residual 
the calculus of residuals or residues. See II. Residual 
charge, a charge of electricity spontaneously acquired by 
coated glass, or any other coated dielectric arranged as a 
condenser after a discharge, apparently owing to the slow 
return to the surface of that part of the original charge 
which hail penetrated within the dielectric, as in the Ley- 
den jar. (Faraday.) In such cases there is said to be elec- 
tric absorption. It is doubtless due to the fact that the 
solid dielectric does not immediately recover from the 
strain resulting from the electric stress. Also called di- 
electric after-wor/ting. Residual estate, residuary es- 
tate. Residual figure, in geom., the figure remaining 
after subtracting aless from a greater. Residual mag- 
netism. See magnetism. Residual quantity, in alff., 
a binomial connected by the sign (minus) : thus, a b, 
a V b are residual quantities. 
II. it. 1. A remainder; especially, the re- 
mainder of an observed quantity, after sub- 
tracting so much as can be accounted for in 
a given way. 2. The integral of a function 
round a closed contour in the plane of imagi- 
nary quantity inclosing a value for which the 
function becomes infinite, this integral being 
divided by 2m. An earlier definition, amounting to 
the same thing, was the coefficient of x 1 in the develop- 
ment of the function a in a sum of two series, one ac- 
cording to ascending, the other according to descending 
powers of x. If the oval includes only one value for which 
the function becomes infinite, the residual is said to be 
taken for or with respect to that value. Also residue. 
3. A system of points which, together with an- 
other system of points of which it is said to be 
the residual, makes up all the intersections of 
a given curve with a plane cubic curve Inte- 
gral residual the residual obtained by extending the in- 
tegration round a contour including several values of the 
variable for which the function becomes infinite. Total 
residual, the residual obtained by integrating round a 
contour including all the values of the variable for which 
the function becomes infinite. Also called principal re- 
sidual. 
residuary (re-zid'u-a-ri), a. [= F. residuuirc, 
< NL. 'residuarius, t. L. residuum, residue : see 
residuum, residue.] Of or pertaining to a resi- 
due or residuum ; forming a residue, or part not 
dealt with : as, residuary estate (the portion of 
a testator's estate not devised specially). 
"Tis enough to lose the legacy, or the residuary advan- 
tage of the estate left him by the deceased. 
Ayliffe, Parergon. 
Residuary clause, that part of a will which in general 
language gives whatever may be left after satisfying the 
other provisions of the will. Residuary devisee or 
legatee, in law, the legatee to whom is bequeathed the 
residuum. Residuary gum, the dark residuary matter 
from the treatment of oils and fats in the manufacture of 
stearin, used in coating fabrics for the manufacture of 
roofing. Residuary legacy. See legacy. 
residuate (re-zid'u-at), v. t. ; pret. and pp. re- 
siduated, ppr'. residuating. [< residu(al) + -ate 2 .] 
In math., to find the residual of, in the sense of 
the quotient of 2m into the integral round one 
or more poles. 
residuation (re-zid-u-a'shon), n. [< residuals 
+ -ion.] In math., the act of finding the resid- 
ual or integral round a pole divided by SJTJ ; the 
process of finding residuals and co-residuals 
upon a cubic curve by linear constructions. 
Sign Of residuation, the sign V prefixed to the expres- 
sion of a function to denote the residual. The rules for 
the use of this sign are not entirely consistent. 
residue (rez'i-du), n. [Early mod. E. also rest- 
dew ; < ME. residue, < OF. residu, F. residu = Sp. 
Pg. It. residuo,<li. residuum, a remainder, neut. 
of residuus, remaining, < residere, remain, re- 
side: see reside. Doublet of residuum.'] 1. 
That which remains after a part is taken, sepa- 
rated, removed, or dealt with in some other 
way; what is left over; remainder; the rest. 
John for his charge taking Asia, and so the residue 
other quarters to labour in. Hooker, Eccles. Polity, vii. 4. 
The residue of your fortune 
Go to my cave and tell me. 
Shak., As you Like it, ii. 7. 196. 
2. In law: (a) The residuum of a testator's 
estate after payment of debts and legacies. 
(6) That which remains of a testator's estate 
after payment of debts and particular lega- 
cies, and is undisposed of except it may be by 
a general clause or residuary legacy. 3, In 
the theory of numbers, the remainder after 
division, especially after division by a fixed 
modulus; in the integral calculus, the integral 
of a monodromic function taken round a pole 
or poles : same as residual, 2 Biquadratic resi- 
due, the same as a cubic residue, except that it refers to 
a fourth power instead of to a cube. Thus, any fourth 
power of an integer divided by5 gives as remainder either 
or 1. These arc, therefore, the biquadratic residues of 5. 
Cubic residue, a number which, being added to a 
multiple of a number of which it is said to be a residue, 
gives a cube. Thus, every exact cube divided by 7 gives 
as remainder either 0, 1, or 6. These are, therefore, the 
cubic residues of 7. Method of residues. See method. 
