vard had also on the same subject laboured with great success. It was decided to divide the prize between them: but Bonaparte, who presided on that day, amended the resolution by doubling the prize, and thus giving to each the sum of about a hundred and twenty guineas. Laplace considered this to be too small a sum for the labours of Burg, and proposed a new prize of about two hundred and fifty pounds; and on the 25th of July, the committee of the board of longitude waiting on Bonaparte with a report on Burg's work, he doubled this prize also, and desired that Burg might be invited to come to Paris, and receive a pension of a hundred and twenty guineas a year. His tables were put to the press, and a copy sent to professor Maskelyne, for the use of the nautical almanac. The Arabic text of Ibn Junis is printed, and the translation by Caussin put to the press. Henzenberg at Hamburg, from 31 experiments on falling bodies, from the height of 235 feet, determines against the perpendicular descent, there being a declination of four lines towards the east, and one and a half towards the south. The French minister has established a board for meteorological observations, which has received communications from 30 places, established between the convent of Mount Cenis and the sea. Several persons have sent communications on the tides, currents, and winds in different parts of the world. The account of the Bibliography of Lalande forms an article in this book, to which is added a supplement, containing a list of books that the author has become acquainted with since its publication. The measuring of a degree in Sweden is detailed with the precision which the importance of the subject required. That by Maupertuis and his associates had long been generally looked upon as incorrect, no doubt can now be entertained upon this head. He measured an arc of only 0° 57′ 28′′67; the arc measured by the Swedish mathematicians, contains 1° 37′ 19 39. Their astronomical observations were made at the two extremes of a meridional are at Malorn, in lat. 65° 31' 32'14, and Pahlavara in lat. 67° 8' 51'53. They used iron rods, a French toise in length, to mea-. sure their first base, and wooden rods for their second base. All the angles in each triangle were measured several times, till they were assured that the error could not amount to more than a second, excepting in two triangles, in which the third angle was deduced from the other two angles, The polar star was used in their astronomical observ. ations, and from very accurate calcula. tions they conclude that a degree on the meridian in lat. 66° 20′ 12′′ amounts to 57209,22 toises, the thermometer at the time of measuring being at zero; and if it is at ten, it will be 57197. As that of Maupertuis is estimated, at the same height of the thermometer, to be 57405, the difference between them is 208 toises, a difference which Mr. Melanderhselm, the Swedish astronomer, attributes to an error in the French calculation of latitudes. This detail of the Swedish degrees is followed by an estimation of the ancient Egyptian measures, from the orbit dug up by Girard in the ruins of the nilometer at Elephantis. Several observations are given, made by Haugergues at Vivier, in 1802 and 1803, on the eclipses of Jupiter's moons, the appearances of Saturn's ring, and on the spots of the sun. A singular observation, and the explanation of the appearance of the spots de serves our notice. They are generally considered to be black; but examined with attention in a dark room, through a good refracting telescope, they are ra ther of a greyish blue, and sometimes approaching to a red; and Mr. Haugergues is of opinion, that if these spots could be detached from the sun, and were seen by us in the heavens at night, they would surpass Jupiter and Venus in splendour. To explain the reason of their appearing of a dark colour, he placed a small looking-glass in such a manner that it should reflect the light of heaven to the eye, and be at the same time projected on the sun's disk. Look ing then at the sun and glass, through a smoked glass, the looking-glass appeared on the sun's disk as a perfectly black spot. Now, as the light of heaven is superior to that of Venus or Jupiter, it is inferred that the spots of the sun, though appearing dark, may possess a brilliancy far superior to that of the two planets. Laplace's remarks on the bulk of Saturn, and the tables of Jupiter, display his usual, but uncommon ingenuity. From the accounts given of the stones falling from the atmosphere at Aigle, it is concluded that they must have been formed at the same time in the air as the =ball of fire. An account of Herschel's power of penetrating space by telescopes, and a paper in the Philosophical Transactions by don Mendoza Rios, conclude this interesting part of the work, which we cannot put out of our hands without applauding the French for their exertions, and regretting that similar encouragement is not held out to the promotion and diffusion of science in our own country. ART. III. A Collection of Mathematical Tables, for the Use of Students in Universities and Academies, for the Practical Navigator, Geographer, and Surveyor, for Men of Busines, c. By A. MACKAY. THIS collection contains 216 pages of tables, the same as in the Complete Navigator, and 44 pages more with hyperbolic logarithms, the reciprocals of numbers, the square roots and cube roots of numbers, amount and present value of 1. at compound interest, and of annuities for