But of all other branches of learning, there is not one lefs ftudied or understood at present in Portugal than mathematics; nor one that was formerly better understood. In the most brilliant æra of the monarchy, it formed the principal study of moft of its great men: witness prince Henry, king John I. and II. king Emanuel, Vafco de Gama, Magellan, De Barros, Pedro Nunes; the last was the best of the Portuguese mathematicians; he flourished at the beginning of the fixteenth century, and was the first profeffor the univerfity of Coimbra had in this fcience; he was preceptor to the brave Don John de Caftro, to the infante Don Luis, brother to John III. and to king Sebastian. Even the Portuguese churchmen, in those days, as if calling to mind the fage maxim of Ticho Brahe, thought "midnight oil and mathematics neceffary to make a found divine."

At Coimbra they have an obfervatory, and at Lisbon another; but there is neither an aftronomer nor an inftrument in either, and I am affured that there is not a practical aftronomer in the kingdom. Indeed, the Portuguese, like the Spaniards, feem to have been deterred from the study of this fublime science, by the fate of Alfonfo X. of Caftile; who, according to Mariana, loft the earth by studying the heavens.' r. 158.

The last remark feems to have been jocularly introduced; for certainly the people in general, who have little to lofe, have no great reafon to dread the ill effects of the study of aftronomy.

The longest chapter in the work is affigned to the communication of anecdotes relative to diftinguished Portuguese characters. The first perfon in the lift is a Francifcan frier named Francifco de Macedo, who was a poet, orator, hiftorian, and philofopher.

• We cannot find a greater instance of a rich treasure of knowledge and prefence of mind, than father Macedo gave during three days that he maintained a thefis upon every subject, in the prefence of the proctor of St. Mark, many of the fenators and nobles of Venice, and a great number of foreigners, whom fame had drawn thither. The doctors and mafters of all the orders interrogated and tried him with innumerable queftions and arguments, which he anfwered to their wifhes, as if every thing had been premeditated.' P. 161.

Don Garcia de Neronha is mentioned in the catalogue for no other diftinction than that of having amaffed an immense fortune in India by forgery; but the other characters have less difputable merit, except Azevedo, a rapacious and inhuman

governor.

The interesting narrative of don Pedro de Mentirofo forms the next chapter; and, after fome observations on the origin

of Portugal,' anecdotes are given of the kings; but of Jofeph, the immediate predeceffor of the prefent fovereign, nothing is faid, though fome particulars refpecting his character and reign, might have been expected.

We cannot highly praise the compofition of this work. The arrangement is not very judicious; and the style is inelegant and incorrect. But the volume abounds with information, which will fupply the deficiencies, and rectify the errors, of former accounts of the Portuguese realm. It is embellifhed with plates, illuftrative of the drefs, diverfions, &c. of the natives: views of the bay of Lisbon, and of the city of Coimbra, are alfo given; and an accurate map of Portugal is

annexed.

Philofophical Transactions of the Royal Society of London. For the Year 1798. Part I. 4to. 8s. 6d. fewed. Elmily. 1798.

IN this new volume of the labours of our learned and fcientific fociety, fome important articles are obfervable; and to these we fhall pay that attention which they deserve.

I. The Bakerian Lecture. Experiments upon the Refiftance of Bodies moving in Fluids. By the Rev. Samuel Vince, A. M. F. R. S. Plumian Profeffor of Aftronomy and Experimental Philofophy in the University of Cambridge.'

The difficulty of afcertaining the time in which fluids were discharged from veffels, and the little agreement between theory and experiment, were noticed in a former paper, offered to the fociety by Mr. Vince. Theory alone, he thinks, will not affift us; for it confiders only the impulfe, and fuppofes the particles of the fluid to be afterwards inactive; but, if their action fhould be taken into the account, the fame principles would be found defective. His prefent object is to examine the resistance of non-elaftic fluids. In his experiments, the refult differs from what is taught by theory. The latter supposes the refiftance to vary as the cube of the fine: from experiment, however, it appears to decrease in a lefs ratio than that, but not as any conftant power of the fine, nor as any function of the fine and co-fine' hitherto discovered.

