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is carefully carried on, and the products diligently separated. If the acid is weak, the watery parts first come over ; but if already pretty Atrong, the most concentrated parts appear about the middle of the operation. These facts are highly useful.
Our neighbours, who carry their science into many seemingly trilling subjects, under the term analyfis, have included memoirs of an uncommon kind. . The chevalier Borde observes, that in elections, by scrutiny, if there are three candidates, it may happen that the successful one has not the majority. If there are twenty-one voters; A bas eight, B seven, 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 successful 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 sometimes surpasses, the number of electors,
The next Memoir is apparently trifling, yet it is only determined by the properties of the hyperbola, and some very cu. rious applications of the differential calcuius, or the method of Auxions. In carrying earth from one place, to lay it in an equal fpace, it is evident that both trouble and expence may be saved. The force to be einployed is equal to that of the masses, multiplied by the space through which each load is carried ; but this sum muft vary, according to the distribution of the loads. The object of mons. Monge is to ascertain the method in which the fum mentioned is the least possible. Our readers will scarcely wish that we should follow the author in this calculation.
The next Memoir under this head, by the marquis de Condorcet, is giore 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 considers, first, where the equality between the real and mean values, which the rule, taken ftrialy, fupposes to be the same, is delusive ; fecondly, where there is no possibility of substituting the real for the mean, value. These exceptions do not often occur ; but they deserve to be examined. The second part of the Memoir is itill farther from mens business and bosoms.'
Under the head of Mechanics, we find some remarks on the ascensional power of air-balloons. They were the last legacy of the celebrated and venerable Euler, whose black board (mathematicians 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 springs of life were ready to break, Euler, however, considered balloons, as
fubjects of calculation only; and his labours were foon intere rupted by an irresistible 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 sails, is a problem which has exercised the ingenuity of mathematicians; yet, by dint of feeling their way, practical mechanics have arrived nearly at the same results. The mills near Lille are simple in their conitruction; like the Englith fulling-inills, 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 passes on at the rate of twenty feet in a second, and with a force capable of raising one thousand pounds, at the rate of two hundred and eighteen feet in a second. 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 same purpose. The quantity of force loft is about a fixth of that which is employed with advantage. M. Coulomb was prevented by the jealousy of the severai ovners, from examining the mills with accuracy; and he requests the affiltance of others, who may be more fortunately situated. He delires that the effects of the machine, and a calculation of the forces, may be added to the description. He purposes to apply these experiments to the investigation of a theory of these machines, which has been sought, in vain, a priori.
The lalt mechanical Memoir is a Defcription of a new Species of Telescope Level, hy M. de Fouchy. The telescope is formed of two object and an eye-glass; with four glasses our author could not succeed. The deicription would be unintelligible without the plate.
In analytical astronomy, M. du Sejoir endeavours to determine the parallax of the sun, from the transits of Venus in 1761, and 1769. He makes it 8" Té. If we recollect rightly, the English alironomers found it somewhat less, though it exceeded eight seconds. The difference in the results, from the two observations, did not amount to the fiftieth part of a second.
In calculating the quantity of the preceffion of the equinoxes, mons. de la Lande prefers a series of modern observations to the less accurate, though more distant ancient ones. He compares Flamiteed and de la Caille's Catalogue of Stars, and neglects those of the first magnitude, as they seem to have some motions perculiarly their own. He calculates from those which have been molt iteadily and accurately observed among the smaller stars; and the results, in different trials, were nearly the same : by taking the mean of these, he fixes the quantity of precision at 50 every year.
Eclipses, which by calculation are total, fometimes appear annular, in consequence of the inflection of the folar rays, when they pass near the body of the moon. The quantity of
this infection, mons. le Monnier calculates, from fome obfer· vations, to exceed twenty-four seconds. Other astronomers have reckoned it, by different methods, to be about three seconds. This variation is supposed to be owing to the refraction of the rays from a lunar atmosphere.
M. Coles observed an eclipse of the fourth satellite of Jupi, ter, at China, in very favourable circumítances. From thence he calculates the inclination of its orbit to be 2° 36' 24". He differs but 24" from the calculations of messrs. Wargentin and Maraldi.
M. de Fouchy, in the following Memoir, describes a new quadrant, which is neither dearer or of more difficult conveyance than the common quadrant; at the same time it serves as an azimuthal instrument. If this new instrument, of which there is a plate, can be easily made and used, as seems probable from the description, it will be highly advantageous.
There are also in the Memoirs, Observations on the Eclipses of the sun, on the 23d of April, and 17th of October, 1781, by M. Monnier ; on the last of these are other observations by messrs. Jeaurat and Pingré. The paths of the two comets of 1781, are also described, and traced on an Atlas, by M. Metier. But these Memoirs cannot be with advantage enlarged on.
