recidivation 
falling back, < reeidirare, fall back: sec rrriili- 
nite."] A falling back; relapse; return to an 
abandoned course ; backsliding. 
Recidiwtion is so much more dangerous than our first 
sickness, as our natural strength is then the more feebled, 
and unable to endure means of restoring. 
Rev. T. Adams, Works, I. 447. 
recidivist (re-sid'i-yist), 11. [< F. recidivists, 
< recidive, a repetition of a fault or crime, < 
L, recidii-us, falling back: see recidivous.'] In 
l''ri'ch law, a relapsed criminal; one who falls 
back into the same criminal course for which 
he has already been condemned. 
The French Cabinet offered a pledge that no recidivists 
should be sent to the islands. 
Appletan'i Ann. Cyc., 1886, p. 00. 
recidivOUSt (re-sid'i-vus), a. [= OF. recidif = 
It. recidiro, < L. recidirxs, falling back, return- 
ing, recurring, < recidere, reccidere, fall back, < 
re-, back, + cadere, fall: see cadent.] Liable 
to backslide to :i former state. Imp. Diet. 
recipe (res'i-pe), r. /. [L., impy. of recipere, 
take: see receive.'] Take: a Latin imperative 
used (commonly abbreviated R. or R) at the 
beginning of physicians' prescriptions, as for- 
merly and in part still written in Latin. 
recipe (res'i-pe), n. [= OF. recipe, F. recipf = 
Sp. recipe = Pg. It. recipe, a recipe, < L. recipe, 
take, used as the first word in a prescription, 
and hence taken as a name for it : see recipe, r.j 
1. A formula for the compounding of a remedy, 
with directions for its use, written by a phy- 
sician ; a medical prescription. 
He deals all 
With spirits, he ; lie will not hear n word 
Of Galen or his tedious recipes. 
B. Joiaon, Alchemist. II. 1. 
2. A prescribed formula in general, but espe- 
cially one having some relation or resemblance 
to a medical prescription; a receipt. 
There was a greatness of mind in Paracelsus, who, hav- 
ing furnished a recipe to make a fairy, had the delicacy to 
refrain from its formation. 
/. D'ltraeli, Curios, of Lit., IV. 186. 
The one grand recipe remains for you the be-all and 
the end-all of your strange existence upon earth. Move 
on I Dickens, Bleak House, xix. 
= 8yn. Receipt, etc. See reception. 
recipiangle (re-sip'i-ang-gl), n. [< F. rccipi- 
angle, irreg. < L. recipere, receive, + angulus, 
angle: see receive, and angle 3 , .] In engirt., an 
instrument formerly used for measuring angles, 
especially in fortification. Buchanan. 
recipience (re-sip'i-ens), 11. [< recipien(t) + 
-ce.j A receiving; "the act of or capacity for 
receiving; receptivity. [Rare.] Imp. Diet. 
recipiency (re-sip'i-en-si), n. [As recipience 
(see -cy)?\ Same as recipience. 
We straggle fain to enlarge 
Our bounded physical recipiency, 
Increase our power, supply fresh oil to life. 
Browning, Cleon. 
recipient (re-sip'i-ent), . and n. [= F. recipi- 
ent, a receiver, water-clock, = Sp. Pg. It. recipi- 
ents, receiving, a receiver, < L. recipien(1-)s, ppr. 
of recipere, receive: see receive.'] I. a. Receiv- 
ing; receptive; acting or serving as a receiver; 
capable of receiving or taking in. 
The step from painting on a ground of stanniferous 
enamel to a similar surface on a metallic recipient body is 
an easy and obvious one. Cat. Soulages Coll., p. 99. 
Recipient cavity, inentmn., a cavity in which an organ 
or part is received at the will of the insect; specifically, 
a cavity of the mesosternum which corresponds to a spine 
of the prosternum, the spine and cavity forming in the 
Elateridee a springing-organ. See spring. 
