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extent, and make a very beautiful figure for many weeks. Mem. Acad. Par. 1727.
TANACETUM, Tanzy, m botany, the name of a genus of plants, the characters of which are thefe : The flower is of the ftofculous kind, confuting of numerous fmaU flofcules, which are divided into many fegments at the ends, are placed on the embryo feeds, and are contained in a fort of fcaly cup, of a femi-orbicular figure. The embryos ripen into feeds, which have no down adhering to them. To this it is to be added, that the flowers are collected into large clutters. The (pedes of Tanzy, enumerated by Mr. Tournefort, are thefe: 1. The common yellow-flowered garden "Tanzy. 2. The garden Tanzy with curled leaves. 3. The garden Tanzy, with the leaves and the fmell of mint, called by authors, co- rymbiferous minty and cojlvtary. Tourn. Inft. p. 461. Theleaves of the common Tanzy, either dried and given, in decoction, or the exprefled juice of them taken, are excellent in nephritic and hyfleric cafes. The good women in the country give the juice with great fuccefs againfi: worms, and in the colic. The infufion of the dried plant is a remedy againfl: flatulencies and colics, and is given in dropfies, and in fuppreflions of the menfes, and of the urine. It is pretended by ibme, that the diftilled water deftroys worms; but this is lefs probable.
TANGARA, in zoology, the name of a Brafilian Bird, of which there are two fpecies : The firft is of the fize of the green-finch, and is of a fine fhining fea-green on its head and neck; and lias a black (pot on the front of the head, juft above the infection of the beak ; its moulders are black, and the reft: of the back yellow. Its belly is of a very beautiful blue, and the wings variegated with blue and black. The tail is broad, and is variegated with blue and black. It feeds on vegetables, and is kept in cages for its beauty ; where its only note is zip, zip.
The fecond kind is of the fize of the common fparrow ; its head is of a fine gay red, and its back, wings, and belly of a fine deep black ; its thighs are covered with white feathers, and have each a large red fpot, looking like a blotch of blood ; the tail is fhort, and the legs grey. Marggrave's Hilt. Brafil.
TANGARAC, a poifonous Brafilian plant ; but the root, fays Pifo, is an antidote to the leaves, flowers, and fruit. Boyle, Works abr. vol. 1. p. 14.
TANGENT (Cycl.) — The definition of a Tangent, commonly given, is mentioned by Mr. Chambers; but it does not ex- tend beyond the conic feet ions ; for in curves of higher orders a line may both touch and cut. A general definition is there- fore neceflary. As a right line is the Tangent of a circle, when it touches the circle fo clofely, that no right line can be
drawn through the point of contact between it and the arch, or within the angle of contact that is formed by them ; fo, in general, when a right line ET touches any arch of a curve, as E H in E, in fuch a manner that no right line can be drawn through E, betwixt the right line ET and the arch EH, or within the angle of contact HET, that is formed by them, then is ET the tangent or* the curve at E. Maclau- Tin's Fluxions, Art. 181.
The Tangent of an arch is the right line that limits the pofi- tion of all the fecants that can pafs through the point of contact, though, ftridtly fpeaking, it is no fecant. Ibid, Art. 505.
As to the methods of investigating Tangents by Fluxions, fee the faid treatife, book I. c. 7. where it is demonftrated inde- pendently of infinitefimals.
To determine the Tangents of curves, fuppofed to be defenbed by the interfections of right lines revolving abour given poles. See Mr. Maclaurin's Fluxions, Art. 210. feq. In finding the tangents of curves by the method of infinitefi- mal differences, it has been objected, that the conclufion is found by a double error. i°. By taking the curve for a poly- gon of an infinite number of fides. 1°. By the falfe rule for taking the differential of a power. But there is no need of fuch fuppofitions in the method of fluxions, for it may be geometrically demonftrated, that the fluxions of the bafe, or- dinate, and curve, are in the fame proportion to each other, as the fides of a triangle reflectively parallel to the bafe, ordi- nate, and Tangent. When the bafe is fuppofed to flow uni- formly, if the curve be convex towards the bafe, the ordinate and curve increafe with accelerated motions ; but their fluxions at any term are the fame as if the point which defcribes the curve had proceeded uniformly from that term in the Tangent. Any farther increment which the ordinate or curve acquires, is to be imputed to the acceleration of the motions with which they flow. See Madaur'ufs Fluxions, Book. i. chap. 7 and 8. Any two arches of curve lines touch together, when the fame
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right line is the Tangent of both at the fame point. But whe^ they are applied to each other in this manner, they never per- fcaly coincide, unlefs they be fimilar arches of fimilar and equal figures.
