit the attention of the educated class of the community; nor do we think that they possess the merit of that lucidus ordo, which of all other qualities in writing, best becomes the philosophical treatise. A remarkable instance of the want of this redeeming quality is to be found in their treatise on Arith metic and Algebra, where the two sciences are attempted to be taught together, and where the principles of both are blended so confusedly, and without regard to the genius of each, that a learner is completely mystified and lost in the labyrinth of perplexity.

The French, in imitation of us, have brought out in their capital, an immense number of ele mentary works of the same kind as we have been describing, possess ing various degrees of merit, but, in general, so far as we have seen, much superior to our own. The philosophic turn of that ingenious people is nowhere so distinctly observable as in their scientific treatises, and in those adapted for the common people it shines in no ordinary degree. Admitting that our treatises are commonly more prac. tical, we find that the French uniformly excel us in the simplicity and pointed statement of first principles. Nor do they perpetually keep the reader at the threshold of the sciences, as we do, but carry him forward to the most extensive application of the theory at every step of his progress. Other places of the Continent have been seized with the same ardour in the simplification and reduction of human knowledge, of which the beautiful little volumes, whose title we have placed at the head of this article, will show. The author has endeavoured to comprise in a methodical

arrangement, and in the smallest possible compass, the principles of the various branches of Natural Philosophy. The first volume is divided into five sections, comprehending, 1. The Properties of Bodies in general; 2. Solid Bodies, under three heads, viz. their General Properties, the Laws of Equilibrium, and the Laws of Motion; 3. Liquid Bodies, under three heads, viz. their General Properties, their Equilibrium, and their Motion; 4. Aëriform Bodies, under three heads,' viz. their General Properties, their Equilibrium, and their Motion; 5. Acoustics, under three heads, viz. Sound in general, the Vibration of Cords, and the Vibration of Rods and Surfaces. The second volume is divided into three sections, comprising, 1. Heat, under six heads, viz. its Pro. perties and Sources-its Modifications-the Laws of its Propagation, and of Cooling-Vapours, and their Mixture with Gas, including Steam

Hygrometry, and the Temperature of the Globe-and the Artificial Production of Heat and Cold; 2. Electricity, under six heads, viz. its principal Properties and Sources -its Action-its Distribution and Diminution-its Accumulation and Mechanical Effects Atmospheric Electricity - Galvanism; 3. Magnetism, under five heads, viz. its principal Properties and Sourcesthe Laws of its Action, and the Method of magnetizing Bodies - the Action of the Globe on MagnetsMagnetism of Rotation and of Heat, and Electro-Magnetic Phenomena.

From this glance at the principal subjects of these volumes, it will be seen at once that it is indeed a Résumé of Natural Knowledge, or Table of Information

on every subject which is included in the philosophy of the material world. It is most ingeniously drawn up, and the author has spared no pains in his re-, searches after the latest intelligence. We find here the results of the labours of the most distinguished philosophers of the present century, both living and dead. Laplace, Davy, Gay-Lussac, Dalton, Berze

lius, Poisson, Leslie, Biot, Arago, Hansteen, Perkins, Dulong, Petit, Wollaston, Thomson, and many other eminent chemists and mathematicians, have contributed to fill a corner in this little work, which serves as a complete memorandumbook of science to those who wish to avoid details, as well as a textbook to lecturers and students in general. Indeed, it seems to have been partly employed as such, by the author, in his course of public lectures given at the Museum of Brussels.

The style of the work is clear and intelligible, and partakes of the accuracy which distinguishes all good treatises on pure science. The general principles are stated in the shortest and most distinct manner, and are, generally, followed by one, two, three, or more, examples of their application in well known or striking instances.

The first Six Books of the Elements of Euclid, &c. &c. By the REV. DIONYSIUS LARDNER, LL.D., &c. &c., Professor of Natural Philosophy and Astronomy in the University of London.

