is carefully carried on, and the products diligently feparated. If the acid is weak, the watery parts first come over; but if already pretty ftrong, the most concentrated parts appear about the middle of the operation. These facts are highly ufeful. Our neighbours, who carry their fcience into many feemingly trifling fubjects, under the term analyfis, have included memoirs of an uncommon kind. The chevalier Borde obferves, that in elections, by fcrutiny, if there are three candidates, it may happen that the fuccefsful one has not the majority. If there are twenty-one voters; A bas eight, B feven, and C fix; A gains the election, though eight is a number very diftant from a real majority. The rule he gives to obtain the real majority is the following. The number of voices for the fuccefsful candidate must be in a greater proportion to the number of electors, than that of the number of candidates, minus one to the whole number. It is remarkable that this is the rule obferved in the election of the kings of Poland, where the number of candidates equals, and fometimes furpaffes, the number of electors. The next Memoir is apparently trifling, yet it is only determined by the properties of the hyperbola, and fome very curious applications of the differential calcuius, or the method of fluxions. In carrying earth from one place, to lay it in an equal space, it is evident that both trouble and expence may be faved. The force to be employed is equal to that of the maffes, multiplied by the space through which each load is carried; but this fum muft vary, according to the diftribution of the loads. The object of monf. Monge is to afcertain the method in which the fum mentioned is the leaft poffible. Our readers will scarcely with that we should follow the author in this calculation. The next Memoir under this head, by the marquis de Condorcet, is more important. It is on the Calculation of Chances. It is well known, that in estimating risks which are unequal, or unequally probable, the value must be multiplied by the probability. This rule gives only the mean value; but there are two exceptions which the marquis confiders, firft, where the equality between the real and mean values, which the rule, taken ftrictly, fuppofes to be the fame, is delufive; fecondly, where there is no poffibility of fubftituting the real for the mean value. These exceptions do not often occur; but they deferve to be examined. The fecond part of the Memoir is still farther from ' mens business and bofoms.' Under the head of Mechanics, we find some remarks on the afcenfional power of air-balloons. They were the laft legacy of the celebrated and venerable Euler, whofe black board (ma thematicians will understand us), was covered with calculations, which his eyes could scarcely difcern, though written with chalk. The force of his mind still remained, while the fprings of life were ready to break. Euler, however, considered balloons as fub. fubjects of calculation only; and his labours were foon interrupted by an irrefiftible power. · The next Memoir, in this department, is by monf. Coulomb, on Wind-mills. It is well known, that the most advantageous angle for the fails, is a problem which has exercifed the ingenuity of mathematicians; yet, by dint of feeling their way," practical mechanics have arrived nearly at the fame refults. The mills near Lille are fimple in their conftruction; like the Englith fulling-mills, which differ only by being moved with water, and their force is easily calculated. They work eight hours in a day, by the action of a wind, which paffes on at the rate of twenty feet in a fecond, and with a force capable of raifing one thousand pounds, at the rate of two hundred and eighteen feet in a fecond. Sixty-one men, according to Bernouilli's calculation (in which our author thinks the strength of a man, in continued labour, is over-rated), would be required for the fame purpofe. The quantity of force loft is about a fixth of that which is employed with advantage. M. Coulomb was prevented by the jealoufy of the feveral owners, from examining the mills with accuracy; and he requests the affiftance of others, who may be more fortunately fituated. He defires that the effects of the machine, and a calculation of the forces, may be added to the defcription. He purpofes to apply thefe experiments to the investigation of a theory of thefe machines, which has been fought, in vain, a priori. The laft mechanical Memoir is a Defcription of a new Species of Telescope Level, by M. de Fouchy. The telescope is formed of two object and an eye-glafs; with four glaffes our author could not fucceed. The