TANNERS Bark. This is a fubftance of prodigious ufe in gardenings and is the bark of the oak-tree chopped and ground into a fort of coarfe powder, for the dreffing of fkins, after which ufe it becomes of fervice to the gardener. Its fermen- tation is very lafting and very equal ; hence it is the moft va- luable of all things for the making of hot -beds; and when it has ferved to this ufe, and is thoroughly rotted, it makes a very valuable manure for land, one load of it doing as much fervice as four loads of dung.
It has not been of very long ufe in England, and was brought to us from Holland in the reign of King William, and then ufed for the raifing of orange-trees; but after this period it became difufed ; and it is of a much later date that it has been brought into ufe again for the raifing the pine-apple, fmce which time it is become generally ufed, wherever it is to be hadi for all the purpofes of the hot-bed, in railing tender plants.
There are feveral fizes of this tan* and they heat in a different manner in proportion to their fize, the fraud left heating much quicker, and cooling again in a finaller time ; and the largeft acquiring its heat more gradually, but keeping it much longer. The fkilful gardener therefore muft ufe one or the other of thefe, or a mixture of both, according to the feveral occafions he wants them for*
It fhould always be taken within a fortnight after it comes out of the pit, and laid up in a round heap for a week, to drain out the moifture ; after which it fhould be formed into a bed, and fhould be laid at leaft three feet thick. A hot-bed, pro- perly prepared, of this fubftance, will retain a moderate heat fix months. M/ikr's Gardener's Diet.
1 ANNING (Cycl.) — The operation of Tanning is perform- ed, on leather, better in the Weft Indies than in England. They ufe three forts of bark* the mangravc bark, the olive bark, and another ; and the whole bufmefs is fo foon done, that a hide delivered to theni is in fix weeks ready to be worked into fhoes, though they beftow lefs labour than we do. Phil. Tranf. N b . 36.
Every part of the oak-tree, of what age or growth foever, is fit for the tanners ufe, and all oaken coppice-wood, of any age or fize, being cut and procured in barking-time, will tan all forts of leather, at leaft as well as the bark alone. When this material is got at the proper feafon, it muft be very well dried in the fun, more than the bark alone ; thence it is to be cut up, and preferved in a covered place for ufe. When it is to be ufed, the greater wood muft be firft cleft fmall, to fit it for the beating and cutting engine; and the fmaller muft be put into the engine as it is. Which done, it* muft be again dried upon a kiln, and after that ground in the* fame manner that the tanners grind their bark. Such wood as is to be ufed prefently after 'tis gotten, wiil require the bet- ter and the more drying upon the kiln ; and if this is omitted, it will blacken and fpoilall the leather it is ufed about. Where oak is fcarce, black-thorn will tolerably well fupply its place ; and where that is not to be had in fufficient plenty, the white thorn will do. Phil. Tranf. N°. 108.
Birch alfo, being ordered in the fame manner with oak, is fie for fome ufes in tanning, particularly it does very well for tan- ning of fhoe-foal leather. All thefe ingredients will tan much better than bark alone, and that with much lefs charge; fo that this difcovery may vciy well fave the felling of trees when the bark is wanted, at a feafon when the fap is up, which, when 'tis done, caufes the outfides of the trees to rot anoV grow worm-eaten ; whereas if the trees had been felled in winter, when the fap is down, they would have been almoft all heart, as the people exprefs it, and not fubteA to worms. This manner of ufing the wood with the bark, in tanning, will alfo increafe the value of underwoods very confiderably. Phil. Tranf. N<\ 105.
The engine neceflary for cutting the wood confifts of a long fquare wooden block, and fome pieces of iron to be faftened on, and ufed about it, viz. a hammer, an anvil, an iron holding the wood to be bruifed and cut, and a knife to cut it. The whole is a very fimple and cheap machine, and is de- fcribed at large, and figured in the above-mentioned numbee of the Philofophical Tranfactions.
By Mr. de Button's experiments upon different fkins, it was found that a decoction of young oak wood fucceeded perfectly well in tanning fheep and calves fkins, but did not do equally well for ox, and the other harder fkins. This, however, he imagines might be only for want of knowing the beft me- thod of ufing the wood. And certainly thefe trials deferve to be farther profecuted ; fince the fmall branches of the oak, which are of little value, might be thus made to fupply the place of a much dearer commodity, the bark ; and as in many trees the bark of the young branches is found to be of greatly more virtue than that of the larger branches, or the trunk, the ufe of thefe (mall boughs, bark and all, might very proba- bly be found to anfwer to all the effects of the bark, of the larger kind alone. Memoirs Acad. Scien. Par. 1736. See the Phil. Tranf. above cited.
TANT,