The last Memoir is on the Position of Trebizonde. D’Anville, and every other gengrapher, had been consistent in fixing the longitude of this place; but in the Atlas, engraved for Raynal's Philosophical History, it is placed stor 6 degrees far. ther to the east. This was done on the authority of a Menaoir, published in the Memoirs of the Academy 1699, by M. Gouye, from the Observations of father Beze. M. Buache examines the effect of this variety on the Caspian sea. The northern part must be stationary, for the latitude of Guriew, at the mouth of the Jaik, is fixed by astronomical observations, and this change will place it in an oblique pofition, and make its length five times greater than its breadth. These two circumstances, are inconsistent with the account of every intelligent traveller, and the change in the situation of other places renders the al. teration, on fimilar accounts, equally objectionable. Besides, in the Memoir referred to, the result of the calculations are only given ; so that we cannot decide on their value, or be se. cure from mistake. On the other hand, in page 6 of the Atlas, we find several strong reasons for the position they have determined on, though noc suficient to counterballance the arguments of M. Buache; and, in the following page, we find the authors with difficulty reconciling the politions of Constantino, ple and Smyrna, to the new place of Trebizonde, confiflently with the observations of de Chazelles, and father Feuillée. On the whole, we think the Memoir before us deferves atten. rion ; 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, they are sufficiently accurate; but, in more than one initance, they deserve reprehenfion.
The lives, or more properly the eulogiums in this volume, are those of the learned, but the timid and indecisive Bertin, who was chiefly known and celebrated as an anatomift ; le marquis de Courtanvaux, a learned academician, who had no particular predilection for any science, but a competent knowledge of all; mons. le compte de Maurepas, a minister at the ages of fourteen and of eighty; and the fagacious Tronchin, the friend and physician of Voltaire, Bonnet, Trembley, and Rousseau. These Lives are written with spirit and with ele. gance ; but with too much complaisance, and too little discri. mination.
POLITICAL. The Principle of the Commutation- da established by Facts, B, Francis Baring, Esq. 8vo.
Sewell. AMONG the many
frivolous publications on political subjects, we sometimes find them treated of by men of real knowledge. The information, of which the public is then in poffeffion, more than compensates for the wrong judgments that must necessarily result either from unfairness or ignorance. The general effect of the measure which is the fubject of this pamphlet, is sufficiently felt and understood; yet it will be allowed, that Mr. Baring, from professional 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 exifted in design. In consequence of his having been early prepolsessed in favour of it, and from its success, he rejoices as an author, and a good citizen.
• The author of these sheets, he says, writes neither from party views, nor upon party principles. The only connexion he ever had with the treasury arose from bis being employed in a very considerable fimplification of the public expenditure, in the business of supplying the whole of the army vi&tualling contracts, during the time that the marquis of Lansdown presided at that board. The execution of that great and important work, together with his situation in the city, naturally led to his being confidentially consulted respecting other affairs, of a commercial nature, which were either depending, or in contemplation. The tea-proposition (which was presented to his lordship by Mr. Richardson, of the East-India
kouse), and many other plans were then in agitation; and more or less progress was made in them, as time and other cir.' cumstances would permit. The proposition respecting the duties upon tea was also communicated to several principal persons belonging to the excise and customs, and to others who were competent to judge of its merits ; and was generally approved ; Under these circumstances, the author's inost sanguine wilhes were early embarked in the success of this measure ; and it af. fords him the greatest satisfaction to declare, that he feels himself infinitely gratified by the event.'
He gives an account of the quantity of tea usually sold by, the company, before the act passed, which, on an average,, amounted to fix millions three hundred and fifty-eight thouaj fand one hundred and forty-four pounds annually. The falés of last year was fixteen millions one hundred and fifty-two thousand lix hundred and seventy: we cannot abridge calculations ; fuffice it to say, the public has gained, by lowering the duties, two millions fifty-five thousand four hundred and fixty-two pounds. Those who want to see the particulars, will be fully gratified by consulting the pamphlet.; The author, next enters on the produce of the house-tax, .&ç, but for this, we must also refer to the pamphlet. He says that fe
• The fituation of the India company is fo completely rea versed by the commutation act, and fo entirely are they relieved from the difficulty which would have arisen from the circumstance before mentioned, that, in order to guard against event the possibility of a deficiency in the quantity neceffary to an swer the increased demand of the public, the company havet been obliged to have recourse to the continent and have acol tually purchased, of the tea which was in Europe previous to the year 1784, and of what arrived in that reason about # 6,600 000 ; and the vigorous'efforts which they are making in the present season, for the purpose of importing å fufficient quantity directly from China, in order to preclude the necellity in future of depending on their rivals for a fupply, will afford the means, in due time, of securing, both to the nation and to the company, the whole of those important advantages, which have already in part arisen from this measure, and which the public have a right to expect.'
After fome other necessary detail of calculation, he observes, that the company have gained three hundred and eleven thou- } fand nine hundred and five pounds; a considerable part of which, it seems, arises from the high prices at which some i forts of tea's have been fold, and which the directors have exa! erted their útmost endeavours to prevent. As it is to much for the interest of the smuggler that the company's tea Should be fold dear, we may fairly prefume, that it was puthed , Vol. LXI. Feb. 1786.