Quadratic residue. See quadratic. Trigonal resi- 
due, a number which, added to a multiple of another num- 
ber of which it is said to be a residue, will give a trigonal 
number. Thus, 1,3, 6, 10, 2, 8, are the trigonal residues 
of 13. = Syn. 1. Kent, etc. See remainder. 
residuent (re-zid'u-ent), n. [< residit(um) + 
-ent.] In chemical processes, a by-product, or 
waste product, left after the removal or sepa- 
ration of a principal product. 
residuous (re-zid'u-us), a. [< L. residuus, re- 
maining, residual: see residue, residuum.] Re- 
maining; residual. Landor. [Rare.] 
residuum (re-zid'u-um), n. [< L. residuum, 
what remains: see residue. Doublet of resi- 
due.] 1. That which is left after any process ; 
that which remains ; a residue. 
The metal [copper] is pronounced to be chemically pure, 
leaving no residuum when dissolved in pure nitric acid. 
W. F. Roe, Newfoundland to Manitoba, vi. 
Residuum shall be understood to be the refuse from 
the distillation of Crude Petroleum, free from coke and 
water, and from any foreign impurities, and of gravity 
from 16 to 21 Beaume. 
New York Produce Exchange Report (1888-9X p. 279. 
2. Specifically, in law, that part of an estate 
which is left after the payment of charges, 
debts, and particular bequests ; more strictly, 
the part so left which is effectively disposed 
of by a residuary clause. Sometimes the subject of 
a particular bequest which proves ineffectual passes by 
law to the heir or next of kin, instead of falling into the 
residuum. 
resign 1 (re-zin'), v. [< ME. resignen, resynen, < 
OF. resiner, resigner, F. resigner (> G. resignie- 
ren = Dan. resignere = Sw. resignera) = Pr. Sp. 
Pg. resignar = It. risegnare, rassegnare, < L. re- 
signare, unseal, annul, assign back, resign, lit. 
' sign back or again,' < re-, back, + signare, sign : 
seesign.] I. trans. 1. To assign back ; return 
formally ; give up ; give back, as an office or a 
commission, to the person or authority that con- 
ferred it ; hence, to surrender; relinquish ; give 
over; renounce. 
As yow [Love] list, ye maken hertes digne ; 
Algates hem that ye wol sette a fyre, 
They dreden shame and vices they resigne. 
Chaucer, Troilus, iii. 26. 
He [More] had resigned up his office, and the King had 
graciously accepted it. 
Family of Sir T. More, Int, to Utopia, p. xv. 
The Earl of Worcester 
Hath broke his staff, resign'd his stewardship. 
Shak., Rich. II., ii. 2. 59. 
What sinners value I resign; 
Lord ! 'tis enough that thou art mine. Watts. 
2. To withdraw, as a claim; give up; aban- 
don. 
Soon resigned his former suit. Spenser. 
Passionate hopes not ill resign'd 
For quiet, and a fearless mind ! 
31. Arnold, Resignation. 
3. To yield or give up in a confiding or trusting 
spirit; submit, particularly to Providence. 
What more reasonable than that we should in all things 
resign up ourselves to the will of God ? Tillotson. 
Then to the sleep I crave 
Resign me. Bryant, A Sick-bed. 
4. To submit without resistance ; yield ; com- 
mit. 
Be that thou hop'st to be, or what thou art 
Resign to death. Shak., 2 Hen. VI., iii. 1. 334. 
He, cruel and ungrateful, smil'd 
When she resign'd her Breath. 
Prior, The Viceroy, st. 32. 
/Knriis heard, and for a space resign'd 
To tender pity all his manly mind. 
Pope, Iliad, xiii. 590. 
5f. To intrust; consign; commit to the care of. 
Gentlemen of quality have been sent beyond the seas, 
resigned and concredited to the conduct of such as they 
call governors. Evelyn. 
= Syn. 1. To abandon, renounce, abdicate. Resign dif- 
fers from the words compared under forsake in expressing 
primarily a formal ahd deliberate act, in being the ordi- 
nary word for giving up formally an elective office or an 
appointment, and in having similar figurative use. 
II. intrans. 1. To submit one's self; yield; 
endure with resignation. 
O break, my heart ! poor bankrupt, break at once ! . . . 
Vile earth, to earth resign; end motion here. 
Shak., R. and J., iii. 2. 59. 
Amazed, confused, he found his power expired, 
Resign'd to fate, and with a sigh retired. 
Pope, R. of the L., iii. 146. 
2. To give up an office, commission, post, or 
the like. 
resign 1 t (re-zin'), n. [< resign 1 , v.] Resigna- 
tion. 
You have gain'd more in a royal brother 
Than you could lose by your resign of Empire. 
Shirley (and Fletcher ?), Coronation, IT. 2. 
resign 2 (re-sin'), r. 1. [< re- + sign.] To sign 
again. 
resignalt (re-zi'nal), n. [< resign! + -al] Res- 
ignation. 
resilient 
A bold and just challenge of an old Judge [Samuel] 
made before all the people upon his resignal of the gov- 
ernment into the hands of a new King. 