"Two thousand years have now rolled away," 99 says our author, "since Euclid's Elements' were first used in the School of Alexandria; and to this day they continue to be esteemed the best introduction to mathematical science!" The first part of this sentence is nearly true, but not the second. The French, who outshine us in mathematics, have entirely abandoned Euclid, and have numerous neat little systems of geometry of their own. The author considers this an evil; he dreads lest the words "rigour and exactitude" should lose all definite meaning; and he fears lest"Geometry, in the ancient sense of the word," should be altogether frittered away, or be only considered as a particular application of arithmetic and algebra. As to the words "rigour and exactitude," we have no fear of their losing their meaning, even although geometry

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should be frittered away; and as to its being "only considered as a particular application of arithmetic and algebra," in our opinion, it is a consummation devoutly to be wished. Geometry would then be much more easily learned, and would be rendered much more useful to mechanics, and even to the general mass of the community. The learned and reverend Doctor really seems afraid that Geometry shall become at last too easy! There would, certainly, be some disadvantage in this, to individuals-as Professors of Mathematics would no longer be necessary; and it might go far to render Professors of Physics and Astronomy equally unnecessary; and then what would become of the University of London? alas! what would become of our Mechanics' Institute? for no man would then need to teach his brother geometry, as all might know it from the least to the greatest.

But to come ad rem, to the point at once. The Doctor has retained Euclid's Definitions almost in toto; the first of which pompously announces that "a point is that which has no parts." Now, this is rank nonsense-sheer absurdity; for that which has "no parts" is nothing at all. So, then, geometry commences with a definition of nothing! If geometry, according to the Doctor, rested on this basis, it might, indeed, soon be frittered away. The second definition is equally absurd

66

a

line is length without breadth;"this is literally as true as-" an ass is a man without understanding." The third is nugatory: the fourth is

"" a right line is that which lies evenly between its extremities;" now, right here means straight, and evenly means straightly; hence the definition runs thus-" a straight line is that which lies straightly between its extremities." This is a fine definition truly, and conveys about as much information as the sapient enunciation - "Coals are coals," which will at least prevent us from thinking that they are slates.

The seventh definition is another specimen of this learned trifling;

"A plane surface is that which lies evenly between its extremities." Now, plane means flat, and evenly, when applied to a surface, also means flat; hence, the definition amounts to this,-A flat surface is that which lies flatly between its extremities. In the language of slang, he must be a flat indeed, who would take this for a definition. It is nothing to us, whether these definitions are two thousand years old, or only two years, or two hours; no length of time, no series of ages, can sanction nonsense, or hallow absurdity. We admire the geometry of the Greeks, but we do not admire the paltry fences which they have stuck up at the entrance,—the gates of so noble a study.

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Turn we now to the Doctor's mode of arriving at a proper conception of these absurdities. Having first obtained a rude and incorrect notion of a line by drawing one with a pen, we can imagine," says Dr. Lardner, "that while its length remains unaltered, it may be infi. nitely attenuated, until it ceases altogether to have breadth, and thus we obtain the exact conception of a mathematical line." So we finite creatures must grasp this infinite notion, before we proceed with the study of geometry! This is simplification of the elements truly to introduce the idea of infinity! If we cannot obtain an idea of a mathematical line without infinity, or infinite attenuation, we shall never arrive at it at all. This is, indeed, to darken counsel by words without knowledge. This mode of arriving at the notion of a mathematical line, is only excelled by that which the Doctor proposes in order to reach the notion of a mathematical point. "The mind," says he, 66 having obtained the notion of an extremely

minute magnitude, may proceed without limit in a mental diminution of it; and that state at which it would arrive, if this diminution were infinitely continued, is a mathematical point." We had always understood that magnitudes in geometry were not physical, but ideal: the Doctor told us that we arrive at a notion of a mathematical line by the infinite attenuation of a physical line; he now tells us that we arrive at a notion of a mathematical point, by the infinite diminution of a magnitude (which, of course, we understand to be geometical). The Doctor is here evidently at fault, in his words; we have no doubt that he means a material point, instead of a magnitude. Either way, however, it is absurd. The state at which a material point or physical magnitude would arrive, by the infinite continuation of mental diminution, is what neither the Doctor nor any other man can tell; and we have no doubt that every one will consider this process an infinite absurdity.

(To be continued.)

INTERIM NOTICES.

The communication from "A Proprietor" of the Thames Tunnel has been received, and is under consideration.

