remarkable landscapes. The Porta aurea (an antient triumphal arch), the amphitheatre, and the Temple of Augustus, at Pola in Istria; the temples of Jupiter and Esculapius at Spalatro; and the remains of sarcophagi, altars,' and inscriptions, at the foot of the mountain of Clissa in Dalmatia; are the most prominent objects among the antient remains; the cataracts of the river Kerka, that of the river Cettina called Welika-Gubowiza, and the grotto and cataract of the Ruecca, are truly surprising objects of romantic landscape beauty. The same taste prevails in these plates as in those of the Syrian Picturesque Journey; in both, great attention seems to have been paid to the costume of the present inhabitants; and they equally convey, to the eye of the beholder, striking instances of antient taste and grandeur, and actually existing ignorance and wretchedness. We have particularly noticed, in this point of view, the plate No. 27. representing the residence of the Podestat or chief magistrate (of Pola, as we suppose, from the number of the plate) and governor, between two antient temples of an elegant taste. Nothing could impress more forcibly on the mind, the quantum of decline which the country has suf fered. The size of this work is the same with that of the Syrian Picturesque Journey; and though we have seen nothing of the typographical part, except the Prospectus which has accompanied these Numbers, we are disposed to believe that it is as beautiful as in its sister publication. ART. XV. An Universal European Dictionary of Merchandice, in the T Corrêa. HE grand problem of an universal language will not, perhaps, be resolved by abstruse philological speculators on the best possible organization of inflective and derivative syllables:-but an approximation to the adoption of universal words has already been effected in many sciences, particularly in botany and chemistry, and is daily extending to some new branch of knowlege, to the exclusion of partial and national nomenclature. In this way, disconnected, insulated, and improper terms gradually give place to systematic, allied, and appropriate names. From books, they pass into the conversation of the cultivated, and thence into vulgar use; and thus a perpetual progress is made towards an idiom universally intelligible. There There is no good reason why the terms of commerce and of art should submit more reluctantly to the correction of the philologist, than those of philosophy and science. Many merchants' clerks pique themselves on adorning our magazines with sonnets: let the technical jargon of trade be bolted to the bran in the sieves of etymology; and these gentlemen will pique themselves on writing an invoice, as if they understood the words of which it consists. We have already noticed (Rev. vol. xi. p. 561.) one attempt of M. NEMNICH to catholicize the phraseology of natural history; and we have now to record a similar attempt on the commercial language of Europe. The catalogue of words is arranged in the following order: English, German, Low Dutch, Danish, Swedish, French, Italian, Spanish, Portuguese, Russian, Polish, and Latin. By these means, a single glance discovers which of the rival, names is most generally intelligible, this is one ground of preference; and which is etymologically purer,-this is a higher motive of choice. The lingua franca of the counting-house is so little fettered by printed authorities, and so likely to find a convenience in warying the terms, which have most emphatically been maintained in the tariffs and books of duties of the several sea-ports, that there is no reason for despairing of introducing any rational innovation. Terms so inexpressive or improper as Barbadoes Tar for Bitumen, Benjamin for Benjoin, Brownstone for Manganese, Dutch Pink for a yellow paint, &c. will disappear by simple exposure. Others of a somewhat vulgar complexion, such as Dragon's blood, Fistinuts, Jews' ear, Jews' trumps, Sowbread, Wake-Robin, Worm-Seed, will gradually be exchanged for terms more scientific or more polite.-A few words are mis-spelt by our author-Bellowses for Bellows, Bezoard for Bezoar, Cruel-ribbons for Crewel-ribbons, Callimanco for Calamanco, and perhaps, but for this there are many authorities, Train-oil for Drain-oil; as it is the oil which drains from blubber. A few others are ill defined: Canvas is not exclusively descriptive of Irish sail-cloth, but of many kinds of hempen cloth, from whatever country: 'smallcoal is not synonimous with charcoal: nor is Petty Wares the technical term for Haberdashery. A great number of words are totally omitted, particularly the names of manufactured articles of commercea list which might best be completed by the assistance of the riders or travellers of manufacturing houses. To the Catholicon, or Universal Dictionary, succeeds a separate vocabulary for each language, with an English interpretation. This part of the work cannot but greatly facilitate the the farther diffusion of our language, as the medium of commercial intercourse between the Baltic nations. As far as it goes, it is well executed: but there are in course deficiencies, which the author hopes to remedy in a future edition; and he solicits corrective contributions. ART. XVI. Memorias da Acad. R. das Sciencias de Lisboa, &c. e. Memoirs of the Royal Academy of Sciences of Lisbon. Vol. I. WE [Article concluded, see our last Appendix, p. 551-554-] E now resume the consideration of this volume, in order to attend to those papers which have not yet been noticed, and which belong to the class of MATHEMATICS. Tay. General Solution of Kepler's Problem of the Mensuration of Wine Pipes, and other Casks. By J. MONTEIRO DA ROCHA. This problem was proposed by Kepler in his Stereometria doliorum; and several solutions were exhibited by different mathematicians, which are considered by the present author in the first part of his memoir. He then proposes the problem according to the following form: "To determine the area of any segment of a solid of Revolution, made by a plane parallel to the axis of the same." Memoir on the true Principles of the Method of Fluxions. By Mr. STOCKLER. This memoir