defcription would be unintelligible without the plate. In analytical aftronomy, M. du Sejoir endeavours to determine the parallax of the fun, from the tranfits of Venus in 1761, and 1769. He makes it 8". If we recollect rightly, the English aftronomers found it fomewhat lefs, though it exceeded eight feconds. The difference in the refults, from the two obfervations, did not amount to the fiftieth part of a fecond. In calculating the quantity of the preceffion of the equinoxes, monf. de la Lande prefers a series of modern obfervations to the lefs accurate, though more distant ancient ones. He compares Flamfteed and de la Caille's Catalogue of Stars, and neglects those of the firft magnitude, as they feem to have fome motions perculiarly their own. He calculates from those which have been moft fteadily and accurately obferved among the smaller ftars; and the refults, in different trials, were nearly the fame: by taking the mean of thefe, he fixes the quantity of precifion at 50" every year. Eclipfes, which by calculation are total, fometimes appear annular, in confequence of the inflection of the folar rays, when they pass near the body of the moon. The quantity of this inflection, monf. le Monnier calculates, from fome obfervations, to exceed twenty-four feconds. Other aftronomers have reckoned it, by different methods, to be about three feconds. This variation is fuppofed to be owing to the refraction of the rays from a lunar atmosphere. M. Coles obferved an eclipfe of the fourth fatellite of Jupi, ter, at China, in very favourable circumftances. From thence he calculates the inclination of its orbit to be 2° 36′ 24′′. He differs but 24" from the calculations of meffrs. Wargentin and Maraldi. M. de Fouchy, in the following Memoir, defcribes a new quadrant, which is neither dearer or of more difficult conveyance than the common quadrant; at the fame time it ferves as an azimuthal inftrument. If this new inftrument, of which there is a plate, can be eafily made and used, as feems probable from the defcription, it will be highly advantageous. There are alfo in the Memoirs, Obfervations on the Eclipfes of the fun, on the 23d of April, and 17th of October, 1781, by M. Monnier; on the laft of these are other obfervations by meffrs. Jeaurat and Pingré. The paths of the two comets of 1781, are alfo defcribed, and traced on an Atlas, by M. Meffier. But thefe Memoirs cannot be with advantage enlarged on. The laft Memoir is on the Pofition of Trebizonde. D'Anville, and every other geographer, had been confiftent in fixing the longitude of this place; but in the Atlas, engraved for Raynal's Philofophical Hiftory, it is placed 5 or 6 degrees farther to the eaft. This was done on the authority of a Memoir, published in the Memoirs of the Academy 1699, by M. Gouye, from the Obfervations of father Beze. M. Buache examines the effect of this variety on the Cafpian fea. The northern part must be stationary, for the latitude of Guriew, at the mouth of the Jaik, is fixed by aftronomical obfervations, and this change will place it in an oblique pofition, and make its length five times greater than its breadth. These two circumftances, are inconfiftent with the account of every intelligent traveller, and the change in the fituation of other places renders the alteration, on fimilar accounts, equally objectionable. Befides, in the Memoir referred to, the refult of the calculations are enly given; fo that we cannot decide on their value, or be fecure from mistake. On the other hand, in page 6 of the Atlas, we find several strong reafons for the pofition they have determined on, though not fufficient to counterballance the arguments of M. Buache; and, in the following page, we find the authors with difficulty reconciling the pofitions of Conftantino ple and Smyrna, to the new place of Trebizonde, confiflently with the obfervations of de Chazelles, and father Feuillée. On the whole, we think the Memoir before us deferves attention; and we have been more particular in our account of it, as we begin to find the authority of Raynal's maps quoted in England with a respect which they do not always deferve. In. 8 general, general, they are fufficiently accurate; but, in more than one inftance, they deferve reprehenfion. The lives, or more properly the eulogiums in this volume, are thofe of the learned, but the timid and indecifive Bertin, who was chiefly known and celebrated as an anatomist; le marquis de Courtanvaux, a learned academician, who had no particular predilection for any science, but a competent knowledge of all; monf. le compte de Maurepas, a minister at the ages of fourteen and of eighty; and