terms of years, with probabilities of life at different places, and annuities on lives, with several other tables, among which one is a page of chronology. It is needless to observe, that where so much is attempted, the purchaser must not expect much in any peculiar branch; but in schools and colleges these tables will be found useful. ART. IV. Observations on the Effects which Carriage Wheels, with Rims of different Shapes, have on the Roads: respectfully submitted to the Approbation of the Board of Agricultu e, and to the Consideration of the Legislature. By A. CUMMING, Esq. ENGLAND is celebrated for the gravel walks in its gardens, and the excellence of some of its turnpike roads. Very great pains are taken with both, yet no one ever thought of rolling his garden walks with a conical roller. How comes it to pass then, that the turnpike roads of this country are suffered to be rolled by conical wheels, on which are raised waggons of enormous weight? The question may surprise many of our surveyors of roads, and is only one among many proofs how custom blinds the eyes, and the most absurd practices will prevail in spite of every effort of reason and even self-interest. The author of this work has studied the subject with very great attention, and has shewn, by an ingenious set of experiments, the dif ferent operations of cylindrical and conical wheels upon roads: the whole might be comprised in few words, that the cylindrical wheel preserves, the conical wheel destroys, the roads. This will be evident to every one who considers the nature of the cone and the cylinder. Every point on the surface of a cylinder has the same rotatory motion; it is different with the cone, for if a cone is drawn forward in the same direction with the cylinder, and the circumference of the largest circle in the cone is the same as that of the cylinder, the points in the circumference of this largest circle alone have the same rotatory motion as the points in the surface of the cylinder; and the other points on the cone have different rotatory motions, according to their distance from the vertex of the cone. Hence if a cone and cylinder are drawn forward in the same straight line, and with the same velocity, there must be a constant dragging forward of the thinner parts of the cone, and the road, instead of being equally pressed down by every part of the surface, will have different pressures at different places, and will of course, according to the weight of the cone, sustain injury by the crushing of the materials upon it, or opening interstices to the bad effects of the weather. The introduction of the conical shaped wheels is naturally accounted for, by the endeavour to accommodate the wheel to the carriage upon it; little regard being paid by the possessor of the carriage to the state of the road. The surveyors of roads, not being men of very great observation, though accustomed to see various carriages pass before them, did not calculate the effects of each upon the road. The waggoner was still less like ly to notice the different effects of wheels, on the horses which drag the carriage; and the wheelwright, whose business it is to turn out the best made wheel on any construction, troubles himself not at all with their use in carriages. Thus the possessor of the carriage gained his point by enlarging his waggon, and thought he had gained a great point by the increased convenience in stowing his goods, not considering the loss he sustained by the labour imposed on his horses, to drag a quantity of this weight, instead of drawing it by means of a circular motion. contrary, to improve them by producing the effect of ramming the stones on which they pass, by the dead ressure produced from the uniform velocity of all the parts; "11. And they advance in a straight course with the least possible resistance, and with advantages superior to any other possible shape; 12. They serve equally to improve the roads, to relieve the cattle, and to pre serve the tires of the wheels. "And all these properties are as pecular to, and inseparable from the cylindrical shore cattle. as they are favourable to the roads and to the "2. The consequences of this fatal error are much greater than a cursory observer would apprehend. It makes a difference in the number of horses employed in transporting the commodities of this kingdom, and in the materials. and horses employed to carry them on the roads, which amounts to some mil-". lions; and if the improvement of roads, the saving of labour, and the saving of money, are any objects to a people, the legislature will have few subjects proposed to them of such importance as this in the work before us. From considering this importance, and with the view to induce all persons concerned with wheel carriages and the management of roads to study this work with the attention it deserves, we transcribe the author's judicious summation of the dif ferent effects of the cylindrical and conical rims. "The Cylindrical Rims. 1. Naturally advance in a straight line; 3. No rubbing against the sides of deep ruts; 4. No throwing up of dirt by the bind part of the wheel; 5. Do not increase friction on the axis; 6. Have no pressure against the linch pin; 7. The only resistance to their rolling in a straight line is from compressing, smoothing, and levelling the substances on which they roll; 8. They have no tendency to displace, de- "9. Their frequent rolling on compressible "Conical Rims. They naturally roll in a circular direc- "3. When constrained to move in a straight 4. They increase friction on the axis; "6. And a throwing up of dirt from the hind "7. In dry weather they pulverise the best materials; 8. Which occasions much sludge in wet seasons, and much dust in dry "9. In a compressible state of the roads ther derange and break the texture of the parts, and leave them in a broken ste ready to imbibe water, which introduces all the ruinous effects of wet seasons and severe frosts; "10. They promote the destruction of par ed streets and causeways, by forcish opening the joints and admitting water under the stones, which ultimately floats and discharges the gravel, loosens the stones, and sinks the pavement into holes ; "11. They increase the labour of the cattle. 