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But of all other branches of learning, there is not one less ftudied or understood at present in Portugal than mathematics; nor one that was formerly better understood. In the most brilliant æra of the morfarchy, it formed the principal study of most of its great men: witness prince Henry, king John I. and II. king Emanuel, Vasco 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 university of Coimbra had in this science ; he was preceptor to the brave Don John de Castro, 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 sage maxim of Ticho Brahe, thought “ midnight oil and mathematics necessary to make a found divine."

• At Coimbra they have an observatory, and at Lisbon another ; but there is neither an astronomer nor an instrument in either, and I am assured that there is not a practical astronomer in the kingdom. Indeed, the Portuguese, like the Spaniards, feem to have been deterred from the study of this sublime science, by the fate of Alfonso X. of Caftile; who, according to Mariana, loft the earth by studying the heavens. P. 158.

The last remark seems to have been jocularly introduced; for certainly the people in general, who have little to lose, have no great reason to dread the ill effects of the study of astronomy.

The longest chapter in the work is affigned to the coinmunication of anecdotes relative to distinguished Portuguese characters. The first person in the list is a Franciscan frier named Francisco de Macedo, who was a poet, orator, historian, and philosopher.

4. We cannot find a greater instance of a rich treasure of knowledge and presence of mind, than father Macedo gave during three days that he maintained a thesis upon every subject, in the presence of the proctor of St. Mark, many of the senators and nobles of Venice, and a great number of foreigners, whom fame had drawn thither. The doctors and masters of all the orders interrogated and tried him with innumerable questions and arguments, which he answered to their wishes, as if every thing had been premeditated.'

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

The interesting narrative of don Pedro de Mentiroso forms the next chapter; and, after some observations on the « origin

of Portugal,' anecdotes are given of the kings; but of Joseph, the immediate predecessor of the present sovereign, nothing is faid, though some particulars respecting his character and reign, might have been expected.

We cannot highly praise the composition of this work. The arrangement is not very judicious; and the style is inelegant

and incorrect. But the volume abounds with information, which will supply the deficiencies, and rectify the errors, of former accounts of the Portuguese realm. It is embellish ed with plates, illustrative of the dress, diversions, &c. of the natives : views of the bay of Lisbon, and of the city of Coimbra, are also given ; and an accurate map of Portugal is annexed.

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Philosophical Transaktions of the Royal Society of London.

For the Year 1798. Part I. 40. 8s. 6d. Jewed. Elmsly. 1798.

In this new volume of the labours of our learned and scientific society, some important articles are observable ; and to these we shall pay that attention

which they deserve. • I. The Bakerian Lecture. Experiments upon the Refistance of Bodies moving in Fluids. By the Rev. Samuel Vince, A. M. F. R. S. Piumian Profeffor of Astronomy and Experimental Philosophy in the University of Cambridge.'

The difficulty of ascertaining the time in which fluids were discharged from vessels, and the little agreement between the ory and experiment, were noticed in a former paper, offered to the society by Mr. Vince, Theory alone, he thinks, will not affist us ; for it considers only the impulse, and supposes the particles of the fluid to be afterwards inactive; but, if their action should be taken into the account, the same principles would be found defective. His present object is to examine the resistance of non-elastic fluids. In his experiments, the result differs from what is taught by theory. The latter supposes the resistance to vary as the cube of the fine: from experiment, however, it appears to decrease in a less ratio than that, but not as any constant power of the fine, nor as any function of the fine and co-line' hitherto discovered.

• Hence, the actual resistance is always greater than that which is deduced from theory, affuming the perpendicular resistance to be the fame; the reason of which, in part at least, is, that in our theory we neglect the whole of that part of the force which, after resolution, 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 ; also, the resistance of the fluid which

Crit. Rey. VOL. XXIV. Sept. 1798.

escapes from the plane, into the surrounding fluid, may probably tend to increase the actual resistance above that which the theory gives, in which that consideration does not enter ; but, as this latter circumstance affects the resistance at all angles, and we do not know the quantity of effe&t which it produces, we cannot say how. it may affect the ratio of the resistances at different angles.

In theory, the resistance perpendicular to the planes is suppofed 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 ačtual resistance was found to be =0,2321 oz. Hence, the actual resistance of the planes : the resistance in our theory : : 0,2321 ; 0,1598, which is nearly as 3 : 2.' P. 3.