is introduced by some preliminary observations. on the methods of explaining the fluxionary calculus, as given by its inventors and by succeeding geometricians. That conciseness and rigorous exactness, that perspicuity and precision, are not by the nature of things incompatible, will be readily allowed; yet, in the doctrine of fluxions, it is undoubtedly true that, whatever advantage its methods have from their generality and facility of application, they are deficient in that evidence and geometrical rigor which characterize the methods of the antient geometricians. As in the present Appendix (see the first article) this curious and important subject has been so particularly discussed, we shall here content ourselves with examining what Mr. STOCKLER has done, and with what. success. In the first part of the memoir, he animadverts with judg ment on the methods pursued by Leibnitz, Newton, Maclaurin, Euler, and D'Alembert, for the purpose of elucidating and establishing the fundamental truths of the theory of fluxions. In the explanation of his own method, Mr. S. supposes quan tity to be generated by motion, or to pass through its several states of change either by a constant or variable flux. The common definition of a fluxion is, that it is not the quantity really generated, but what would be generated, were the motion continued uniform from any point. This quantity, however, is not immediately assignable; to ascertain it, the author reasons nearly after the following manner;-suppose the motion continually to vary then in the interval of two instants of time, during which the quantity increases, there is always a certain point at which the rate of motion is such, that, if it continued constant, for a time (t), a quantity would be generated equal to the real increment generated in variable motion. This rate of motion, or velocity, or tendency, is called the hypothetical fluxion, to distinguish it from the true and proper fluxion; and, from its definition, it follows that the product of it and the time (in which the real increment is generated) is equal to the increment; now the hypothetical fluxion (taking two instants of time) is always contained between the proper fluxions at the first and second instant; that is, is always greater than the true fluxion at the first instant, and less than the true fluxion at the second, if the motion increases; and the contrary, if the motion diminishes, By diminishing the interval of time, however, the hypothetical fluxion may be made to approach to the true fluxions more nearly than by any assignable quantity. Hence the ratio of the proper or true fluxions is the limit of the ratio of the hypothetical fluxions, and the real object of investigation is this limit. P Let be any quantity involving x, y, z, &c. Fp a function of it; let Ap be the hypothetical fluxion of : then Ap is the increment; and let do represent the proper fluxion of 9, &c. Now, since becomes p+tAp, it follows that tAFq=F (9+tAp)-Fo: hence AFq= F(o+tAo)-Fp: but the limit of the ratio of the hypothetical fluxions is the ratio of the proper fluxions, which limit is obtained by putting to; in which case Ap becomes dp, &c. Hence dFp (the proper fluxion of Fp)=F(0+tdp)-Fo t(o) but the developement for the function F(p+tdp) being F4+ Ptdp+P't do3, &c. we have dFq=P'dq The quantities P', P", P'", &c. are different functions of Fo; it appears, then, in order to find the fluxion of F, only neces sary to calculate the second term of the series, Fp+P ́tdp+, &ic. Such Such is essentially the method of Mr. STOCKLER.-We shall now consider to what degree he has succeeded in rendering the metaphysique of fluxions luminous and exact. In the first place, the objection justly made against the method of Newton, Maclaurin, &c. is equally valid against that of Mr. S. which is grounded on the principle of motion;-a principle foreign to the nature of the subject. By the introduction of the hypothetical fluxion, we are enabled, perhaps, to form a more distinct idea of the nature of the proper fluxion: but the grounds of the method, the fundamental principles, are not new; they are precisely the same as in the method of prime or ultimate ratios or limits; for, in this latter method, the ratio of the fluxions of quantities is the limiting ratio of their increments; which limiting ratio is obtained by putting the incremento. In Mr. S.'s method, the ratio of the proper fluxions is the limiting ratio of the hypothetical fluxions; which limiting ratio is obtained by putting the time-o-but the hypothetical fluxion multiplied into the time is the increment; the two methods are therefore essentially the same: that of Mr. Stockler may appear different, since in it are introduced a new term and a new symbol, which give to the old method a different and rather an improved appearance: but the body remains the same, the garb only is altered. The author has combined with the theory of limits that of the developement of functions into series; it is indeed this latter theory which comprehends the true principles of the fluxionary or differential calculus; yet what he has done on this subject is to be noted as deficient; for in the Formula Fp+P'w+P"w, &c. the developement of F(p+w) is not demonstrated; neither is it shewn that all the powers of ware whole positive powers (and there are particular cases in which a fractional power enters); nor why P', P", &c. are independent of w; nor after what manner they are derived from the original function Fp. In the latter part of the memoir, it is observed that the formula of Taylor, for the conversion of functions into series, may be demonstrated by the help of the forms previously established. The Series of Taylor was proved in the Berlin Acts for 1772 by M. de la Grange, by means of the expansion of the function f(x+i) into a series of the form ƒx+pi+qi2+ri3, &c. and, in the same memoir, the learned author remarked that the true principles of the theory of fluxions were contained in the theory of the developement of analytic functions. Persuaded that the theory of Mr. STOCKLER possessed the semblance only of novelty and originality, and that the method of |