derivation 
tangent at the first point cuts the curve, (c) 
The operation of passing from any function to 
any related function which may in the context 
be termed its derivative. The word derivation, in 
its first mathematical sense, was invented by Lagrange, 
who thought it possible to develop the calculus without 
the use of infinitesimals. 
5. In biol., descent with modification of an or- 
ganism from antecedent organisms ; evolution : 
as, the derivation of man ; the doctrine of deriva- 
tion that is, the derivative theory (which see, 
under derivative). 
According to the doctrine of derivation, the more com- 
plex plants and animals are the slowly modified descen- 
dants of less complex plants and animals, and these in turn 
were the slowly modified descendants of still less complex 
plants and animals, and so on until we converge to those 
primitive organisms which are not definable either as ani- 
mal or as vegetal, but which in their lowest forms are 
mere shreds of jelly-like protoplasm. 
J. Fiske, Cosmic Philos., I. 442. 
6. In gun., the peculiar constant deviation of 
an elongated projectile f rom a rifled gun, due to 
its angular rotation about its longer axis and 
to the resistance of the air. Sometimes called 
drift. 7. The thing derived or deduced; a de- 
rivative; a deduction. [Kare or obsolete.] 
Most of them are the genuine derivations of the hypothe- 
sis they lay claim to. Glanmlle. 
Arbogast's calculus of derivations [named for the 
French analyst L. F. A. Arboyast, 1769-1803], a method 
of expanding and otherwise dealing with functions of 
functions expressible as series in ascending powers of one 
or more variables. 
derivational (der-i-va'shpn-al), . [< deriva- 
tion + -al.~] Relating to derivation. 
derivationist (der-i-va'shon-ist), n. [< deriva- 
tion + -ist.~\ Same as denvatist. 
We have sometimes in the preceding pages used the 
words evolutionist or derivationist. 
Le Conte, Pop. Scl. Mo., XXXII. 311. 
derivatist (de-riv'a-tist), n. [< derivative + 
-ist.] A believer in the doctrine of derivation 
or evolution; an evolutionist. [Bare.] 
The doctrine of evolution of organic types is sometimes 
appropriately called the doctrine of derivation, and its 
supporters derivatists. 
E. D. Cope, Origin of the Fittest, p. 21J. 
derivative (de-riv'a-tiv), a. and n. [= F. deri- 
vatif= Sp. Pg. It. 'derivativo, < LL. derivative, 
derivative (in grammatical sense), < L. derivare, 
derive: see derive.'] I. a. 1. Derived; taken or 
having proceeded from another or something 
preceding; secondary: as, a derivative word; 
a derivative conveyance. 
As it is a derivative perfection, so it is a distinct kind of 
perfection from that which is in God. Sir M. Hale. 
Exclusive sovereignty of ownership of the soil is a de- 
rivative right. Story, Salem, Sept. 18, 1828. 
Making the authority of law derivative, and not original. 
H. Spencer, Data of Ethics, 19. 
2. In biol. , relating to derivation, or to the doc- 
trine of derivation : as, the derivative theory. 
8. In med., having a tendency to lessen in- 
flammation or reduce a morbid process. 
It [a hot-air bath] is stimulating, derivative, depurative. 
Encyc. Brit., XII. 644. 
Derivative certainty. See certainty. Derivative 
character. See character. Derivative chord, in mu- 
sic, a chord derived from a fundamental chord ; specifi- 
cally, a chord derived from 
another by inversion ; an in- 
version. Derivative convey- 
ance. See conveyance. De- 
rivative function, in math., a 
function expressing the rate of 
change of the value of another 
function relatively to that of the variable. Derivative 
theory, in biol., the view that species change in the 
course of time by virtue of their inherent tendencies, not 
by natural selection. 
II. n. 1. In med., a therapeutic method or 
agent employed to lessen a morbid process in 
one part by producing a flow of blood or lymph 
to another part, as cupping, leeching, blisters, 
catharsis, etc. 2. That which is derived; that 
which is deduced or comes by derivation from 
another. 
For honour, 
Tis a derivative from me to mine. 
Shak., W. T.,iii. 2. 
Specifically 3. A word derived or formed 
either immediately from another, or remotely 
from a primitive or root: thus, 'verb,' 'verbal,' 
'verbose' are derivatives of the Latin verbum; 
'duke,' 'duct,' 'adduce,' 'conduce,' 'conduct,' 
'conduit,' etc., are derivatives of the Latin du- 
cere; 'feeder' is a derivative of 'feed,' and 
' feed ' a derivative of ' food.' See derivation, 3. 
4. In music : (a) The root or generator from 
which a chord is derived. (6) Same as derivative 
chord (which see, above). 5. In math. : (a) A 
derivative function; a differential coefficient. 
(6) The slope of a scalar function; a vector 
imental and Deriv; 
tive Chords. 
