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Pudding-PiPE-iree, a name by which the CaJJth of botanifts is
fometimes called. See the article Cassia, Suppl. PIPER, in ichthyology, the Englifh name of a fpecies of Trig/a, with a bifid roltrum, and tubulofe noftrils. it is called by the generality of authors Lyra. , See the articles Trigla and Lyra, Suppl. PIPERIDGE-rr^?, a name fometimes given to the Berberis,
or barberry-bufh. See the artideBERBERis, Suppl. PIQUET, a well-known game at cards, and which has in fome cafes been the object of mathematical computations. Thus Mr. de Moivre has propofed and i'olvcd the following problems :
i° To find at P'tquct the probability which the dealer has for taking one ace or more in three cards, he having none in his hands. He concludes from his computation, that it is 29 to 28 that the dealer takes one ace or more. 2° To find at Piquet the probability which the eldeft has of taking an ace or more in five cards, he having no ace in his hands. Anfwer ; 2321091, or 5 to 2, nearly. 3 . To find at Piquet the probability which the eldeft has of taking both an ace and a king in five cards, he having none in his hand. Anfwer; the odds againft the eldeft hand tak- ing an ace and a king are 331 to 315, or 21 to 20 nearly. 4 . To find at Piquet the probability of having twelve cards dealt to, without king, queen, or knave ; which cafe is com- monly called cartes blanches. Anfwer ; the odds againft chartes blanches are 323 to 578956, ot 1791 to 1 nearly. 5 . To find how many different fets effentially different from one another, one may have at Piquet before taking in. An- fwer ; 28,967,278. This number falls (hort of the fum of all the difhncr. combinations, whereby twelve cards may be taken out of 32, this number being 225,792,840; but it ought to be coniidered, that in that number feveral fets of the fame import, but differing in fuit, might be taken, which would not introduce an eflential difference among the fets. Mr. de Moivre alfo gives fome obfervations on this game, which he had from an experienced player. See Doctrine of Chances, pag. 151 to 159.
Monf. de Morimort has alfo treated of Piquet in his Analyfe des jeux de Hazard, pag. 162. PISHAMIN, or Persimon, names by which fome call the Lacryma Jobi, a diftinct genus of plants. See the article Lacryma, Append. PISTACHIA, in the Linnsean fyftcm of botany, the name of a genus of trees, called by Tournefort Terebinthus, See the article Terebin thus, Suppl. /^W-Pistachia, a name given to the Staphylodendron, or bladder-nut-tree. See the article Staphylodendron, Suppl. PISTON (Cycl.) — There are two forts of Pijlons ufed in pumps ; the one with a valve, which is called a Bucket ; and the other without a valve, which is called a forcer. See the articles Forcer and Pump, append. VlTCH-tree, in botany, a name fometimes given to the Fir- tree. See the article Eir, Suppl. PITCHING, a word fometimes ufed for paving. See the ar- ticle Pavement, Cycl. PITH (Suppl,) — Dr. Hales fhews that the Pith ferves to fup- ply the dilating moifture for the tender flioots of plants, and that the figure of thefe may be oblong, and not round, like the fruit, there are tough diaphragms, or partitions in the Pith at fmall diftances from each other, which check the la- teral expanfion ; as alfo horizontal fibres, which ferve for the fame purpofe.
>Of the fame fort is the Pith in the large growing feathers of birds; being compofed ofveficles that can be diftended length- wife, but have fphiftcters at the ends, to prevent too large a lateral dilation. Vid. Halcs's Veget. Statics, vol 1. p. 337. PLAGIURL "Under this clafs of fifties are comprehended the following' geneva : ThePhyfeter, Delphinus, Batena, Mo- nodon, Catodon, and Thrichechus ; which fee under their refpective articles Physeter, &c. PJL.ANE-/7W (Suppl.)— Bajlardox Falje Plane-/t«, a name by which fome call the Acer, or Maple-tree. See the article Maple, Suppl. 'PLANETARIUM, an aftronomical machine, made to repre- fent the motions of the planets, as they really are in nature, or at leaft agreeably to the Copernican fyftem, and commonly called an Orrery. See the article Orrery, Suppl, The moft remarkable of thefe machines was that invented by Huygens, and defcribed by himfelf. See Defcript. Automati planctarii, ap. Huwen. Opufcul. pofthum. Tom. 2. p. 157. edit. Amft. 1728.
In this Planetarium, the five primary planets perform their revolutions about the fun ; and the moon performs her revo- lution about the earth, in the fame time that thefe revolutions are really performed in the heavens. The orbits alfo of the moon and planets arc reprefented with their true proportions, excentricity, pofition, and declination, from tbe ecliptic or orbit of the earth : So that by this Planetarium the fituation of the planets, their conjunctions, oppofitions, &c. may not only be known for the prefent time, but for any time paft, or future, as in a perpetual ephemeris.
This machine is nowprefcrved among the curtofitles of the univerfity of Leyden.