Sanderson, Works, II. 330. (Dames.) 
resignant (rez'ig-nant), a. [< F. resignant, ppr. 
of resigner, resign: see resign 1 .] In her., con- 
cealed : said of a lion's tail. 
resignantt (re-zi'nant), n. [< OF. resignant (= 
Sp. Pg. resignante), a resigner, ppr. of resigner, 
resign: see resign 1 .] A resigner. 
Upon the 25th of October Sir John Suckling brought 
the warrant from the King to receive the Seal ; and the 
good news came together, very welcome to the resignant, 
that Sir Thomas Coventry should have that honour. 
Bp. Hacket, Abp. Williams, ii. 27. (Dames.) 
resignation (rez-ig-na'shqn), n. [< OF. resi- 
gnation, resignacion, F. resignation = Pr. resi- 
gnatio = Sp. resignacion = Pg. resignaqao = It. 
rassegnazione, risegnazione, < ML. (?) resigna- 
tio(n-), < L. resignare, resign: see resign 1 .] 1. 
The act of resigning or giving up, as a claim, 
office, place, or possession. 
The resignation of thy state and crown 
To Henry Bolingbroke. 
Shak., Rich. II., iv. 1. 179. 
2. The state of being resigned or submissive ; 
unresisting acquiescence; particularly, quiet 
submission to the will of Providence; con- 
tented submission. 
But on he moves to meet his latter end, . . . 
Sinks to the grave with unperceiv'd decay, 
While resignation gently slopes the way. 
Goldsmith, Des. Vil., 1. 110. 
3. In Scots law, the form by which a vassal re- 
turns the feu into the hands of a superior. 
= Syn.l. Relinquishment, renunciation. 2. Endurance, 
Fortitude, etc. See patience. 
resigned (re-zmd'), j>. a. 1. Surrendered; 
given up. 2. Feeling resignation; submis- 
sive. 
What shall I do (she cried), my peace of mind 
To gain in dying, and to die resign'd > 
Crabbe, Works, I. 112. 
= Syn. 2. Unresisting, yielding, uncomplaining, meek. 
See patience. 
resignedly (re-zi'ned-li), adv. With resigna- 
tion; submissively. 
resignee (re-zl-ne'), n. [< F. resigne, pp. of re- 
signer, resign: see resign 1 .] In law, the party 
to whom a thing is resigned, 
resigner (re-zl'ner), n. One who resigns. 
resignment(re-zin'ment),n. [(resign 1 + -ment.] 
The act of resigning. 
Here I am, by his command, to cure you, 
Nay, more, for ever, by his full resignment. 
Beau, and Fl., Mons. Thomas, iii. 1. 
resile (re-zil'), v. i.; pret. and pp. resiled, ppr. 
resiling. [< OF. resilir, resiler, F. resilier, < L. 
resilire, jump back, recoil, < re-, back, + salire, 
jump, leap: see salient, and cf. resilient.] To 
start back; recede, as from a purpose; recoil. 
If the Queue wold herafter resile and goo back from 
hat she semeth nowe to be 
be in her power soo to doo. 
that she semeth nowe to be contented with, it shuld not 
1 goo 
ith, i 
State Papers, I. 343. (Halliwell.) 
The small majority . . . resiling from their own pre- 
viously professed intention. Sir W. Hamilton. 
resilement (re-zll'ment), n. [< resile + -ment.] 
The act of drawing back ; a recoil ; a withdrawal. 
Imp. Diet., art. "back," adv., 7. 
resilience (re-zil'i-ens), n. [= It. resilienza; 
as resilien(t)' + -ce.] 1. The act of resiling, 
leaping, or springing back ; the act of rebound- 
ing. 
If you strike a ball side-long, not full upon the surface, 
the rebound will be as much the contrary way ; whether 
there be any such resilience in ecchos . . . may be tried. 
Bacon, Nat. Hist., 246. 
2. In mach. See the quotation. 
The word resilience, used without special qualifications, 
may be understood as meaning extreme resilience, or the 
work given back by the spring after being strained to the 
extreme limit within which it can be strained again and 
again without breaking or taking a permanent set. 
Thomson and Tail, Nat. Phil., 691, b. 
Coefficient of resilience. Same as coefficient of elasticity 
(which see, under coefficient). 
resiliency (re-zil'i-en-si), n. [As resilience (see 
-cy).] Same as resilience. 
The common resiliency of the mind from one extreme 
to the other. Johnson, Rambler, No. 110. 
resilient (re-zil'i-ent), a. [< L. resilien(t-)s, ppr. 
of resilire, leap back: see resile.] Having re- 
silience f inclined to leap or spring back ; leap- 
ing or springing back ; rebounding. 
Their act and reach 
Stretch'd to the farthest is resilient ever, 
And in resilience hath its plenary force. 
Sir H. Taylor, Edwin the Fair, iii. 5. 
A highly resilient body is a body which has large co- 
efficients of resilience. Steel is an example of a body with 
large, and cork of a body with small, coefficients of resili- 
ence. J. D. Everett, Units and Phys. Const., p. 46. 