If our friend, Mr. Johnston, would make his article somewhat clearer to ourselves, we should be happy to insert it.

The article by "M. A.," on spinning machinery, is rather long, and, we fear, not sufficiently original.

We shall be happy to avail ourselves of the offer of "A Friend to Popular Education."

We have a great regard for the London Mechanics' Institute, and therefore cannot insert all that "B. G." would say on the subjeet.

Communications from P. S.-A Birmingham Tradesman-R. N.-Major T.-and a Spitalfields Weaver, &c. have been received.

Published by THOMAS KELLY, 17, Paternoster Row; to whom Communications (post paid) for the Editor are to be addressed.

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IMPROVED BEE-HOUSE.

Sir,-As no drawing has yet appeared in the "Mechanics' Magazine" of a bee-house, I am induced to send you a sketch of one I have constructed, as it may be of interest to others, as well as myself, who are beefanciers, or who may be pleased to have such an ornament to a flower border.

Having very frequently remarked, that, when the entrance of a bee-house is on the windy side, the bees, on bringing home their load, are blown down, (on which it is curious to observe how the other bees will assist them to rise,) I have had mine so constructed that the entrance must always be on the side opposite to that from which the wind blows. Another desideratum I have accomplished is, that of being able to weigh the hive at any time with the greatest nicety, and to know the weight of each day's produce, without disturbing the bees in the least. The contrivances by which these things have been effected will, I presume, be readily understood by an inspection of the accompanying drawing. A represents a vane that turns the house on the stage B, so that the entrance for the bees at C is always from the wind; D the centre, which the house revolves on; E the place where the wire is fixed that is attached to the hive within the house, which hive is made of straw, in a conical form, with a deal bottom; F, a pin that passes through a loop, so that the wind will not disturb the bees in the hive. When I wish to know the weight of the bees, I take out the pin F, and then place weights on GHH, the beam. I is the beam pointer; J the end which takes out when I wish to change the hives. On one edge are two pins, and on the other a lock. The pins fit in to the stile, so that my bees are quite safe from intruders. I am, Sir, &c. Lancaster, Sulyard Street, May 23, 1829.

M. SAUL.

THE MOTION OF THE EARTH.

J. B. C.'s "Objections to the Copernican System," which were so well refuted by P. M. W. in our last Number, have been also very ably handled

in two other letters, which we have received from Mr. Lake and. Mr. Sergeant Mason.

The first part of Mr. Lake's letter contains an investigation (rather abstruse for general readers) of the relation of the force of gravitation and the centrifugal force at the equator, and of the principles by which the diminution of the centrifugal force may be ascertained in any latitude. His results agree very nearly with those of P.M.W.; and he shews that 1 lb. at London, instead of weighing 1528 lbs., as J. B. C. concludes, at the Poles, would weigh 1 lbs. there. The concluding part of Mr. Lake's letter contains an exposure of an error in J. B. C.'s paper not adverted to by P. M. W.; and this we shall give at length in Mr. L.'s own words.

Wilstone, near Tring, June 15, 1829.
Sir,

*

Having thus proved the fallacy of J. B. C.'s mode of calculating the effects of the centrifugal force, I shall now make a few remarks on the mode of finding the distance of the sun from the earth. Suppose a line drawn from S to N, in J. B. C.'s second figure, then the angle NSE will represent the sun's horizontal parallax. Now this angle has been ascertained, by means of the transit of Venus over the sun's disk, to be no more than 8"-65. This, therefore, being given, the sun's distance may be calculated as follows: as sin NSC : 1 (= one semidiameter) cos NSC (sin (90o— Sin (90 NSC) NSC)): = SC. Now, because the NSC is extremely small, it may be rejected in the numerator without sensible error; we shall, therefore, have Log. SC Log. 90° - Log. 8"-65 10.0000000 5-62191404.3780860, the natural number answering to which is 23882.84, which is the sun's distance in semi-diameters of the earth. This, therefore, multiplied by 3985 gives 95,173,117 for the sun's distance from the earth in miles. A very little consideration will, I think, convince J. B. C. that his mode of finding the sun's distance is as erroneous as his mode of calculating the effects of the

Sin NSE