1552 
function whose direction is that of most rapid 
increase of a scalar function (of which it is said 
to be the derivative), and whose magnitude is 
equal to the increase in this direction of the 
scalar function per unit of distance, (e) More 
generally, any function derived from another. 
Derivative of a manifold of points, the aggregate 
of all points having a number of points of the manifold 
greater than any assignable number within any assign- 
ed distance, however small. Rational derivative of a 
point on a plane cubic curve, a point whose trilinear co- 
ordinates are rational integral functions of those of the 
former point. Schwartzian derivative of any func- 
tion // of x, the function 
C_! l^LV' 
tf 2\y'l 
where the accents signify differentiations relative to X. 
derivatively (de-riv'a-tiv-li), adv. In a deriva- 
tive manner ; by derivation. 
The character which essentially and inherently belongs 
only to him [Christ] will derivatively belong to them [his 
disciples] also. Home, On Ps. xv. 
derivativeness (de-riv'a-tiv-nes), n. The state 
of being derivative. Imp. Diet. 
derive (de-riv'), v. ; pret. and pp. derived, ppr. 
deriving. ' [< ME. deriven, < OF. deriver, F. de- 
river = Sp. Pg. derivar = It. derivare = G. de- 
riviren = Dan. derivere = Sw. derivera, < L. de- 
rivare, lead, turn, or draw off (a liquid), draw 
off, derive (one word from another, in last 
sense for earlier ducere), < de, away, + rivus, a 
stream : see rival.'] I. trans. If. To turn aside 
or divert, as wateror other fluid, from its natural 
course or channel : as, to derive water from the 
main channel or current into lateral rivulets. 
The solemn and right manner of deriving the water. 
Uolland, tr. of Livy, p. 190. 
The whole pond is very great; but that part of It which 
is derived towards this font is but little. 
Coryat, Crudities, I. 36. 
2f. Figuratively, to turn aside ; divert. 
And her dew loves deryv'd to that vile witches shayre. 
Spenser, F. Q., I. iii. 2. 
That saving grace which Christ originally is or hath for 
the general good of his whole Church, by sacraments he 
severally deriveth into every member thereof. 
Hooker, Eccles. Polity, v. 67. 
The Siamites are the sinke of the Easterne Superstitions, 
which they deriue to many Nations. 
Purchas, Pilgrimage, p. 460. 
If we take care that the sickness of the body derive not 
' itself into the soul, nor the pains of one procure impa- 
tience of the other, we shall alleviate the burden. 
Jei: Taylor, Works (ed. 1836), I. 332. 
3. To draw or receive, as from a source or ori- 
gin, or by regular transmission: as, to derive 
ideas from the senses; to derive instruction 
from a book ; his estate is derived from his an- 
cestors. 
For by my mother I derived am 
From Lionel duke of Clarence. 
Shall., 1 Hen. VI., 11. 6. 
Elizabeth clearly discerned the advantages which were to 
be derived from a close connection between the monarchy 
and the priesthood. Macaulay, Hallam's Const. Hist. 
It is from Home and Germany that we derive our do- 
mestic law. W. E. Hearn, Aryan Household, p. 186. 
Specifically 4. To draw or receive (a word) 
from a more original root or stem : as, the word 
'rule' is derived from the Latin; 'feed' is de- 
rived from 'food.' See derivation, 3. 5. To 
deduce, as from premises; trace, as from a 
source or origin: involving a personal subject. 
A sound mind will derive its principles from insight. 
Emerson, Society and Solitude. 
These men derive all religion from myths. 
Dawson, Nature and the Bible, p. 202. 
I should be much obliged if any of your readers could 
help me in deriving the name of the village of Allonley, 
in Cumberland. N. and Q., 6th ser., IX. 207. 
6. To communicate or transfer from one to 
another, as by descent. [Rare.] 
His [Bathurst's] learning, and untainted manners, too, 
We find, Athenians, are derived to you. 
Dryden, Epilogue spoken at Oxford, 1. 22. 
Our language has received innumerable elegancies and 
improvements from that infusion of Hebraisms which are 
derived to it out of the passages of Holy Writ. Addison. 
The plaintiff could not prove the place in question to 
be within his patent, nor could derive a good title of the 
patent itself to Mr. Ttigby. 
Winthrop, Hist. New England, II. 314. 
An excellent disposition is derived to your lordship from 
the parents of two generations. Felton. 
Derived conductors, in elect., the two or more branches, 
reuniting further along, into which a conductor is some- 
times divided. Derived current, in elect., a current 
flowing through a derived conductor. Derived group. 
Seeorowp. 
II. intrans. To come, proceed, or be derived. 
[Rare.] 
It were but reasonable to admire Him, from whom 
really all perfections do derive. 
Jer. Taylor, Works (ed. 1835), I. 22. 