II. n. 1. A receiver or taker; especially, 
one who receives or accepts something given 
or communicated ; a taker of that which is of- 
fered or bestowed: as. recipients of charity or 
of public education; the recipients of the eu- 
charist. 
Whatever is received is received according to the ca- 
pacity of the recipient. 
Cudworth, Intellectual System, p. 725. 
Something should have been inserted to signify that, 
when the recipient is fitly qualified and duly disposed, 
there is a salutary life-giving virtue annexed to the sac- 
rament. Waterland, Works, V. 423. 
The first recipients of the Revelation. 
J. H. Nemnan, Development of Christian Doctrine, ii. 1. 
2. That which receives; formerly, the receiver 
in an apparatus or instrument. 
The form of sound words, dissolved by chymical prepa- 
ration, ceases to be nutritive, and, after all the labours 
of the alembeck, leaves in the recipient a fretting corro- 
8 ' v e. Decay of Christian Piety. 
recipiomotor (re-sip'S-o-mo'tpr), (i. [Irreg. < 
L. recipere, receive, + motor, mover.] Re- 
ceiving a motor impulse or stimulus ; afferent, 
5000 
as a nerve, in an ordinary sense: correlated 
with lilifromotor and dirigomotor. See motor. 
Each afferent nerve is a recipio-nwtor agent. 
H. Spencer, Prin. of Psychol., f 18. 
reciprocal (re-sip'ro-kal), . and n. [< NL. as 
if "recijimcaiis, < L. reciprocus, returning, al- 
ternating, reciprocal (> It. Pg. reciproco= Sp. 
reciproco = OF. reciproque, > obs. E. reciprofk) ; 
perhaps lit. 'moving backward and forward,' < 
*recw (< re-, back, + adj. formative -CM*: see 
-ic) + procus (< pro, forward, + adj. formative 
-cus). Cf. reciproeous, reciprock.] I. a. 1. Mov- 
ing backward and forward; alternating; re- 
ciprocating. 
The stream of Jordan, south of their going over, was 
not supplied with any reciprocal or refluous tide out of 
the Dead Sea. 
Fuller, Plsgah Sight, II. 1. 17. (Varies, under refhuna.) 
Obedient to the moon, he spent his date 
In course reciprocal, and had his fate 
Link'd to the mutual flowing of the seas. 
Milton, Second Epitaph on Hobson the Carrier. 
2. Mutually exchanged or exchangeable; con- 
cerning or given or owed by each (of two or 
more) with regard to the other or others: as, 
reciprocal aid ; reciprocal rights, duties, or ob- 
ligations ; reciprocal love or admiration. 
Let our reciprocal vows be remembered. 
Shale., Lear, iv. 6. 267. 
The Liturgy or service . . . conslgteth of the reciprocal 
acts between God and man. 
Bacon, Advancement of Learning, ii. 878. 
I take your gentle offer, and withal 
Yield love again for love reciprocal. 
Beau, and /'/.. Knight of Burning Pestle, 1. 2. 
The king assured me of a reeiprncal affection to the king 
my master, and of my particular welcome to his court. 
Lord Herbert of Cherbury, Life (ed. Howells), p. 129. 
The liberty of the enemy's fishermen in war has been 
protected by many French ordinances, and the English 
observed a reciprocal indulgence. 
Wooltey, Introd. to Inter. Law, f 170. 
There is much the same relation of reciprocal depen- 
dence between judgment and reasoning a> between con- 
ception and judgment. 
J. Sully, Outlines of Psychol., p. 414. 
3. Having an interchangeable character or re- 
lation ; mutually equivalent or correspondent ; 
concordant; agreeing. 
Knowledge and power are reciprocal. 
Bacon, Physical Fables, x., Eipl., note. 
Sometimes a universal affirming maybe converted saving 
the quantity, to wit when consisting of reciprocal terms : 
as, every man is a rational animal, and therefore every 
rational animal is a man. 
Burgertdiciug, tr. by a Gentleman, I. 32. 
He [the king) must guide the vast and complicated 
machine of government, to the reciprocal advantage of all 
his dominions. A. Hamilton, Works, II. 66. 