Mr. Vince proceeds to determine the resistance of globes and semi-globes, and the comparative resistances of globes and cylinders. He afterwards considers the action of a fluid, in motion, on a quiescent body. From these experiments it appears certain, that the velocity of a fluid, Howing out of a yeffel, is equal to the velocity which a body acquires in falling down the altitude of the fluid, above the orifice; and the {quare of the velocity is consequently proportioned to that altitude, agreeing with what takes place when the body moves in the fluid.

• II. Experiments and Obfervations, tending to show the Composition and Properties of Urinary Concretions. By George Pearson, M. D. F. R. S.

After such a frequency of inquiries and experiments, it is with pleasure that we announce the facts to be completely ascertained, and the analysis carried to its utmost extent: it is with surprise that we perceive the result to be, in some re{pects, different from what was before fuppofed by chemists of high authority. In the experiments of Dr. Pearson upon some urinary calculi, one half of their fubftance was diffolved by a lye of foda, and was precipitated by acids. This preci


trial, was not acid; it could not be sublimed, and therefore could not be the acid fublimate or succinic acid of Scheele; it was not putrescible, and did not forin á viscid folution with water, consequently was not animal mucilage. From various properties, liowever, it was found to ba what is called an animal oxyd ; and its distinguishing characters were imputrescibility, facility of crystallisation, and inSolubility in cold water: it was also 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 inethod of communi

pitate, from

cating oxygen, the result was only aminoniac, or carbonic acid a discovery which will lead to important consequences in pathology and therapeutics, and which we hope the ingenious author will pursue. The remainder of the calculus, not foluble in lye of caustic soda, was phosphat of lime. Three hundred grains of it contained 175 of animal oxyd, ninety-six of phosphat of lime, and twenty-nine of phosphoric ammo niac, mucilage, and water.

Dr. Pearson 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 taste was bitter, and sharp rather than four; the form was that of white fpiculæ ; and the chemical properties were essentially 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 specimen perhaps in England, he found that it weighed nearly 10{ ounces, was of a greater specific gravity than any human calculus, was uniform in its texture, without any apparent nucleus, and was radiated in the centre. It contained no ani. mal oxyd, but consisted principally of phosphat of lime, pho.phat of ammoniac, and animal matter. The calculi, from the intestines of dogs and horfes, appear to be fimilar in their composition. Urinary concretions of horses contain phosphat of lime, phosphat of ammoniac, and comnion anir, mal matter. Calculi of the stomach and intestines contain the fame principles. The concretion of the stomach, called oriental bezoar, and an intestinal concretion of a sheep, consist of vegetable matter. In general, the uric oxyd is not found in the concretions of any phytophagous (plantivorous or granivorous) animal. The conclusions to which this fact would lead, the author means to consider at a future time. We shall only observe, 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 praising the clear scientific manner in which the fube ject is treated.

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

All the papers of Dr. Herschel are valuable; and even this, which in part consists of surmises and suspicions not always verified, deserves great attention. The suggestions are sometimes


curious. We must first mention an observation, which will affect the hypothesis of M. de la Place, that

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the motions of the two known satellites of the Georgium Sidus are retrograde. The remarks for which this peculiarity, if fully established, may give occasion, need not now

Dr. Herschel has discovered four additional fatellites; and it is interesting to observe, in the reports, the appearances which suggested the suppositions, 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 respective arrangements of the new and old satellites. The nearest satelles is a new one; the second was formerly supposed to be the nearest to the planet. The third satelles, in the present order, is new; and the fourth the farthest old one. Two still more distant have been observed ; but, if there are any nearer to the planet, they are invisible to us.' The poles of the Georgium Sidus are flattened; but the existence of a ring is, at least, doubtful : the appearance on which it was founded seems to be an optical deception.

The circumstance, which in discovering the satellites often misled, was, that sfars near the planet look smaller than usual, so as to resemble fecondary planets; and the latter, at a certain distance from it, disappear. The first satelles, for instance, usually disappears within the distance of 18'', and the second at about 20" froin it. The cause of this obfcuration Dr. Herschel endeavours to explain, though we think with, out fuccess.

• A dense atmosphere of the planet would account for the defalcation of light fufficiently, were it not proved that the satellites are equally lost, whether they are in the nearest half of their orbits, or in that which is fartheft from us. But, as a satellite cannot be eclipsed by an atmosphere that is behind it, a surmise of this kind cannot be entertained. Let us then turn our view to light itself, and see whether certain affections between bright and very bright objects, contrasted 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, almost equally, over a space of several minutes all around these planets. Their satellites also, having a great share of brightness, and moving in a sphere that is strongly illuminated, cannot be much affected by their various distances from the planets. The case then is, that they have much light to lose, and comparatively lose but little.

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

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