carabine fomewhat different from those which are used by the light dragoons. The advantages this carabine poffeffes over thofe of the common fort, are its fuperior ftrength, its being lighter by about two pounds, and fhorter by about feven inches, at the fame time that it carries full as far as the other. It alfo primes itself. Besides the above-mentioned inftrument, this paper describes other improvements of lefs note, relative to the faddle, the drefs, and other articles belonging to the accoutrements of a dragoon foldier. A plate, exhibiting a delineation of the above-mentioned carabine, with its bayonet, &c. is annexed to this paper. XI. A new Method of expreffing the Coefficients of the Developement of the Algebraic Formula (a+b2-2ab cof ¢)", by Means of the Perimeters of two Ellipfes, when n denotes the Half of any Odd Number; together with an Appendix, containing the Investigation of a Formula for the Reclification of any Arch of an Ellipfe. By Mr. William Wallace, Affiftant Teacher of the Mathematics in the Academy of Perth. - "In calculating", this author fays, "the effect of the mutual action of two planets upon each other, it has been found neceffary to develope the algebraic formula (a2 + b2. 2ab cof into a series of this form, A+B cof 4+C cof 20 + D col 37 + &c. Here a and b denote the diftances of the planets from the fun; denotes the angle of commutation; and the values of n, more immediately the subject of confideration, are — 3, and. The determination of the coefficients A, B, C, &c. in these cafes, appears to have been confidered as a matter of difficulty by the mathematicians who firft applied to the folution of the problem; for they found, that although it was only neceffary to compute the first two coefficients A and B, the reft being eafily derived from them, yet it did not appear that they could be expreffed in finite terms, nor even by ineans of circular arches, or by logarithms. Recourfe was therefore had to other methods, and chiefly to the method of infinite feries; but as the feries which moft readily occurred to them, converged in fome cafes fo flowly as to be in a manner ufelefs, no fmall degree of analytical address has been found neceffary, either to render it more convergent, or to find the fum of a competent number of its terms, with a moderate degree of labour. "But in confidering the fubject, it has occurred to me, that although we cannot exprefs the values of the coefficients in finite algebraic terms, nor even by means of circular arches, or by logarithms, yet when is the half of an odd number, either pofitive or negative, we may always exprefs them by means of the proportion which the perimeters, or femi-perimeters, of two ellipfes bear to thofe of their circumfcribing circles. The problem may therefore be reduced to the rectification of the circle and ellipfe, and mathematicians know that that fuch reduction is confidered as the next degree of refolution, in point of fimplicity, to our being able to effect the folution by means of circular arches, or by logarithms only." P. 253. This author then proceeds to fhow the invefligation of the method, which is very operofe. The investigation of the formula for the rectification of any arch of an ellipfe, is given by way of Appendix, which is longer than the preceding part of the paper. With respect to the contents of this Appendix, we must unavoidably refer our readers to the paper itself. XII. Chemical Analyfis of an uncommon Species of Zeolite. By Robert Kennedy, M.D. F.R.S. Edin. &c. The Zeolite, which forms the fubject of the prefent paper, was found enclosed in a mafs of prehnite, in the bafaltic rock upon which the castle of Edinburgh is built. It poffeffes fome of the characteristic properties common to other ftones of the fame clafs, but differs in other refpects. Its colour in fome parts is nearly white: in others greyish white. Though its fibres appear to be the effect of cryftallization, yet this author could not discover a perfectly regular and determinate form in any of them. The fmall fpiculæ, or fibres of this stone, are tranfparent and colourlefs, with a confiderable degree of luftre. The unbroken parts of the ftone poffefs lefs luftre and lefs tranfparency. The fpecific gravity of different fpecimens of it, at the temperature of 60°, was found to vary from 2,643 to 2,740. Either friction or heat render this ftone luminous in a dark place. The light which it gives by flight friction is fully equal to that which is given by two quartz pebbles when ftruck against each other. After the defcription of the external characters or proper ties of this mineral, the principal of which we have abundantly mentioned, this author relates the experiments which he made for the analyzation of the fame, the refult of which shows that 100 parts of this Zeolite contain, Silex Lime Argil Oxyd of iron Soda, about Carbonic acid, and other volatile matter with fome traces of magnesia and muriatic acid, 51.5 32. 0.5 0.5 8.5 5. 98. ART ART. V. An Enquiry into the real Difference between actual Money, confifting of Gold and Silver, and Paper Money of various Defcriptions. Alfo an Examination into the Conftitution of Banks, and the Impoffibility of their combining the two Characters of Bank and Exchequer. By Magens Dorrien Magens, Efq. 8vo. 68 pp. 2s. 6d. Afperne. 1804. WE E regard this tract as a collection of ftrictures on Mr. Thornton's work on paper credit, although Mr. Magens no where announces it as fuch; giving it, like the other, the form of an elementary treatife. In oppofition to Mr. T. he maintains with Mr. Boyd, that the bill of exchange is not a part of the national currency: to fettle this point it is neceffary a definition of currency fhould be given; and it may be defined to be coin, or whatever elfe performs its proper functions as fuch, to a confiderable extent. Extent of ufe, intitles the things performing these functions, to be called monies, or currency. Under this title, Mr. M. admits notes payable on demand to the bearer to fall. As they bear intereft, and the holders rather retain them than bills payable to order, they change hands lefs frequently; therefore we have formerly denominated them inert and active currency respectively. Now thefe, it is evident, may be received at their nominal value; and yet, falling to a difcount in the poffeffion of the receiver, ftill continue currency, although depreciated