12. And promote the wearing of the ures of the wheels by their constant draggi and grinding on the roads, none which take place with the cylindrical wheels. "Such are the effects that unavoidab arise from the conical shape, and they seem as much calculated for the destruction of the roads, as those of the cylindrical wheels are for their preservation and improvement. "33.-And, seeing that the cylindrical rim is the most favourable that can possibly be adopted for the preservation and improve ment of the roads, and that the conic! is the most destructive, a certain adrantage must be gained by using the former instead of the latter; and as this advantage must be in proportion to the space or surfass that is rolled; it cannot be thought exces- improving roller, instead of an impairing sive to rate that difference at one shilling one." for every acre of road that is rolled with an ART. V. Elements of Mechanical Philosophy: being the Substance of a Course of Lectures on that Science. By JOHN ROBISON, LL. D. &c. 8vo. pp. 696. PROFESSOR Robison is well known to the scientific world. This work is intended to give the substance of his lectures in the university of Edinburgh, for the space of thirty years. The first volume only is published, and whilst we are writing we have to lament that death has cut off its author. In what state he has left his papers we do not know, but from what we have seen we feel a great interest in the completion of this work, of which the present volume contains dynamics and astronomy. By the advertisement of the author it should seem that in the short space of a six months session it was expected that a course of lectures in natural philosophy should be given, and on such a plan it is evident that " justice could not be done to the various branches of this extensive science Of course the professor had the choice of one of two things: either to enter very superficially into every subject, or to omit some particular branch. With great judgment he selected the latter, and thus in one session he omitted magnetism and electricity, which were discussed in the next session, optics being then omitted. This very rational plan was not how ever approved, and this work was to enable him to shorten the lecture, and to include "all the articles in one course." In what mould the students of Edin. burgh are formed, we do not know, but their powers must be far beyond those of their colleagues in the south, if they can in so short a time digest to any good purpose so great a quantity of matter. The volume before us contains six hundred and ninety-six pages, and in it we find the most difficult things in the Newtonian philosophy. There cannot be less than another volume of the same size, and to read either, the previous study of Euclid, algebra, and fluxions, is absolutely necessary. Several pages require many hours' close application, and there is a danger that in such a course of lecturing, the hearers will retire with a very superficial knowledge of the articles discussed, and, what is worse, they will flatter themselves that they do understand the discoveries of our great philosopher, which are meditated upon with such profound attention, and so much longer application, by the students of the university of Cambridge. But, whatever may be the effect of the lectures at Edinburgh, this book will be found very useful to every teacher of natural philosophy where our language is known, and to the teachers particularly; to the tutors of Cambridge it may be recommended, as more beneficial to them than to the student.. It opens with an explanation of the symbols; and in noticing the term ultimate ratio, the author justly observes that there is an impropriety in the term ultimate, because the ratio under that term is never attained. Hence he conceives that the term limiting ratio is more proper, and desires to be understood only in this sense when he speaks of prime and ultimate ratios. We can have no hesitation in acceding to this just distinction, and particularly so, because when Newton talks of two quantities being ultimately equal, he both unnecessarily and improperly gives a modification to the idea of equality of which it is not susceptible. Having explained the symbols, the professor begins his subject with the na ture of motion, under the two heads of uniform and variable motions, and the latter is subdivided into accelerated and retarded motions. From these we are led to compound motions and curvilinear motions, the latter being explained agreeably to the first proposition of the second section of Newton. Matter is now defined, and we enter upon dynamics. The three laws of motion are explained, and we rush into all the per plexities of forces, accelerating motions, and central. From