involucrum 
involve.'] 1. In soiil., a kind of sheath or involu- 
cre about the bases of the thread-cells of aca- 
lephs. 2. In bot.: (a) Same as involucre, (b) 
Same as velum. Persoon. 
involuntarily (in-vol'un-ta-ri-li), adv. In an 
involuntary manner; not spontaneously ; with- 
out one's will. 
involuntarineSS (in-vol'un-ta-ri-nes), n. The 
quality of being involuntary. 
involuntary (in-vol'un-ta-ri), a. [= P. invo- 
lontaire = Sp. Pg. involuntario, < LL. involun- 
tarius, unwilling, < L. in- priv. + voluntaries, 
willing: see voluntary.'] 1. Not voluntary or 
willing; contrary or opposed to will or desire ; 
unwilling; unintentional: as, involuntary sub- 
mission; an involuntary listener. 
The gathering number, as it moves along, 
Involves a vast involuntary throng. 
Pope, Dunciad, iv. 82. 
2. Not voluntary or willed; independent of vo- 
lition or consenting action of the mind ; with- 
out the agency of the will : as, involuntary mus- 
cular action ; an involuntary groan. 
This at least I think evident, that we find in ourselves 
a power to begin or forbear, continue or end several ac- 
tions of our minds, and motions of our bodies, barely by 
a thought or preference of the mind ordering, or, as it 
were, commanding the doing or not doing such or such a 
particular action. . . . The forbearance of that action, 
consequent to such order or command of the mind, is 
called voluntary ; and whatsoever action is performed 
without such a thought of the mind is called involuntary. 
Locke. 
Steals down my cheek the involuntary tear. 
Pope, Imit. of Horace, IV. i. 38. 
Involuntary action. See action, i (b). involuntary 
bankruptcy. See bankruptcy. Involuntary escape. 
See escape, 3. 
involuntomotory (in-voFun-to-mo'to-ri), . [< 
involunt(ary) + motory.] Having or pertain- 
ing to motor influence or effect which is not 
subject to the will, as the involuntary muscu- 
lar action of the heart, intestines, etc. : specifi- 
cally applied by Remak to that one of the four 
germ-layers of the embryo which corresponds 
to the splanchnopleure of other writers. This is 
the inner division of the mesoblast, distinguished from the 
voluntomotory or somatopleural division. 
The inoolunto-motory, corresponding to the visceral wall 
or splanchno-pleure. Ericyc. Brit., VIII. 167. 
involutant (in-vo-lu'tant), n. [< involute + 
-ant.'] In math.,'the topical resultant of the 
powers and products of powers of two ma- 
trices of the same order. 
involute (in'vo-lut), a. and n. [= OF. involu 
= It. involutoj < L. involutus, pp. of involvere, 
roll up, wrap up: see 
involve.'] i, a. 1. 
Rolled up ; wrapped 
up. Specifically (a) 
In bot., rolled inward 
from the edge or edges : 
said of leaves in verna- 
tion, of the petals of 
flowers in estivation, and 
of the margin of the cup 
in the Discomycetes, etc. 
Also involutive. (b) In 
conch. , having the whorls 
closely wound round the 
axis, and nearly or en- 
tirely concealing it, as 
the shells of Cyprceidce, 
Olividce, etc. Also in- 
volved, (c) In entom., 
lute leaves; 2, outline of transverse curved Spirally, as the 
section of an involute leaf. antennte of certain By- 
menoptera. 
2. Involved; confusedly mingled. [Rare.] 
The style is so involute that one cannot help fancying 
it must be falsely constructed. Poe, Marginalia, cxvii. 
II. 11. 1. That which is involved. [Rare.] 
Far more of our deepest thoughts and feelings pass to 
us through perplexed combinations of concrete objects, 
pass to us as involutes (if I may coin that word) in com- 
pound experiences incapable of being disentangled, than 
ever reach us directly, and in their own abstract shapes. 
De Quincey, Autobiog. Sketches, i. 
2. In geom., the curve traced by any point of 
a flexible and inextensible string when the lat- 
ter is unwrapped, under tension, from a given 
curve ; or, in other words, the locus of a point 
in a right line which 
rolls, without slid- 
ing, over a given 
curve. The curve by 
unwrapping which a se- 
ries of involutes is ob- 
tained is said to be their 
common evolute, and 
any two involutes of a 
curve constitute a pair 
of parallel curves, their 
corresponding tangents 
being parallel, and their corresponding points, situated on 
the same normal, being at a constant distance from one 
another. 
. Branch of Poplar, sho' 
Involute of a Circle. 
3176 
involuted (in'vo-lu-ted), n. Same as involute. 
involution (in-vo-lu'shon), n. [= P. Involution 
= Pr. encolueio '= It. involuzione, < LL. involu- 
tio(n-), a rolling up, < L. involvere, pp. involutus, 
roll up: see involve.'] 1. The act of involving, 
infolding, or inwrapping ; a rolling or folding 
in or round. 
