REC 



RED 



' wllich 



equation, vi:. z . 



is thus derived ; let the right line 

 C R be conceived to revolve about the 

 centre C; then since the celerity of the 

 generating point R, in a direction per- 

 pendicular to C R, is to (jc) the celerity of 

 the point N, as C B (y} to C N (a), it will 



therefore be truly represented by -^- ; 



which being to (j>) the celerity in the di- 

 rection of C R, produced as C B (s) : R P 



(0, it follows that : ir : : l : **i 

 a* 



i/ 1 ^ 1 . ., ., 

 whence, by composition,- r- T" # : U 



-s 1 -f t- (y-} : t* ; therefore ~~ -f 2/ 1 



J,l,',l /</ Z X 1 



~-, and consequently /- 



fr- 



(= ^-)=r. Q.E.D. 



But the same conclusion may be more 

 easily deduced from the increments of the 

 flowing quantities : for, if R TO, r m, and N 

 n be assumed to represent (z, y, a-) any 

 very small corresponding increments of 

 A R, C R, and B N ; then will C N (a) : 

 C R (z/) : : x (the arch N M) : the similar 



arch R r = -^-. And if the triangle R r 



a 



m (which, while the point m is returning 

 back to R, approaches continually nearer 

 and nearer to a similitude with C R B) be 

 considered as rectilinear, we shall also 

 obtain i i (= R m 1 = R r 2 + r m 1 } = 



Jl -*-> and /^ *' I '' ( ") 



=r r, as before. 



See Simpson's " Flvixions." 



RECTIFICATION, in chemistry, is no- 

 thing but the repetition of a distillation, 

 or sublimation, several times, in order to 

 render the substance purer, finer, and 

 freer from aqueous or earthy parts. 



RECTIFIER, in navigation, an instru- 

 ment consisting of two parts, which are 

 two circles, either laid one upon, or let in- 

 to, the other, and so fastened together in 

 their centres, that they represent two 

 compasses, one fixed, the other move- 

 able ; each of them divided into the thir- 

 ty-two points of the compass, and three 

 hundred and sixty degrees, and number- 

 ed both ways, from the north and the 

 south, ending at the east and west, in 

 ninety degrees. 



RECTIFYING the globe. See GLOBE. 



VOL. V. 



RECTORY, in law, is taken for an en- 

 tire parish-church, with all its rights, 

 glebes, tithes, and other profits whatso- 

 ever. 



RECTUM, in anatomy, the third and 

 last of the large intestines. 



RECURRING series, is a series consti- 

 tuted in such a manner, that having ta- 

 ken at pleasure any number of its terms, 

 each following term shall be related to 

 the same number of preceding terms, ac- 

 cording to a constant law of relation. 



RECURVIROSTRA, the awset, in na- 

 tural history, a genus of birds of the or- 

 der Grallx. Generic character : the bill 

 long, very thin, and bending considerably 

 upwards ; nostrils narrow and pervious ; 

 tongue short ; feet palmated ; hind toe 

 very short and high. There are three 

 species. We shall notice only that which 

 is found in this island. The R. avosetta, 

 or scooping avoset, is as large as a lap- 

 wing, and has extremely long legs ; its 

 bill is three inches and a half in length. 

 In winter it is often seen in England, par- 

 ticularly at the mouth of the Severn, and 

 on the coasts of Suffolk. In the fens of 

 Cambridgeshire these birds are known to 

 breed, and appear often in vast flocks. 

 Their subsistence is on insects and 

 worms, which they procure from the soft, 

 muddy bottoms with their bills. They 

 often wade into the water to the top of 

 their legs, and are able to swim ; but are 

 seldom seen swimming, and never, unless 

 at a very small distance from the shore. 

 In France, on the coasts of Bas Poictou, 

 their nests are plundered annually of se- 

 veral thousands of eggs, which form a 

 nourishing and valued food for the pea- 

 santry of that district. See Aves, Plate 

 XIII. fig. 4. 



RECUSANT, a person who refuses to 

 go to church, and worship God after the 

 manner of the church of England, as by 

 law established : to which is annexed the 

 penalty of 201. a month for nonconformi- 

 ty. 23 Elizabeth, c. 1. 



RED. See COLOUR, DYING, OPTICS, 

 fee. 



RED book, of the Exchequer, an ancient 

 record, or MS. volume, in the keeping of 

 the King's remembrancer, containing di- 

 vers miscellaneous tracts relating to the 

 periods before the conquest. 



REDDENDUM, a clause in a lease, 

 whereby the rent is reserved to the les- 

 sor. See DEED. 



REDDLE, red-chalk, in mineralogy, a 

 species of the iron genus : its name be- 

 speaks its colour: it soils strongly, and 

 writes; is easily frangible; adheres 

 4 A 