currency, and this he in effect admits: therefore, by parity of reason, a note so increasing in value, ftill retains its title to that defcription. Such is the bill of exchange, having a term to run, which is conftantly fo increafing to the end of that term: (p. 25) and even Bank paper, in places where an adverfe exchange with England takes place, continually increafes in value for that period. Mr. M. therefore gratuitously fays, that currency is what circulates without increase or diminution of value (p. 16). What he lays down to controvert Mr. Thornton's proof, that a bill of exchange given for commodities is not a reprefentative of any actual, that is, fpecific property, might be fhown to confute it felf if we could here enter into it. We are fenfible, alfo, with him, of the general iniquity of the practice of drawing and redrawing, and that of its objects; yet we find fome hefitation in fuppofing, that money was ever fo raised to obtain high intereft by fecurities Cowries, falt, nails, &c. on on Weft Indian eftates (p. 10). If he were to compute how many drafts must pafs and repafs, in order that the parties fhould retain in their hand the fraudulently borrowed capital, for five years only, he would find that purpofe is not to be effected by the most complicated circuity of draft and remittance. A leading propofition which Mr. M. inculcates is, that a mercantile bank fhould never in any fhape become the exchequer of the ftate, or make advances to it. What he has faid to inforce this is of so mixed a kind, that while parts of it deferve reprehenfion, there are others entitled to an equal degree of approbation. The advances of the Bank of England to the ftate, having been made in their own paper, have, he affirms, fo much increafed its quantity, that they have already brought it to a discount; the measure of which is determined by the rife of bullion. The fame argument was alfo infifted upon by Mr. Fofter, and an answer was given to it in our observations on his tract. On a former occasion also it has been shown by us, that in a country where no paper is current, and penalties are by law inflicted on the exportation of coin, whenever it has an adverfe balance to pay, which must be done with gold and filver, thofe metals will rife higher than the mint price. Mr. M. further urges, that the aid given by the Bank to merchants has been restricted in proportion as its dealings with government have been extended: but we muft diftinguifh the aid given by the Bank to commerce into two kinds; the direct, when discounts are granted to the merchant in the firft inftance, and the circuitous, arifing from the total of its paper, current at any one time. Now it is contended, that the chief aid which the company gives to trade is by means of the latter; and its tranfactions with government greatly increafe the number of notes in circulation; Mr. Magens therefore ought here to have shown the contrary to what Mr. Thornton lays down, that a confiderable reduction of the customary quantity of Bank notes, would involve the whole commercial world in the greatest distress;* for Mr. M. fuppofes, that with the ceffation of advances to the ftate, fuch reduction would take place; and it will be urged against him, that thereby the general inconvenience might much overbalance the benefit which a few individuals would obtain from an increase of discounts. We will not fay, however, that such an answer could not have been given to Mr. Such diftrefs might be great, but it would be only temporary; for prices and credits, and every other circumftance, probably, would foon adapt themfelves to the new fituation of the money market; but if the measure were gradual, fuch distress would not, probably, take place. T.; T., and we are led to believe that it might, from the folidity with which Mr. M. replies to another pofition of that eminent writer, that the bufinefs of this country cannot be carried on by guineas, which he feems to have affumed gratuitoufly. We have on a former occafion given our teftimony in behalf of banks of depofit like that of Amfterdam, when compared with national banks of credit or emiflion;* and Mr. Magens recalls to our recollection a great point of view which we omitted there to bring forward; this is, that when a nation like our own makes ufe of the agency of such a bank, in all its great money tranfactions, domeilic and foreign; it abfolutely becomes an effective fourth in its conftitution, poffeffing a complete negative power on many measures of the other three. Thus in our time we have seen the directors of the Bank determining whether the state should, or fhould not, fend pecuniary aid to a great foreign power: the fpirit of exultation with which the Bank "veto" was mentioned at that time, is in every body's memory. But we never have heard that the Bank of Amfterdam ever dictated, in political measures, to the StatesGeneral, or remonftrated against the fubfidies which they fometimes granted to their poorer allies; and the reafon was, because its conflitution was fuch, that although the fame evils muft follow its derangement, as must be the confequence of a derange-. ment of the Bank of England, yet the exportation of bullion to any amount, would produce no further effect on its emoluments or payments in coin, than barely the lofs of cellar-rent for a fhort time. We fee in Mr. Magens's tract fome further account of the difcredit its money fell into on the capture of Holland by the French, and of the cause of it. In violation of their conflitution, the directors had, in the courfe of fifty years, lent about a million fterling to the States and the East India Company; but on the approach of the enemy, they removed their treasure to places where they reputed it would be more fecure from being feized; and it was the risk of its not returning which depreffed its notes to a difcount, at which they continued until the peace of Amiens; when a tax was laid on the inhabitants of Amfterdam to reflore the coin to the Bank; as that city had given fecurity for its folvency. Then foon it rofe to an agio of four or five per cent. as formerly. Our fentiments on the quantity of information contained in this work, may be gathered from what we have faid: the general tenor of the flyle is plain and manly; although there is fomething of vulgar quaintnefs in the names the author * Review of Wheatley on currency, p. 126. affumes |