R E C 



RED 



}=» 



s = 



wlicnce, by addition 



/(A + B + C + ..K) i y(B.fC+ I) -I I.) 1 ] _ „ 

 r(C + B + D+..M) - (D + E+F + N) j "" ° 



Or, rcprefenting the whole lum by S, 



^(S-L-M-N)+j(S-A-M-N + 

 r(S-A-B-N)- (S-A-B-C 



whicli, by addition and divifion, gives 



/. (L + M + N) + y (A + M + N) + ;■ (A + B 

 + N)- (A + B +C) 



where the fum depends merely upon the three firft and the 

 three lad terms of the ferics ; and a fimilar expreffion, it is 

 obvious, may be obtained for any other fcale of relation. 



It may not be amils to obferve, that when the propofed 

 feries is wholly numeral, (the fum of whicli, as we have be- 

 fore obferved, is to be found by making .v = i ) ; both this 

 formula and the preceding one fail, in the cafe in which the 

 denominator of the fraftion becomes zero, and we mull, there- 

 fore, in fuch cafes, have recourfe to other methods of fumma- 

 tion, as given under tlie article Skkiks. 



On this fubjeft the reader (liould confnlt De Moivre's 

 Mile. Analyt. and his Doclrine of Chances, and Euler's 

 An.ilyfis Infinitornm, where he will find an explanation of its 

 application to the approximation to the I'oots of equations. 

 Colfon's Comment on Newton's Fluxions. Stirling's Me- 

 thodus Differ. Cramer's Analyfis des Lignes Courbes. 

 Bernoulli de Serieb. Inf. &c. See alio a chapter on this 

 fubjeft, in vol. ii. of Bonnycaftlc's Algebra. 



RECURVIROSTRA, the Avocet, in Ornithology, a 

 genus of birds of the order Grallx, of which the generic 

 charaiSer is ; bill depreded, lubulate, recurved, pointed, 

 flexible at the tip ; the feet are palmate, four-toed, the 

 hind toe not connefted, very ftiort, and placed high up ; 

 the noftrils are narrow, pervious ; the tongue is (hort. 

 There are only three 



Species. 



* AvocETTA ; Scooping Avocet ; called alfo in different 

 parts of this country, butter-dip, fcooper, yelper, crooked- 

 bill, &c. This bird is variegated with white and black ; 

 the bill is three inches and a half long ; irides hazel ; crown 

 black ; a white ipot behind and beneath the eyes ; rell of 

 the head, neck, back, exterior part of the wmgs, leffer 

 quill-feathers, tail, and under part of the body, white ; 

 inner fcapulars and greater quill-feathers without and at the 

 tips black ; legs blueifli, and very long ; membrane conneft- 

 ing the toes indented. It refides in the temperate parts of 

 Europe, weighing thirteen ounces ; and meafuring, from 

 the tip of the bill to the end of the tail, eighteen inches. 

 It breeds in the fens of Lincolnfliire, and on Romney Marlh, 

 in Kent. The female lays two white eggs, tinged with 

 green, and marked with large black fpots. In winter thefe 

 birds atfemble in fmall flocks of fix or feven, and frequent 

 tlie fhores, particularly the mouths of large rivers, in fearch 

 of worms and marine infeijts, which they icoop out of the 

 nuid or fand. They feem to be particularly fond of the 

 cancer, pulex, or loculla. By means of their long legs, 

 they run over fhores that are covered five or fix inches with 

 ...iter. In their movements they are lively, alert, vol.atile, 

 ..'.d difficult to catch. When the female is frightened off 

 '.,ti nell Ibe counterfeits laraenefs ; and when a flock is dif- 

 turbed, they fly with their necks ftretched out, and their 

 legs extended behind, over the head of the fpcCtalor, mak- 



mj^ a llinil nolle, and uttering a yelping cry of twit, twit, 

 all tlie time. 



AiMERKANA ; American Avocet. The head and neck 

 are rcddifh ; back black, beneath it is white. It inhabits 

 North America and New Holland : is fourteen inches long. 

 Bill black ; front dnfky-white ; neck above wfiite ; primary 

 and tertiai wini^-coverts black, the middle one;, and fome of 

 the fecondary iinill-fcithers, white. 



Ai.HA ; Wliite Avocet. This fpecies is white ; the lower 

 wing-coverts brownifh ; l)ill orange ; legs brown. Inhabits 

 Hudfon'ii Bay ; fourteen inches and a quarter long. Bill 

 tipt with black ; edge of the wings, greater quill-feathers, 

 and tail, tinged with yellowifli. 



RECUSANTS, in a general fenfe, perfons, whether 

 Papiits <n- others, who rcfufc to go to church and to wor- 

 fliip God after the manner of the church of England. 

 Popifh reculants are Papifls, who fo refufe ; and a popifh 

 recufant convift is a Papift legally convifted of fuch offence. 

 See Papist, Pk.»:mun'ike, and Toi.kkation. 



RECUSATION, Recusatio, an act by which a judge 

 is defired to refrain from judgnig fome certain caufe, on ac- 

 count of his relation tio one of the parties ; or of fome 

 capital enmity, or the hke. 



By the French laws, kinlliip within the fourth degree is 

 deemed a legal caufe of recufation ; as alfo the judge's being 

 godfather, &c. of one of the parties. 



By the laws of England alfo, in the times of Brafton 

 and Fleta, a judge might be refufed for good caufe ; but 

 now the law is otherwife, and it is held that judges or juf- 

 tices cannot be challenged. Co. Litt. 254. See Chal- 

 lenge. 



RED, in Phyfics, one of the fimple or primary colours 

 of natural bodies, or rather of the rays of light. 



The red rays are thofe which .ire of all rays the leali re- 

 frangible : hence, as fir Ifaac Newton fuppofes the different 

 degrees of relrangibility to arife from the different magni- 

 tudes of the luminous particles of which the rays confift, the 

 red rays, or red light, is concluded to be that which confifls 

 of the largeft particles. See Colour, Light, and Ray. 



Authors diflinguifli three general kinds of red ; one bor- 

 dering on the blue, as colombine, or dove-colour, purple, 

 and crimfon ; another bordering on yellow-, as flame-colour 

 and orange ; and between thefe extremes is a medium, 

 partaking neither of the one nor the other, which is what 

 we properly call rtd. 



Acids generally turn black blue, and violet into red ; 

 and red into yellow, and yellow into a very pale yellow. 



Alkalies change red into violet, or purple ; and yellow 

 into feuillemort, or dead leaf-colour. 



Terreltrial and fulphureous matters become red by ex- 

 treme heat ; and fome, at length, black, as we fee in brick, 

 red bole, red chalk, date, &c. All thefe, when vitrified 

 by a burning-glafs, become black. 



Loblters become red by a moderate fire ; and by a violent 

 one, black. Mercury and fulphur mixed and heated over a 

 moderate fire make a beautiful red, called artificial cinnabar. 

 An acid fpirit, as lemon juice, being poured on a blue 

 folution of turnfole, turns it into a beautiful red. Alkali 

 reilores it again to its original blue. Filtrating of fome 

 reddifh wines takes from them all their red colour. 



M. De la Hire oblerves, that a very luminous body 

 viewed through a black one, always appears red ; as when 

 the fun is feen fhiniv.g through a black cloud. He adds, 

 that fome people who fee all the other colours perfeiSly weU, 

 yet have no idea of red, and only fee it as black. 



Red, in Cofmet'ics, a fucus or paint with which the ladies 

 enliven their cheeks and lips. 



There 



