Piazzi and Harding were bot...... the field of the telescope, both round and well-defined, and Piazzi without a nebula, both planets with the magnifying power 130, appeared to have the same magnitude 1",554, but with the magnifying power 288, Pazzi was taken at 1",469, and Harding at 1,795. The distance of Piazzi on that day was 2,686, of Harding 1,730, and between the 9th and 14th of September, according to Gauss's calculation, 1,795.

On the subject of the apparent diameters the German astronomer differs in opinion with Herschel, but he gives very strong reason in support of that which he maintains. Both the author, and his assistant Mr. Harding, have made a vast number of observations, in which they very seldom disagreed to any amount worth mentioning; and besides, in general they agreed with Herschel. That Herschel might be in an error is probable, because he measured Piazzi only thrice, Olbers only once, and his measurements are not consistent. On the 1st of April 1802 he makes the apparent diameter of Piazzi with his seven-foot telescope and magnifying power 370 to be 0,40: on the 21st of April with his ten-foot and magnifier 516 to be 0,38; and on the 22d of April with the last telescope to be 022, that is only half as large as it was on the first of April; the apparent diameter on the 22d of April he de ermines to be 0,13. We cannot help uniting with our author in his testimony, in this respect, against Herschel; for such a change in the apparent diameters of Piazzi would at once determine the body to move in a very different orbit from what is assigned to it by Dr. Herschel himself.

The magnifying powers used by Herschel were far too great for the pale light of the two planets, since the finer nebulas of Piazzi and Olbers were not visible, and hence the apparent diameter was made somewhat too small by him. Several other objections are made, whence some important conclusions will hereafter be drawn on the nature of telescopes, of high magnifying powers; and when two persons of such eminence in their profession differ so very materially in their judgments, the cause must evidently soon be discovered,

Our limits will not permit us to enter at present into the discussion, which we doubt not will be brought before us again in another shape; but the management of the contest does great honour to the author.

From observations and calculations the true diameter of Piazzi is 352, of Olbers 455, of Harding 309 geographical miles; and if we take the diameter of the earth at 1719, of Mercury 608, of the moon 468, then the diameter of Piazzi is to that of the earth as 1 to 4,88, to that of Mercury as 1 to 1,73, to that of the moon as 1 to 1,33. The diameter of Olbers is to that of the earth as 1 to 3,77, to that of Mercury as 1 to 1,33, and to that of the moon as 1 to 1,02. The diameter of Harding is to that of the earth as 1 to 5,56, to that of Mercury as 1 to 1,97, and to that of the moon as I to 1,51: Olbers is therefore nearly about the same size as our moon, and about one quarter greater in diameter than Piazzi, and Harding is the least of these three bodies.

The height of the atmosphere of Piazzi above the surface of the planet is estimated at 146,62 miles, and of Olbers at 101,62 miles. Harding's atmosphere cannot easily be estimated, but it is denser and higher than that of the old planets. These three new planets are also denser than the old ones; then follows Jupiter, and next the earth. The conjecture of Dr. Olbers that the planet of his name, and Piazzi, are fragments of the same greater planet, is in great measure adopted by our author, and it scents to receive some support from the discovery of Harding: but our author does not conceive that the planets were made by a comet destroying the original; but that at the original creation those materials, which were on the point of forming a planet, were by some convulsion separated from each other, and thus became, according to the direction given by the explosion, each a planet round the suu. Whatever may be the fate of this hypothesis, we cannot give the author too much praise both for his industry in observation, his skill in calculation, his modesty in stating his own pretensions, and the merit of a rival, and above all the union of sound religion with true philosophy.

from this prospectus employed himself with great success in experiments on timber, with a view to the perfection of naval architecture. To carry on his views, he very respectfully calls upon the scientific to unite with him in a vast enquiry, by which the law of resistance may be explained. The experiments to be made are divided into classes and orders. The first class contains the case of a body moving with a given velocity, or a fluid moving with a given velocity against a body at rest, to determine the ratio of the distance of the surface. In this class are eighteen orders, presenting different angles to the fluid; and in each order are to be fifty series of experiments.