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But the Planetariums or Orreries now moft commonly ufed, do not reprefent the true times of the ecleftial motions j but only their proportions ; and are ofufe to beginners, to give them an idea of the planetary fyftems, as alfo, if conftrudted with fufficicnt accuracy, to folve feveral queftions relating to the motions of the planets, and of the earth and moon, &c. Thefe machines are made of various fizes, fome reprefenting more planets than others. However, thefe complex ones are far from being improvements upon the original Planetarium^ or Orrery, which fhewed only the motion of the moon round the earth, and of the earth and moon round the fun. They give but very confined, and even falfe ideas of the di- ftances and bignefs of the planets ; which muft always be {o whilft the orbits of the moon, and other fecondary planets, are fixed to the fame machine, which contains the primary ones. In the original one, every thing was well and properly executed ; as the phenomena of day and night, and their gradual increafe and decreafe, according to the feafons ; the places of the earth where the fun is fucceffively vertical, and feems to defcribe its parallels ; the real annual motion of the earth, which gives the fun an apparent annual motion ; the rotation of the fun about its axis ; the periodical and fynodi- cal month ; the folar and fydereal days ; the fuccefiive illumi- nation of all the parts of the moon, &ci It is therefore proper to have a machine for reprefenting the general folar fyftem by itfelf ; the fun moon, and earth ought alfo to be fhewn feparately ; and the fyftem of any other pri- mary planet ; as Jupiter, for inftance, with all its fatellites, fhould have a feparate machine fo contrived, as to reprefent in true proportion their magnitudes, diftances, and other pbasnomena.
As to the magnitudes of the primary and fecondary planets, if the fun's diameter be fuppofed 100, that of Saturn will be 7-rl) of Jupiter 10, of Mars T ^%, of the Earth r, of Venus 1, of Mercury T s / a , and of the Moon ~£ 6 %. As to the fa- tellites of Jupiter and Saturn, they are fuppofed to be about the bignefs of our Earth.
Again, if the diftance of the Earth from the Sun be divided into 10 parts, Mercury will be diftant from the Sun four of thefe parts, Venus feven, Mars fifteen, Jupiter fifty-two, and Saturn ninety-five.
Dr. Defaguliers defcribes a Planetarium of his own contriv- ance, the frame of which, containing the clock-work, is made of ebony ; its outftde is adorned with twelve pilafters, between which are painted, on as many vertical planes, the twelve figns of the zodiac. The upper furface is flat, and made of polifhed brafs ; on the outward circumference of which are fcrewed fix brafs pillars, fupporting a large flat fil- vered ring. On this ring, which reprefents the ecliptic, are drawn feveral circles; the three innermoft being divided into twelve parts for the figns of the zodiac, and each of thefe into 30 degrees ; and among thofe degrees are graved in their proper places, the nodes, aphelia, and greateft north andfouth latitudes of the planets. The next three circles have the months and days of the months, exactly correfponding to the Sun's place at noon each day throughout the year ; and upon the brafs furface of the machine graduated are filver circles, which carry the planets, reprefented by filver balls, and raifed upon arbors or ftems to the height of the ecliptic. Above the ecliptic ftand fome of the principal circles of the fphere, according to their refpective fituation in the heavens, viz. the two colures, one half of the equinoctial circle, the tropic of cancer, the arct ic circle, &c. The whole machine is alfo fo contrived, as to be fet to any latitude, without inju- ring any of theinfide motions.
Within the ecliptic ftand the Sun and other planets ; the Sun being in the center of the whole fyftem, and the reft repre- fented agreeably to the above-mentioned magnitudes and di- ftances. When things are thus difpofed, by turning about the handle, or winch of the Planetarium, all the planets perform their revolutions round the Sun, according to their periodical times ; and being furnifhed with indices of blued-fteel, thefe fhew the longitudes of the planets, by pointing to the divi- fions on the graduated filver circles, as they move round. As the diftances of the planets are in their true proportions' to each other, fo likewife are their magnitudes ; but it cannot be expected, that the diameters of the planets fhould be in pro- portion to the diameters of their orbits ; for to effect this, the machine muft either be made 3000 times bigger than ufual, or the balls reprefenting the planets 3000 times lefs than ufual ; whereby they would all be rendered invifible, except- ing the Sun, and even it would be lefs than .JL- part of an inch in diameter. For the fame reafon it is found impractica- ble to reprefent the fun by a ball, proportionally bigger than thofe reprefenting the other planets.
Now as the orbit of the Moon, as well- as of the fatellites of Jupiter and Saturn, bear no manner of proportion to the orbit of the primary planets, the difproportion between thefe and their fatellites muft be ftill greater. Hence appears the abfurdity of crowding them all into one machine, as is the cafe in the common Orreries.
To give a right notion of the diftances and magnitudes of the
fatellites with refpect to their primary planets, it will be ne-
ceflary to have a feparate machine for each fyftem ; or, the
2 fame.