Thence came her friends of either sex, and all 
With whom she lived on terms reciprocal. 
Cra&e, Works, V. 51. 
Reciprocal consecution. See consecution. Recipro- 
cal cross, a reciprocal hybrid. 
A reciprocal crofts is a double cross between two species 
or varieties, one form being used in one case as the father 
and in the other case as the mother. 
W. K. Brooks, Law of Heredity, p. 126. 
Reciprocal determinant, diagrams, equation. See 
determinant, diagram, etc. Reciprocal ellipsoid Of 
expansion, see ellipsoid. Reciprocal figures in 
geom., two figures of the same kind (triangles, parallelo- 
grams, prisms, pyramids, etc.) so related that two sides of 
the one form the extremes of an analogy of which the 
means are the two corresponding sides of the other. Re- 
ciprocal functions, hybrids, matrix. See function, etc. 
Reciprocal polars, two curves such that the polar of 
any point on either (with respect to a fixed conic) is a tan- 
gent of the other. Reciprocal pronoun, a pronoun ex- 
pressing mutual or reciprocal relation, such as Greek a\- 
ArjAou'(of each other, of one another). Reciprocal pro- 
portion. See proportion. Reciprocal quantities, in 
math,, those quantities which, multiplied together, pro- 
duce unity. Reciprocal ratio. See ratio. Reciprocal 
screws, a pair of screws so related that a wrench about 
one produces no twist al>ont the other. Given any five 
screws, a screw reciprocal to them all can be found. 
Reciprocal terms, in logic, those terms that have the 
same signification, and consequently are convertible and 
may be used for each other. = Syn. Reciprocal, Mutual. 
There is a theoretical difference between these words, 
although it often is not important. That is mutual which 
is a common act on the part of both persons at the same 
time. Mutual is not properly applicable to physical acts 
or material things, as blows or gifts. Reciprocal means 
that one follows another, being caused by It, with empha- 
sis upon that which is viewed as caused : as, reciprocal 
love or hate. See remarks under mutual as to the propri- 
ety of using mutual for common. 
II. n. 1. That which is reciprocal to another 
thing. 
Iso more 
Ye must be made your own reciprocals 
To your loved city and fair severals 
Of wives and houses. 
Chapman, tr. of Homer's Hymn to Apollo. 
Love is ever rewarded either with the reciprocal, or with 
an Inward or secret contempt Bacon, Love (ed. 1887). 
2. In math., the quotient resulting from the 
division of unity by the quantity of which the 
reciprocate 
quotient is said to be the reciprocal. Thus, the re 
ciprocal of 4 is J. and conversely the reciprocal of } is 4 ; 
the reciprocal of 2 is ^, and that of a -f 3; is I/ (a + x). A 
fraction made by inverting the terms of another fraction 
is called the reciprocal of that other fraction : thus, ? is 
the reciprocal of j. Polar reciprocals. Same as re- 
ciprocal polars. See I. 
reciprocality (re-sip-ro-kal'i-ti), n. [< recipro- 
cal + -iti/.'] The state or character of being 
reciprocal. 
An acknowledged reciprocality in love sanctifies every 
little freedom. Richardtton, Clarissa Harlowe, II. i. 
reciprocally (re-sip'ro-kal-i), flrfr. 1. In a re- 
ciprocal manner; with reciprocating action or 
effect; alternatingly ; interchangeably; corre- 
spondingly. 
The Aristotelians . . . believe water and air to be re- 
ciprocally transmutable. Boyle, Works, n. 342. 
Virtue and sentiment reciprocally assist each other. 
Oddmiith, Cultivation of Taste. 
Faults in the life breed errors in the brain, 
And these reciprocally those again. 
Cowper, Progress of Error, 1. 565. 