the fagacious Tronchin, the friend and phyfician of Voltaire, Bonnet, Trembley, and Rouffeau. Thefe Lives are written with spirit and with elegance; but with too much complaifance, and too little difcrimination. MONTHLY CATALOGUE. POLITICA L. The Principle of the Commutation- Ad established by Facts. ; AMONG the many frivolous publications on political fubjects, we fometimes find them treated of by men of real knowledge. The information, of which the public is then in poffeffion, more than compenfates for the wrong judgments that muft neceffarily refult either from unfairness or ignorance. The general effect of the meafure which is the fubject of this pamphlet, is fufficiently felt and understood yet it will be allowed, that Mr. Baring, from profeffional habits of calculation, and his station in the India company, is particularly qualified to write on the commutation-tax, with which he seems to have been acquainted, when it only existed in defign. In confequence of his having been early prepoffeffed in favour of it, and from its fuccefs, he rejoices as an author, and a good citizen. The author of these sheets, he fays, writes neither from party views, nor upon party principles. The only connexion he ever had with the treafury arofe from his being employed in a very confiderable fimplification of the public expenditure, in the bufinefs of fupplying the whole of the army victualling contracts, during the time that the marquis of Lanfdown prefided at that board. The execution of that great and important work, together with his fituation in the city, naturally led to his being confidentially confulted refpecting other affairs, of a commercial nature, which were either depending, or in contemplation. The tea-propofition (which was prefented to his lordship by Mr. Richardfon, of the Eat-India house), boufe), and many other plans were then in agitation; and more or less progrefs was made in them, as time and other circumftances would permit. The propofition refpecting the duties upon tea was alfo communicated to feveral principal perfons belonging to the excife and cuftoms, and to others who were! competent to judge of its merits; and was generally approved ; Under thefe circumftances, the author's most fanguine wishes were early embarked in the fuccefs of this meafure; and it affords him the greatest fatisfaction to declare, that he feels himfelf infinitely gratified by the event.' He gives an account of the quantity of tea ufually fold by, the company, before the act passed, which, on an average, amounted to fix millions three hundred and fifty-eight thou fand one hundred and forty-four pounds annually. The fale of last year was fixteen millions one hundred and fifty-two thousand fix hundred and feventy: we cannot abridge calcu lations; fuffice it to say, the public has gained, by lowering the duties, two millions fifty-five thoufand four hundred and fixty-two pounds. Thofe who want to fee the particulars, will be fully gratified by confulting the pamphlet. The author, next enters on the produce of the houfe-tax, &c. but for this, we must also refer to the pamphlet. He fays that The fituation of the India company is fo completely reverfed by the commutation act, and fo entirely are they relieved from the difficulty which would h have arifen from the circumftance before mentioned, that, in order to guard against event the poffibility of a deficiency in the quantity neceffary to and fwer the increafed demand of the public, the company have been obliged to have recourfe to the continent, and have ac tually purchased, of the tea which was in Europe previous to the year 1784, and of what arrived in that fealon, about 6,600 000; and the vigorous efforts which they are making: in the prefent feafon, for the purpose of importing à fufficient quantity directly from China, in order to preclude the neceflity in future of depending on their rivals for a fupply, will afford the means, in due time, of fecuring, both to the nation and to the company, the whole of thofe important advantages, which have already in part arifen from this meafure, and which the public have a right to expect.' After fome other neceffary detail of calculation, he obferves, that the company have gained three hundred and eleven thoufand nine hundred and five pounds; a confiderable part of which, it seems, arifes from the high prices at which fome forts of teas have been fold, and which the directors have ext erted their utmolt endeavours to prevent. As it is fo much for the intereft of the fmuggler that the company's tea should: be fold dear, we may fairly prefume, that it was pushed. VOL. LXI. Feb. 1786. up L |