Gloom that sought to strengthen itself by tenfold in- 
volution in the night of solitary woods. 
De Quincey, Secret Societies, i. 
2. The state of being entangled or involved; 
complication. 
The faculty to be trained is the judgment, the practical 
judgment at work among matters in which its possessor 
is deeply interested, not from the desire of Truth only, but 
from his own involution in the matters of which he is to 
judge. Stubbs, Medieval and Modern Hist, p. 17. 
3. Something involved or entangled; a com- 
plication. 
Such the clue 
Of Cretan Ariadne ne'er explain'd ! 
Hooks ! angles ! crooks ! and involutions wild ! 
Shenstone, Economy, iii. 
4f. A membranous covering or envelop ; an in- 
volucre. 
Great conceits are raised of the involution or membra- 
nous covering, commonly called the silly-how, that some- 
times is found about the heads of children. 
Sir T. Browne, Vulg. Err., v. 23. 
5. In gram., complicated construction ; the 
lengthening out of a sentence by the insertion 
of member within member; the separation of 
the subject from its predicate by the interjec- 
tion of matter that should follow the verb or 
be placed in another sentence. 
The long involutions of Latin periods. Lowell. 
6. In math.: (a) The multiplication of a quan- 
tity into itself any number of times, so as to 
produce a positive integral power of that quan- 
tity. Thus, the operation by which the third power of 5 
is found, namely, the multiplication of 5 by itself, making 
25, and of the product by 5 again, making 125, is involu- 
tion. In this sense involution is opposed to evolution, 3 (b). 
(b) The raising of a quantity to any power, 
positive, negative, fractional, or imaginary. In 
this sense involution includes evolution as a par- 
ticular case, (c) Aunidimensional continuous 
series of elements (such as the points of a line), 
considered as having a definite one-to-one cor- 
respondence with themselves, such that infi- 
nitely neighboring elements correspond to in- 
finitely neighboring elements, and such that if 
A corresponds to B, then B corresponds to A : 
in other words, the elements are associated in 
conjugate pairs, so that any pair of conjugate 
elements may by a continuous motion come 
into coincidence with any other without ceas- 
ing, at any stage of the motion, to be conjugate. 
This is the usual meaning of involution in geometry ; it 
dates from Desargues (1639). There are either two real 
sibi-conjugate or self-corresponding elements in an invo- 
lution, when it is called a hyperbolic involution; or there 
are none, when it is called an elliptic involution. If U = 
0, V = 0, W = are three quadratic equations determin- 
ing three pairs of points in an involution, then these three 
equations are in a syzygy At! + nV + cW = 0; or if the 
three equations are ax% + bxy + cy% = 0, a'x'2 + b'xy 
+ c'i/2 = o, a"x% + V'xy + c"y% 0, then the syzygy may 
be thus written : 
a b c 
a', V, c' 
a", b", c" 
The six elements are said to be an involution of six, or, if 
one or two of them are sibi-conjugate, an involution of five 
or of four elements. If the points of a line in a plane are 
in involution, let any conic (or degenerate conic) be drawn 
through any pair of conjugate points, and another conic 
through any other pair ; then any conic through the four 
intersections of these conies will cut the line in a pair of 
conjugate points. That point of an involution which cor- 
responds to the point at infinity is termed the center of the 
involution, (rf) Any series of pairs of loci repre- 
sented by an equation All + /tV = 0, where A 
and /i are numerical constants for each locus, 
and U = and V = are equations to two loci of 
the same order, (e) Anyunidimensional contin- 
uum of elements associated in sets of any con- 
stant number by a continuous law. According 
as there are two, three, four, etc., in each set, 
the involution is said to be quadratic, cubic, 
quartic (or biquadratic), etc. (/) The implica- 
tion of a relation in a system of other relations. 
Cayley, On Abstract Geometry, 29. 7. In 
physiol., the resorption which organs undergo 
after enlargement or distention: as, the involu- 
tion of the uterus, which is thus restored to its 
normal size after pregnancy Center of an invo- 
lution. Seecenteri. Elliptic involution. Sen elliptic. 
Involution of six screws, a system of six screws con- 
ferring only nve degrees of freedom on a rigid body. Me- 
chanical involution, a relation between a series of pairs 
of lines such that, taking any three pairs, forces may be 
made to act along them whose statical sum is zero. The 
involution of notions, in Ionic, the relation of a notion 
to another whose depth it includes. 
0. 
invulnerable 
involutive (in'vo-lu-tiv), a. l< involute + -we.'] 
