Porim. pofition, and alfo a point R, to find a point D in one of the given lines, fo that DE and DF being drawn perpendicular to BC, AC, and DR, joined; DE+DF may have to DR a given ratio. It is plain, that having found G, the problem would be nothing more than to find D, fuch that the ratio of GD' to DR2, and therefore that of GD to DR, might be given, the point D being in the circumference of a given circle, as is well known to geometers. The fame porifm alfo affifts in the folution of another problem. For if it were required to find D fuch that DE+DF' might be a given space; having found G, DG' would have to DE+DF2 a given ratio, and DG would therefore be given; whence the folution is obvious. The connection of this porifm with the impoffible cafe of the problem is evident; the point L being that from which, if perpendiculars be drawn to AC and CB, the fum of their fquares is the leaft poffible. For fince DF'+DE': DG :: LO+LM': LG'; and fince LG is less than DG, LO+LM' muft be lefs than DF+DE. It is evident from what has now appear ed, that in fome instances at least there is a close connection between these propofitions and the maxima or minima, and of confequence the impoffible cafes of problems. The nature of this connection requires to be farther investigated, and is the more interefting because the tranfition from the indefinite to the impoffible cafe seems to be made with wonderful rapidity. Thus in the first propofition, though there be not properly fpeaking an impoffible cafe, but only one where the point to be found goes off ad infinitum, it may be remarked, that if the given point F be anywhere out of Plate the line HD (fig. 1.), the problem of drawing GB CCCCX!!! equal to GF is always poffible, and admits of just one folution; but if F be in DH, the problem admits of no folution at all, the point being then at an infinite distance, and therefore impoffible to be affigned. There is, however, this exception, that if the given point be at K in this fame line, DH is determined by making DK equal to DL. Then every point in the line DE gives a folution, and may be taken for the point G. Here therefore the cafe of numberless folutions, and of no folution at all, are as it were conterminal, and so close to one another, that if the given point be at K the problem is indefinite; but if it remove ever fo little from K, remaining at the fame time in the line DH, the problem cannot be refolved. This affinity might have been determined à priori: for it is, as we have feen, a general principle, that a problem is converted into a porifm when one or when two of the conditions of it neceffarily involve in them fome one of the reft. Suppofe, then, that two of the conditions are exactly in that ftate which determines the third; then while they remain fixed or given, fhould that third one vary or differ ever fo little from the ftate required by the other two, a contradiction will enfue: therefore if, in the hypothefis of a problem, the conditions be fo related to one another as to render it indeterminate, a porifm is produced; but if, of the conditions thus related to one another, fome one be supposed to vary, while the others continue the fame, an abfurdity follows, and the problem becomes impoffible. Wherever, therefore, any problem admits both of an indeterminate and an impoffible cafe, it is certain, that thefe cafes are nearly related to one another, and that fome of the conditions by which they Porifin. from the porifmatic cafe of a problem which will affect analyfis belonging to porifms; which, however, does not fubject Porlock. Pork, fubject is taken. He has there promifed a fecond part to his paper, in which the algebraical inveftigation of porifms is to be confidered. This will no doubt throw confiderable light upon the fubject, as we may readily judge from that gentleman's known abilities, and from the fpecimen he has already given us in the first part. PORK, the ficfh of fwine killed for the purposes of food. See Sus. The hog is the only domeftic animal that we know of no ufe to man when alive, and therefore feems properly defigned for food. Befides, as loathfome and ugly to every human eye, it is killed without reluctance. The Pythagoreans, whether to preferve health, or on account of compaffion, generally forbade the use of animal food; and yet it is alleged that Pythagoras referved the ufe of hog's flesh for himself. The Jews, the Egyptians, &c. and other inhabitants of warm countries, and all the Mahometans at prefent, reject the ufe of pork. It is difficult to find a fatisfactory reafon for this, or for the precept given to the Jews refpecting it, tho' unquestionably there was fome good one for it. The Greeks gave great commendations to this food; and Galen, though indeed that is fufpected to be from a particular fondnefs, is everywhere full of it. The Romans confidered it as one of their delicacies; and if some of the inhabitants of the northern climates have taken an averfion to it, that probably arofe from the uncultivated ftate of their country not being able to rear it. Pork is of a very tender structure; increafed perhaps from a peculiarity in its economy, viz. taking on fat more readily than any other animal. Pork is a white