• Hence, the actual resistance is always greater than that which is deduced from theory, affuming the perpendicular refiftance to be the fame; the reafon of which, in part at least, is, that in our theory we neglect the whole of that part of the force which, after refolution, acts parallel to the plane; whereas (from the experiments which will be afterwards mentioned), it appears that part of that force acts upon the plane; alfo, the refiftance of the fluid which CRIT. REV. VOL. XXIV. Sept. 1798.

D

efcapes from the plane, into the furrounding fluid, may probably tend to increase the actual refiftance above that which the theory gives, in which that confideration does not enter; but, as this latter circumstance affects the refiftance at all angles, and we do not know the quantity of effect which it produces, we cannot say how it may affect the ratio of the refiftances at different angles.

In theory, the refiftance perpendicular to the planes is fuppofed to be equal to the weight of a column of fluid, whose base=3,73 in. and altitude the space through which a body muft fall to acquire the velocity of 0,66 feet; now that space is 0,08124 in. confequently the weight of the column 0,1598 Troy oz.; but the actual refiftance was found to be 0,2321 oz. Hence, the actual refiftance of the planes: the refiftance in our theory :: 0,2321: 0,1598, which is nearly as 3: 2.'

P. 3.

Mr. Vince proceeds to determine the refiftance of globes and femi-globes, and the comparative refiftances of globes and cylinders. He afterwards confiders the action of a fluid, in motion, on a quiefcent body. From these experiments it appears certain, that the velocity of a fluid, flowing out of a veffel, is equal to the velocity which a body acquires in falling down the altitude of the fluid, above the orifice; and the fquare of the velocity is confequently proportioned to that altitude, agreeing with what takes place when the body moves in the fluid.

II. Experiments and Obfervations, tending to show the Compofition and Properties of Urinary Concretions. By George Pearfon, M. D. F. R. S.'

After fuch a frequency of inquiries and experiments, it is with pleasure that we announce the facts to be completely ascertained, and the analyfis carried to its utmoft extent: it is with furprise that we perceive the refult to be, in some refpects, different from what was before fuppofed by chemifts of high authority. In the experiments of Dr. Pearfon upon fome urinary calculi, one half of their fubftance was diffolved by a lye of foda, and was precipitated by acids. This precipitate, from every trial, was not acid; it could not be sublimed, and therefore could not be the acid fublimate or fuccinic acid of Scheele; it was not putrefcible, and did not form a vifcid folution with water, confequently was not animal mucilage. From various properties, however, it was found to be what is called an animal oxyd; and its diftinguishing characters were imputrefcibility, facility of cryftallifation, and infolubility in cold water: it was allo particularly marked by its production of a pink or red matter, on the evaporation of its folution in nitric acid.

The oxyd was afterwards treated in different ways, for the purpose of acidifying it; but, in every method of communi

cating oxygen, the refult was only ammoniac, or carbonic acid-a difcovery which will lead to important confequences in pathology and therapeutics, and which we hope the ingenious author will purfue. The remainder of the calculus, not foluble in lye of cauftic foda, was phofphat of lime. Three hundred grains of it contained 175 of animal oxyd, ninety-fix of phosphat of lime, and twenty-nine of phosphoric ammoniac, mucilage, and water.

Dr. Pearfon next fought for the lithic acid of Scheele; and he discovered it in the proportion of about 18 grains in 100, on an average. The tafte was bitter, and fharp rather than four; the form was that of white spicule; and the chemical properties were effentially different from those of the animal oxyd, which our author wishes to call ouric or uric oxyd, from its most frequent occurrence in urine.