them we are led to astronomy, the author giving a just reason why this branch of philosophy should take the precedency of the others, since the knowledge which we can acquire in astronomy approaches near to the certainty of first principles, whilst in those other departments it is only a superficial knowledge of some very general property that we are able to acquire." The phænomena in the heavens are first described, and in noticing the pre cession of the equinoxes a just observation is made, of the litle dependence to be placed on the use ascribed to it by sir 1. Newton in chronology. For we cannot, from the description by Aratus, be certain of the position of the vernal equinox within five or six degrees, and consequently the date of any event depending upon it will not be ascertained within four hundred years. On the astronomical phænomena we do not perceive much of novelty; the usual sub. jects are discussed and arranged in the usual order; but in the next part, physical astronomy, we were highly gratified with the developements of the discoveries of Kepler, the theory of Newton, and the improvements that have been made within the last century on the New tonian system. The intention of the author was, as he informs us," to assist the ignorant in the elements of physical astronomy, and to insert nothing but what seemed to be elementary in the Newtonian philosophy;" but we cannot flatter the ignorant that they will be competent to understand these pages without deep thought and reflection, nor the idle, however endued with talents, that they can derive much satisfaction from a cursory perusal. The theory of gravitation, the irregularities occasioned by the disturbing forces of three or more bodies, the figures of the earth and planets, the nature of the tides, the investigation of complicated expressions, and minute errors, are subjects which cannot be made easily familiar to ignorance, and never to idleness. The professor has, however, done in this part as much as could be expected from him, and the diligent student will, after a few peru sals, acknowledge his obligations. Our limits will not permit us to enter into the detail of particulars, for what would this be but to conduct our readers through the greater part of the Principia? We cannot, however, deny ourselves the pleasure of observing with what care every thing is introduced that has been used, or might be suggested for the establishment of the Newtonian system. Thus, on the attraction of matter, the celebrated experiments of Dr. Maskelyne on Mount Shihallien, and Mr. Cavendish on balls of lead, are accompanied with a suggestion that we hope may not be lost. The professor conceives that the rising of the tide at Annapolis-royal, in Nova Scotia, might afford a very useful experiment. The water rises there above a hundred feet every spring-tide, consequently a leaden pipe, a few hundred feet long, laid at right angles to the coast, and filled with water, so that it should rise to a certain height in glass tubes, set upright at each end, would indicate by the water sinking at one end, as the tide rose, that the accumulation of water on the strand had an effect on the water in the tube. The same might perhaps be shewn by a long plummet or a spirit level. On the subject of the inequalities of the satellites, to the remark made by La Grange, on the perturbations of Jupiter's satellites, one from the author is subjoined, which proves him to have stu died nature in the true spirit of the old English school, and, like our great teacher Newton, not to forget in explaining the properties of created matter, the glory of the creator. "In the course of this investigation, M. de la Grange has made an important observe tion, which he has demonstrated in the most incontrovertible manner, namely, that it ne cessarily results from the small eccentricity of the planetary orbits--their small inclination to each other-the immense bulk of the sun-and from the planets all moving in one direction-that all the perturbations that are observed, nay all that can exist in this sysopposite points of every period. He shews tein, are periodical, and are compensated in also, that the greatest perturbations are so moderate, that none but an astronomer wil observe any difference between this perturbed state and the mean state of the system. The mean distances and the mean periods remain for ever the same. In short, the whole assemblage will continue almost to eternity, in a state fit for its present purposes, and not distinguishable from its present state, exerpi by the prying eye of an astronomer. Cold, we think, must be the heart that is not affected by this mark of beneficent wisdom in the Contriver of the magnificent fabric, so manifest in selecting for its connecting principle a power so admirably fitted for continuing to answer the purposes of its first formation. And he must be little susfeel himself highly obliged to the Being who ceptible of moral impression who does not has made him capable of perceiving this display of wisdom, and has attached to this perception sentiments so pleasing and des lightful. The extreme simplicity of the constitution of the solar system is perhaps the most remarkable feature of its beauty. To this circumstance are we indebted for the it is this alone that has allowed our limited pleasure afforded by the contemplation. For understanding to acquire such a comprehensive body of well-founded knowledge, far exceeding, both in extent and in accuracy, |