REC 
very small corresponding increments of AR, 
C R, and B N ; then will C N (a) : C R (y) 
: ; X (the arch N n) : the similar arch Rr = 
And if the triangle Rrm (which, 
a 
while the point m is returning back to R, 
approaches continually nearer and nearer 
to a similitude with CRB) be considered 
as rectilinear, we shall also obtain (= 
Rm* = Rr^ + rm^) = ?!^+/;and 
yl^ _|_ (= = z, as before. 
See Simpson’s “ Fluxions.” 
Rectification, in chemistry, is nothing 
but the repetition of a distillation, or sub- 
limation several times, in order to ren- 
der 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 into, the 
other, and so fastened together in their 
centres, that they represent two compasses, 
one fixed, the other moveable; each of 
them divided into the thirty-two points of 
tlie compass, and three hundred and sixty 
degrees, and numbered both ways, from 
the north and the south, ending ^at the east 
and west, in ninety degrees. 
RECTIFYING the globe. See Globe. 
RECTORY, in law, is taken for an en- 
tire parish-church, with all its rights, glebes, 
tithes, and other profits whatsoever. 
RECTUM, , in anatomy, the third and 
last of the large intestines. 
RECURRING scries, is a series consti- 
tuted in such a manner, that having taken 
at pleasure any number of its terms, each 
following term shall be related to the same 
number of preceding terms according to a 
constant law of relation. 
RECURVIROSTRA, the avoset, in na- 
tural history, a genus of birds of the order 
Grallse. Generic character : the bill long, 
very thin, and bending considerably up- 
wards ; 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 avo- 
set, is as large >s a lapwing, and has ex- 
tremely long legs ; its bill is three inches 
and a half in length. In winter it is often 
seen in this kingdom, particularly at the 
month of the Severn, and on the coasts of 
Sutfolk. In the fens of Cambridgeshire 
these birds are known to breed, and ap- 
RED 
pear often in vast flocks. Their subsistence 
is on insects and woims, which they pro- 
cure from the soft, muddy bottoms with 
their bills. They often wade into the wa- 
ter 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 several 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 pe- 
nalty of 201. a month for nonconformity. 
23 Elizabeth, c. 1. 
RED. See Colour, Dying, Optics, 
&c. 
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 pe- 
riods before the conquest. 
REDDENDUM, a clause in a lease, 
whereby the rent is reserved to the lessor. 
See Deed. 
REDDLE, red-ehalk, in mineralogy, a 
species of the iron genus : its name bespeaks 
its colour : it soils strongly, and writes ; is 
easily frangible; adheres strongly to the 
tongue ; feels meagre ; specific gravity 3.9. 
Exposed to a red heat, it decrepitates, and 
becomes black ; it may even be melted into 
a greenish grey spumous enamel. In Silesia 
it is found in compact limestone : it is prin- 
cipally used for drawing : the coarser kinds 
are used by the carpenter, the finer by the 
painter. It is sometimes used in its natu- 
ral state, and sometimes pulverized, washed, 
and mixed with gum, and cast into moulds. 
REDEMPTION, and Equity of Re- 
demption, in law. See Mortgage. 
REDOUBT, in fortification, a square 
work raised without the glacis of the place, 
about musket-shot from the town ; having 
loop-holes for the small arms to fire through, 
and surrounded by a ditch. Sometimes 
they are of earth, having only a defence in 
front, surrounded by a parapet and ditch. 
Both the one and the other serve for de- 
tached guards to interrupt the enemy’s 
works; and are sometimes made on the 
angles of the trenches for covering the 
workmen against the sallies of the garrison. 
The length of their sides may be about 
twenty fathoms ; their parapets must have 