2. In a reciprocal ratio or proportion ; inverse- 
ly. Thus, in bodies of the same weight the density is 
reciprocally as the magnitude that Is, the greater the 
magnitude the less in the same proportion the density, 
and the less the magnitude the greater in the same pro- 
portion the density. In geometry two magnitudes are 
said to be reciprocally proportional to two others when 
one of the first pair is to one of the second as the re- 
maining one of the second is to the remaining one of the 
first. 
reciprocalness (re-sip'ro-kal-nes), n. The state 
or character of being reciprocal. 
reciprocant (re-sip'ro-kant), n. [< L. recipro- 
can(t-)n, ppr. of reciprocare, move back and 
forth: see reciprocate.'} 1. The contra variant 
expressing the condition of tangency between 
the primitive quantic and an adjoint linear 
form. 2. A differential invariant ; a function 
of partial differential coefficients of variables 
connected by a single relation, this function be- 
ing such that, if the variables are interchanged 
in cyclical order, it remains unchanged except 
for multiplication by some th root of unity into 
some power of the same root of the continued 
product of the first differential coefficients of 
one of the variables relatively to all the others. 
For an example, see Schtcartzian, n Absolute 
reciprocant, one whose extrinsic factor reduces to unity, 
so that the interchange of variables produces no change 
except multiplication by a root of unity. Binary recip- 
rocant, one having two variables. Characteristic of 
a reciprocant, the root of unity with which it becomes 
multiplied on interchange of the variables. Character 
Of a reciprocant, its kind with respect to it characteris- 
tic. Circular reciprocant, areciprocant which, equated 
to zero, gives the equation of a locus which is its own in- 
verse with respect to every point Degree of a recip- 
rocant, the number of factors (differential coefficients) 
in that term which has the greatest number. Thus, if 
that term is (D^t/)* (Hy)* (D'yX, 'he degree is a + b + e. 
Even reciprocant, one whose characteristic is 1. Ex- 
tent of a reciprocant, the weight of the most advanced 
letter which it contains. Homogeneous reciprocant, 
a reciprocant all the terms of which are of the same de- 
gree in the differential coefficients. Homographic bi- 
nary reciprocant, one which remains unaltered when 
z ana y are changed respectively into (Lx - M) / (x f N) 
and (Vy + Q) / (y + R), where the capitals are con- 
stants. Integrable reciprocant, a reciprocant which, 
equated to zero, gives an equation which can be integrated. 
Isobarlc reciprocant, a reciprocant having the sum 
of the orders of the differential coefficients the same in 
all the terms. Odd reciprocant, one whose character- 
istic is not 1. Orthogonal reciprocant, one which re- 
mains unchanged by an orthogonal transformation of the 
variables. Type of a reciprocant, the combination of 
its character, weight, degree, and extent Weight Of a 
reciprocant, the sum of the orders, each diminished by 
two, of the factors (differential coefficients) of the term 
having the greatest weight. Thus, if that term is (0^)^ 
(DJ)* (DyX (PJvK the weight is a + e -I 2d. 
reciprocantiye (re-sip'rp-kan-tiv), a. [< re- 
ciprocant + -ire.] Pertaining to a reciprocant. 
reciprocate (re-sip'ro-kat), r. ; pret. and pp. 
reciprocated, ppr. reciprocating. [< L. recipf o- 
catint, pp. of reciprocare, move back and forth, 
reverse (> It. reciprocare = Sp. Pg. reciprocar 
= F. rfciproquer, reciprocate, interchange), < 
reciprocus, reciprocal: see reciprocal.'] I. trans. 
1 . To cause to move back and forth ; give an 
alternating motion to. 
The sleeve Is reciprocated from a rock shaft journaled 
in the lower aligning ends of the main frame. 
Sci. Amer., N. S., LXII. 7r>. 
2. To give and return mutually; yield or per- 
form each to each; interchange: as, to recip- 
rocate favors. 
For 'tis a union that bespeaks 
Reciprocated duties. 
Cowper, Friendship, 1. 48. 
At night men crowd the close little caffe, where they re- 
ciprocate smoke, respiration, and animal heat. 
Hoteells, Venetian Life, iii. 
3. To give or do in response ; yield a return of; 
requite correspondingly. 