Dermaptera 
Pow'r from heav'n 
Derives, and monarchs rule by gods appointed. 
Prior, Second Hymn of Uallimachus. 
The wish, that of the living whole 
No life may fail beyond the grave, 
Derives it not from what we have 
The likestGod within the soul? 
Tennyson, In Memoriam, Iv. 
The new school derives from Hawthorne and George 
Eliot. Howells. 
derivementt (de-riv'ment), M. [< OF. derive- 
ment, derivation (in lit. sense), < deriver, de- 
rive: see derive and -ment.] An inference or a 
deduction. 
I offer these derivements from these subjects, to raise 
our affections upward. 
W. Montague, Devoute Essays, II. iv. 4. 
deriver (de-ri'ver), n. I. One who derives or 
deduces from a source. 2. One who diverts 
a thing from its natural course to or upon 
something else. [Rare.] 
Such a one makes a man not only a partaker of other 
men's sins, but also a deriver of the whole entire guilt of 
them to himself. South, Sermons, II. 6. 
clerkt, a., n., and v. An obsolete form of dark 1 . 
Chaucer. 
derlingt, . A Middle English form of darling. 
derm (derm), n. [< NL. derma, q. v.] Same 
as derma. 
derma (der'ma), n. [NL., < Gr. dipfia, the skin, 
hide (of beasts, later of man), < depciv. skin, 
flay, = E. teari, q. v.] 1. The true skin, or 
cutisvera; the corium. 2. Skin; the skin in 
general: synonymous with integument or tegu- 
mentum. 
Also derm, dermts. 
dermad (der'mad), ado. [< Gr. dip/ia, skin, + 
L. ad, to: see -ad 3 .] Toward the skin that 
is, from within outward in any direction; ec- 
tad. Barclay. 
dermahemal, dermahsemal, a. See dermohe- 
mal. 
dermal (der'mal), a. [< derma + -/.] 1. In 
zool., pertaining to skin, or the external cover- 
ing of the body ; consisting of skin ; cutaneous ; 
tegumentary. The word properly relates to the derma 
or corium : as, the dermal layer of the skin ; but it has also 
acquired a more general sense : as, dermal appendages 
that is, hair, feathers, etc. ; the dermal skeleton. 
2. In bot., pertaining to the epidermis. Der- 
mal bone, an ossification in the derma or cutis. Dermal 
defenses, in ichth., the placoid exoskeleton ; the shagreen, 
ichthyodorulites, etc., of elasmobranchiate fishes. Der- 
mal denticle. See denticle. Dermal muscle, a cuta- 
neous or subcutaneous muscle; a muscle developed in, 
attached to, or specially acting upon the derma or skin 
proper, as the platysma myoides of man. 
As we regard the dermil muscles as primitively form- 
ing a common complex with those which belong to the 
skeleton, we must distinguish from it those which belong 
to the integument as such. 
Gegenbaur, Comp. Anat. (trans.), p. 492. 
Dermal musculature, the set or system of dermal mus- 
cles as a whole ; cutaneous muscles, collectively consid- 
ered. 
The dermal musculature is more highly developed in 
mammalia. Gegenbaur, Comp. Anat. (trans.), p. 493. 
Dermal skeleton, the exoskeleton of an animal, or those 
hard parts which cover the body, as the integument of an 
insect or a crustacean. 
dermalgia (der-mal'ji-a), n. [NL., < Gr. dip- 
pa, skin, + d/tyof, pam.'] iupathol., a painful 
condition of the skin arising from nervous dis- 
ease ; neuralgia of the skin. Msodermatalgia. 
Dermalichus (der-ma-li'kus), . [NL., irreg. 
< Gr. iepiia, skin, 
+ M x av, lick.] 
A genus of par- 
asitic mites 
or acarids, of 
the family Sar- 
coptida;, or itch- 
insects, found- 
ed by Koch, 
1843 : synony- 
mous with Anal- 
ges. The species are 
mainly parasitic on 
birds. The larva 
are hexapod, the 
adults octopod ; the 
Dermalick*! mytilaspidis (highly mag- ",l a ' e .' s !ar S er than 
nified). a, ventral vieC ; , lateral view the female, and IS 
often provided with 
exaggerated legs, especially the third pair. The species 
here figured feeds upon the oyster-shell bark-louse of the 
apple. Also Dermaleiclnui. 
dermaneural, a. See dermonewal. 
Dermaptera (der-map'te-ra), n. pi. [NL., prop. 
Dermoptcra (which is iii use in another appli- 
cation), neut. pi. of dcrmopterus, < Gr. &p/j6- 
Tn-fpof, with membranous wings, as a bat: see 
dermopterou.s.'] If. An old and disused group 
of insects ; in De Geer's system, one of three 
groups (the others being Hemiptera and Cole- 