A similar class with orders contains the case of the surface of a moving body, and its angle of incidence being given, to find the ratio of the resistance to the velocity. Other experiments are proposed on the pressure of fluids, and on the nature of the pyroligneous acids, and from the latter the durability of timber, with the effect of iron and copper upon it, are to be ascertained. A curious fact is here mentioned of the mode of preserving vessels by the fishermen of Malabar, who wrap a piece of sheet copper or lead round the nails, which fasten their little vessels together; and it is suggested that the substitution of oxyd of copper or lead might not be unworthy of the notice of our ship-builders: green, white, or red paint would answer the same purpose, but be more expensive.

To make wood more durable, attention

must be paid to the gases contained in it ; these are known to exist from the common experiment of the air-pump, whose receiver on the withdrawing of the air will be filled with gas from the wood. This process is imitated by the author by a steami-vessel, into which, on the admission of the steam, the air will depart from an aperture below, and on the condensation of the steam the gases will rush from the wood to fill the vacuum. Continual immissions and condensations of steam will thus free the wood from all its gases, and when tarred over it will no longer be susceptible of their influence. This process may be applied with great advantage to the timber in the royal navy, as the chips of fir in the yards will supply all the tar that is requisite for the purpose.

By means of his steam-vessel it is proposed also to bring timber to any degree of curvature, and to employ timber thus steamed in the frames of ships. Other improvements are suggested in the structure of the decks, with a view to obviate the effects of the rolling and tossing of ships; and from the ingenuity evident in this prospectus, we cannot doubt that the proposed work is fully entitled to the patronage of the public. Much useful information will be given respecting the management of forests, both in England and in India; and it is with pleasure we learn that we may look to the latter quarter for the supplies of our yards, and the ships of India may hereafter add to the triumphs of the British navy.

THIS is a very elegant abridgment of the history of Bailly; a history too well known to the scientific reader to require here any detail. The chief facts are preserved in this work; and as the title observes, it is intended for the general, not the scientific reader. It is amusing as well as instructive; and the plan of retaining the words of the original author make it much more entertaining than those crude abridgments which at times fall into our hands, and betray bad taste under the appearance of great industry. very one remembers the fate of Bailly;

and his name, connected with the tenniscourt in which the famous oath was taken by the French deputies, will live for ever in the history of that country. This celebrity was dearly purchased by a death on the scaffold for an ungrateful nation; but the astronomer will gratefully remember the pains bestowed by the philosophical mayor of Paris on the history of his science, in five large volumes; and the general reader will be no less thankful to the editor of this abridgment, for having confined, in so short a compass, the most ma terial passages in the original work.

an encomium. It is very difficult to explain the simplest things, and the author should have paid greater attention to Locke's chapter on number. We are told first what arithmetic is, namely, the science of numbers: of course what is meant by number must be explained, and the writer very properly gives a definition of his meaning, but introduces the terms units and quantity. Quantity is then explained; but instead of explaining the meaning of unit, we are led to that of nity, a term which depends on the meaning of unit. Allowing for this very common error on such subjects, we read with pleasure the account of the progress of number by multiples and dividers of tens. We were stopped at the account of arithmetical operations, when we were told that, to make an addition, we were to express by one number the aggregate of several. Now we apprehend that, to a learner, the word aggregate wants more explanation than the word addition. In the definition of subtraction we found the term deducted used, which requires just as much explanation as the word subtraction.

The signs and are curiously explained: "to denote addition, we make use of the sign+, which means plus; and for subtraction the sign which means minus." Now is the English reader at all instructed by this explanation? for plus and minus are two Latin words, which to him are as unintelligible as any other Latin words, and both require to be translated into his own language, before he can understand the propriety of their use. But means add, and means take away; and there is no more reason for applying Latin words to the signs + and -, than there is for applying them to the signs x and.

Fractions are first defined to be numbers, by which we express quantities less

than unity; and two pages after we find that a fraction may be less or greater than a unit, or equal to it. The sections on fractions require considerable revision, and the writer will recollect that, according to his own definition, to multiply a number by another, is to repeat the one as often as there are units in the other: how then can he multiply, as he proposes to do, nine by, since is less than a unit? The want of demonstration in these sections must be very sensibly felt by a learner.