Having examined the urinary calculus of a dog, the only fpecimen perhaps in England, he found that it weighed nearly 10 ounces, was of a greater fpecific gravity than any human calculus, was uniform in its texture, without any apparent nucleus, and was radiated in the centre. It contained no animal oxyd, but confifted principally of phofphat of lime, pho phat of ammoniac, and animal matter. The calculi, from the inteftines of dogs and horfes, appear to be fimilar in their compofition. Urinary concretions of horses contain phosphat of lime, phosphat of ammoniac, and common ani mal matter. Calculi of the ftomach and inteftines contain the fame principles. The concretion of the ftomach, called ori ental bezoar, and an inteftinal concretion of a sheep, confift of vegetable matter. In general, the uric oxyd is not found in the concretions of any phytophagous (plantivorous or granivorous) animal. The conclufions to which this fact would lead, the author means to consider at a future time. We fhall only obferve, that, if the fact be admitted, perhaps the calculus would not be prevented, as there are other principles which, in phytophagous animals, concrete with equal powers of attraction. We cannot conclude our account of this paper without praifing the clear fcientific manner in which the fubject is treated.

III. On the Discovery of four additional Satellites of the Georgium Sidus. The retrograde Motion of its old Satellites announced; and the Caufe of their Difappearance at certain Distances from the Planet explained. By William Herschel, LL. D. F. R. S.'

All the papers of Dr. Herfchel are valuable; and even this, which in part confifts of furmises and fufpicions not always verified, deferves great attention. The fuggeftions are fometimes very curious. We must first mention an observation, which will affect the hypothefis of M. de la Place, that

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the motions of the two known fatellites of the Georgium Si dus are retrograde. The remarks for which this peculiarity, if fully established, may give occafion, need not now detain us. Dr. Herschel has difcovered four additional fatellites; and it is interesting to obferve, in the reports,' the appearances which fuggefted the fuppofitions, and the patience with which they were either verified or abandoned. These, however, must be examined in the volume. It is only in our power to mention the refpective arrangements of the new and old fatellites. The nearest fatelles is a new one; the second was formerly fuppofed "to be the neareft to the planet. The third fatelles, in the prefent order, is new; and the fourth the fartheft old one. Two still more distant have been observed; but, if there are any nearer to the planet, they are invifible to The poles of the Georgium Sidus are flattened; but the exiftence of a ring is, at least, doubtful: the appearance on which it was founded feems to be an optical deception.

us.

The circumftance, which in difcovering the fatellites often mifled, was, that ftars near the planet look fmaller than ufual, fo as to resemble fecondary planets; and the latter, at a certain diftance from it, disappear. The first fatelles, for inftance, ufually difappears within the distance of 18", and the fecond at about 20′′ from it. The cause of this obfcuration Dr. Herschel endeavours to explain, though we think without fuccefs.

A denfe atmosphere of the planet would account for the defalcation of light fufficiently, were it not proved that the fatellites are equally loft, whether they are in the nearest half of their orbits, or in that which is fartheft from us. But, as a fatellite cannot be eclipfed by an atmosphere that is behind it, a furmife of this kind cannot be entertained. Let us then turn our view to light itself, and fee whether certain affections between bright and very bright objects, contrafted with others that take place between faint and very faint ones, will not explain the phænomena of vanishing fatellites.

The light of Jupiter or Saturn, for instance, on account of its brilliancy, is diffused, almoft equally, over a space of several minutes all around thefe planets. Their fatellites alfo, having a great fhare of brightness, and moving in a sphere that is ftrongly illuminated, cannot be much affected by their various distances from the planets. The cafe then is, that they have much light to lose, and` comparatively lofe but little.

The Georgian planet, on the contrary, is very faint; and the influence of its feeble light cannot extend far, with any degree of equality. This enables us to fee the faintest objects, even when they are only a minute or two removed from it. The fatellites of this planet are very nearly the dimmest objects that can be seen in