In hot., same as involute, I (a). 
involutorial (in"vo-lu-to'ri-al), a. [< involute 
+ -ory + -al.~] Of tile nature of geometrical 
involution; connecting a system of objects in 
pairs Involutorial homology, a homology whose pa- 
rameter is 1. Involutorial relation, a relation be- 
tween two variables, x and y, such that y = Fx and x = y : 
a term introduced by Siebeck. 
involve (in-volv'), v. t. ; pret. and pp. involved, 
ppr. involving. [< OF. involver = Sp. envoluer 
= Pg. involver = It. involvere, < L. involvere, roll 
in, roll up, wrap up, < in, in, on, + volvere, roll : 
see volute. Cf. convolve, devolve, evolve, revolve.] 
1 . To roll or fold in or wrap up so as to con- 
ceal; envelop on all sides; cover completely; 
infold ; specifically, in zool. , to encircle com- 
pletely : as, a mark involving a joint ; wings in- 
volving the body. 
If it [the sun] should, but one Day, cease to shine, 
Th' vnpurged Aire to Water would resolue, 
And Water would the mountain tops involve. 
Sylvester, tr. of Du Bartas's Weeks, i. 4. 
A rolling cloud 
Involv'd the mount ; the thunder roar'd aloud. 
Pope, Iliad, xvii. 671. 
The further history of this neglected plantation is in- 
volved in gloomy uncertainty. Bancroft, Hist. U. S. , I. 85. 
2. To entwine ; entangle ; implicate ; bring into 
entanglement or complication, literally or figur- 
atively: as, an involved problem; to involve a 
nation in war ; to be involved in debt. 
Judgement rashly giv'n ofttimes involves the Judge him- 
self. Milton, Eikonoklastes, xii. 
Some of serpent kind, 
Wondrous in length and corpulence, involved 
Their snaky folds. Milton, P. L., vii. 433. 
Fearing that our stay till the very excessive heats were 
past might involve us in another difficulty, that of miss- 
ing the Etesian winds. Bruce, Source of the Nile, I. 43. 
We seem to have certain direct perceptions, and to at- 
tain to others by a more or less involved process of reason- 
ing. Alivart, Nature and Thought, p. 12. 
3. To bring into a common relation or connec- 
tion ; hence, to include as a necessary or logical 
consequence; imply; comprise. 
The welfare of each is daily more involved in the welfare 
of all. H. Spencer, Social Statics, p. 483. 
A knowledge of the entire history of a particle is shown 
to be involved in a complete knowledge of its state at any 
moment. W . K. Clifford, Lectures, I. S. 
All kinds of mental work involve attention. 
J. Sully, Outlines of Psychol., p. 13. 
4. In arith. and alg., to raise to any assigned 
power; multiply, as a quantity, into itself a 
given number of times: as, a quantity involved 
to the third or fourth power. =Syn. 2. Entanyle, etc. 
(see implicate) ; twine, intertwine, interweave, interlace. 
3. Imply, Involve (see imply); embrace, contain. 
involved (in-volvd'),j*. . 1. In. couch., same 
as involute, 1 (6). 2. In her., same as enveloped. 
involvedness (in-vol'ved-nes), n. The state of 
being involved; involvement. [Rare.] 
But how shall the mind of man . . . extricate itself 
out of this comprisure and involvedness in the bodies, pas- 
sions, and infirmities? 
W. Montague, Devonte Essays, II. x. 1. 
involvement (in-volv'ment), H. [< involve + 
-ment.] The act of involving, or the state of be- 
ing involved or implicated; entanglement: as, 
involvement in debt, or in intrigues. 
The spectators were shivering at the Athenian's mishap, 
and the Sidonian, Byzantine, and Corinthian were striving, 
with such skill as they possessed, to avoid involvement in 
the ruin. L. Wallace, Ben-Hur, p. 363. 
invulgart (in-vul'gar), v. t. [< iw- 2 + vulgar.'] 
To cause to become vulgar or common. 
It did so much invile the estimate 
Of th' open'd and invulgar'd mysteries. 
Daniel, Musophilus. 
invulgart (in-vul'gar), a. [< in-3 + vulgar.] 
Not vulgar; refined. 
Judg'd the sad parents this lost infant ow'd 
Were as invulgar as their fruit was fair. 
Drayton, Moses, i. 
invulnerability (in-vul"ne-ra-biri-ti), n. [= 
P. invulnerabilite =: Sp. inviilnerabilidad = It. in- 
vulnerabilita ; as invulnera ble + -ity : see -bility .] 
The quality or state of being invulnerable. 
invulnerable (in-vul'ne-ra-bl), a. [= P. invul- 
nerable = Sp. invulnerable = Pg. iiivulneravel = 
It. invulnerabile, < L. invulnerabilis, invulner- 
able, < in- priv. + (LL.) vulnerabilis, vulnera- 
ble: see vulnerable.'] 1. Not vulnerable; in- 
capable of being wounded, hurt, or harmed. 
Achilles is not quite inwdnpra ble ; the sacred waters 
did not wash the heel by which Thetis held him. 
Emerson, Compensation. 
Hence 2. Not to be damaged or injuriously 
affected by attack: as, invulnerable arguments 
or evidence. 