The difficulties in explaining ratios are well known to every mathematician; they are not removed by this writer. The con version of a proportion into an equation is frequently very useful, and the instances here given are well chosen. We do not see the difficulty of defining algebra intelligibly to those who have not any idea of the science; for when a person understands what arithmetic is, namely, the science of numbers, he can easily comprehend that algebra is only a part of that science. In common arithmetic all the terms are definite and known: in algebra they are frequently indefinite, and letters stand for numbers; some for those that are known, others for the numbers that are not known. The instance to explain the nature of algebra is well chosen; but we were surprised to read so poor a definition of equation, as that it is an assemblage of several quantities separated by the sign

=.

That such an assemblage constitutes an equation we doubt not; but the propriety and meaning of the term equation remains to be explained. The sections on equations scarcely belong to the subject, and may be removed without detriment to the work, which, with a little attention to the nature of learners, and care to adapt language to their use, may be made a very instructive publication.

THE attention of country gentlemen has of late years been very much called to the breeding of cattle, and peers and butch ers discuss at Smithfield every improvement on the fattening of oxen. We would not discourage any useful undertaking; yet one of the writers of the Old Testament does not apprehend this to be a kind of knowledge to be very much cultivated by the higher orders of society. It is strange, however, that another kind

of knowledge, which is of so much consequence to the land proprietor, and enters continually into the discussions of the legislature, should be so much neglected. Geometry is supposed to have taken its rise in Egypt, and the overflowings of the Nile gave importance to mensuration. The continual changes of property in England, by bills of inclosure, render this science no less useful to us; and when we consider how little is required, we

should think it very improbable that any considerable landholder would take the number of his acres upon the mere ipse dixit of the surveyor. We knew one young nobleman who was not contented with a process of this kind: he was going through the regular course of study at Cambridge, and, in one of the vacations, employed his summer months in an actual survey of his father's estates in the Highlands; thus improving himself in geometry, at the same time that he enjoyed the picturesque scenery peculiar to that part of Scotland.

We could mention also persons who, on an inclosure taking place, have found that their lands had been very differently measured by the same man, when measured some time before on their own account, and then on the account of the commissioners. Such a loss as was experienced at that time would have been prevented, if the proprietor, on the first measuring of the land, had been capable of examining the surveyor's account; and all the knowledge requisite is merely that of the four first rules in arithmetic, and the easy properties of a triangle. To render this knowledge familiar to the proprietor and to the surveyor, the author of this work

takes an instance of a supposed parish to be inclosed, which is possessed by a certain number of imaginary proprietors, whose various tenures of possession are agreeable to those found in most parishes. Their lands are then respectively measured, the quality ascertained, and the parish is divided into new allotments, agreeably to the value of each person's previous possessions. The instance is well made, and the practice upon it will give the learner complete insight into the business of land-surveying. We cannot expect the country gentleman to take his chains and rods, and flag-staffs; but without that labour, he may by this instance learn to judge of his surveyor's work, when the plan of his own estate is brought to him, and he may with ease ascertain whether the number of acres is properly estimated. The quality and price of land is a subject of great difficulty: as yet much is given to conjecture, and the mode of ascertaining it ought to be laid down in every bill of inclosure. The number of plates accompanying this work will be found very useful to the young land-surveyor, and he should plan them all out upon a different scale.

THE preceding article is of importance to the landholder, whose profits are derived from the surface of the soil; the work now before us will be found equally useful to one whose gains arise from the bowels of the earth. The quality and quantity of each mine depend upon different circumstances; the former can be known only by comparison of coals of different kinds; the latter from the usual modes of mensuration applied to subterraneous passages. Our author begins need lessly with the very first rudiments of geometry; for it must be supposed that no one will apply himself to the practice of subterraneous surveying, who has not previously been instructed in the principles of geometry and trigonometry. Indeed, as numerical figures are very much used throughout the work, there would have been equal propriety in laying down previously the first four rules in arithmetic. But redundancy is better than defect;

and when we come to the survey itself, we accompany the writer with great plea sure through its different modes, and the many instances he has given cannot fail of rendering the whole process very familiar to the learner.

In surveying under ground the magnet is of great importance. Its variations were formerly little observed, or even understood, and of course many old plans are with difficulty followed by those who are not attentive to this circumstance. It is with great propriety, therefore, that this subject is fully discussed in the work before us, and the methods are pointed our of laying down truly the plan of any mine when the variation of the compass is given, as also of discovering the age of a plan by comparing it with present observations. The work will be found very useful to the young practitioner in this art, and deserves the attention of the possessor of subterraneous property.