meat even in its adult ftate, and then gives out a jelly in very great quantity. On account of its little perfpirability and tenderness it is very nutritious, and was given for that intention to the athlete. With regard to its alka lefcency, no proper experiments have yet been made; but as it is of a gelatinous and fucculent nature, it is probably lefs fo than many others. Upon the whole, Mat. Med. it appears to be a very valuable nutriment; and the reafon is not very obvious why it was in fome countries forbid. It is faid that this animal is apt to be diseased; but why were not inconveniences felt on that account in Greece? Again, it has been alleged, that as Palestine would not rear thefe animals, and as the Jews had learned the use of them in Egypt, it was neceffary they fhould have a precept to avoid them. But the Egyptians themfelves did not use this meat; and this religious precept, indeed, as well as many others, feems to have been borrowed from them. Poffibly, as pork is not very perspirable, it might increafe the leprofy, which was faid to be epidemic in Palestine; though this is far from being certain. Cullen's PORLOCK, in the county of Somerfet in England, is a fmall fea-port town fix miles weft from Minehead. This whole parish, including hamlets, contains about 110 houses, and nearly 600 inhabitants. The fituation of the town is very romantic, being nearly furrounded on all fides, except toward the fea, by fteep and lofty hills, interfected by deep vales and hollow glens. Some of the hills are beautifully wooded, and contain numbers of wild deer. The valleys are very deep and picturefque; the fides being fteep,fcarred with wild rocks, and patched with woods and foreft frubs. Some of them are well cultivated and ftudd with villages or fingle farms and cottages, although agriculture here is very imperfectly understood. JUN Moft of the roads and fields are so steep, that no carriages of any kind can be ufed; all the crops are therefore carried in with crooks on horfes, and the manure in wooden pots called deffels. Many of the poor are employed in fpinning yarn for the Dunfter manufactory. W. Long. 3. 32. N. Lat. 51. 14. PORO. See CALAURIA. PORPESSE, in ichthyology. See DELPHINUS. PORPHYRIUS, a famous Platonic philofopher, was born at Tyre in 233, in the reign of Alexander Severus. He was the difciple of Longinus, and became the ornament of his school at Athens; from thence he went to Rome, and attended Plotinus, with whom he lived fix years. After Plotinus's death he taught phi lofophy at Rome with great applaufe; and became well skilled in polite literature, geography, aftronomy, and mufic. He lived till the end of the third century, and died in the reign of Dioclefian. There are ftill extant his book on the Categories of Aristotle; a Treatife on Abftinence from Flesh; and feveral other pieces in Greek. He alfo compofed a large treatise against the Chriftian religion, which is loft. That work was anfwered by Methodius bishop of Tyre, and alfo by Eufebius, Apollinarius, St Auguftin, St Jerome, St Cyril, and Theodoret. The emperor Theodofius the Great caufed Porphyrius's book to be burned in 338. Those of his works that are ftill extant were printed at Cambridge in 1655, 8vo, with a Latin verfion. 66 Porphyrius (fays Dr Enfield) was, it must be owned, a writer of deep erudition; and had his judgment and integrity been equal to his learning, he would have deferved a diftinguished place among the ancients. But neither the fplendor of his diction, nor the variety of his reading, can atone for the credulity or the dishonefty which filled the narrative parts of his works with so many extravagant tales, or intereft the judicious reader in the abftrufe fubtelties and myftical flights of his philofophical writings." PORPHYRY, a genus of ftones belonging to the order of faxa. It is found of feveral different colours, as green, deep.red, purple, black, dark-brown, and grey. Under the name of porphyry, Mr Kirwan and M. de Sauffure include those ftones which contain either felt-fpar, fchoerl, quartz, or mica, with other species of cryftallized ftone on a filiceous or calcareous ground. There are a great many different kinds. M. Ferber defcribes 20 varieties under four fpecies, but in general it is confidered with relation to its ground, which is met with of the colours already mentioned. When the ground is of jafper, the porphyry is commonly very hard; the red generally contains felt-fpar in small white dots or fpecks; and frequently, together with thefe, black spots of fchoerl. The green is often magnetic, and is either a jafper or schoerl, with spots of quartz. Sometimes a porphyry of one colour contains a fragment of another of a different colour. Those that have chert for their ground are fufible per fe. The calcareous porphyry confifts of quartz, felt-fpar, and mica, in feparate grains, united by a calcareous cement; and, laftly, the micaceous porphyry confifts of a greenish grey micaceous ground, in which red felt-fpar and greenifh foap-rock are inferted. The porphyry of the ancients is a moft elegant mafs of an extremely firm and compact ftructure, remarkably heavy, and of a fine ftrong purple, variegated more or lefs Poro n Porphyry |