relation 
a fact relating to two or more things, and that fact viewed 
as a predicate of one of those things is the relation. 
Thus is relation rect, ryht as adiectif and substantif 
A-cordeth in alle kyndes with his antecedent. 
Piers Ploutman (C), iv. 363. 
The last sort of complex ideas is that we call relation, 
which consists in the consideration and comparing one 
idea with another. Locke, Human Understanding, ii. 12. 
The only difference between relative names and any 
others consists in their being given in pairs ; and the rea- 
son of their being given in pairs is not the existence be- 
tween two things of a mystical bond called a relation and 
supposed to have a kind of shadowy and abstract reality, 
but a very simple peculiarity in the concrete fact which 
the two names are intended to mark. 
J. 5. Mill, Note to James Mill's Human Mind, xiv. 2. 
In natural science, I have understood, there is nothing 
petty to the mind that has a large vision of relations. 
George Eliot, Mill on the Floss, Iv. 1. 
Most relations are feelings of an entirely different order 
from the terms they relate. The relation of similarity, 
e. g., may equally obtain between jasmine and tuberose, 
or between Mr. Browning's verses and Mr. Story's; it is 
itself neither odorous nor poetical, and those may well be 
pardoned who have denied to it all sensational content 
whatever. W. James, Mind, XII. 13. 
4. Intimate connection between facts; signifi- 
cant bearing of one fact upon another. 
For the intent and purpose of the law 
Hath full relation to the penalty, 
Which here appeareth due upon the bond. 
SAoi.,.M. of V., iv. 1. 248. 
The word relation is commonly used in two senses con- 
siderably different from each other. Either for that qual- 
ity by wnich two ideas are connected together in the im- 
agination, and the one naturally introduces the other . . . ; 
or for that particular circumstance in which ... we may 
think proper to compare them. ... In a common way we 
say that "nothing can be more distant than such or such 
things from each other, nothing can have less relation," as 
if distance and relation were Incompatible. 
Hume, Human Mature, part i. 5. 
6. Connection by consanguinity or affinity ; kin- 
ship ; tie of birth or marriage ; relationship. 
Relations dear, and all the charities 
Of father, son, and brother, first were known. 
Milton, P. U, iv. 766. 
6. Kindred; connection; a group of persons 
related by kinship. [Rare.] 
He hath need of a great stock of piety who is first to 
provide for his own necessities, and then to give portions 
to a numerous relation. 
Jer. Taylor, Works (ed. 1835), I. 644. 
7. A person connected by consanguinity or 
affinity; a kinsman or kinswoman; a relative. 
Sir, you may spare your application, 
I'm no such beast, nor his relation. 
Pope, Imit. of Horace, I. vii. 60. 
I am almost the nearest relation he has in the world, 
and am entitled to know all his dearest concerns. 
Jane Austen, Pride and Prejudice, Ivi. 
8. In math.: (a) A ratio; proportion. (6) A 
connection between a number of quantities by 
which certain systems of values are excluded ; 
especially, such a connection as may be ex- 
pressed by a plexus of general equations. 9. 
In music, that connection or kinship between 
two tones, chords, or keys (tonalities) which 
makes their association with each other easy 
and natural. The relation of tones is perceived by the 
ear without analysis. Physically it probably depends 
upon how far the two series of upper partial tones or 
harmonics coincide. Thus, a given tone is closely re- 
lated to its perfect fifth, because the 2d, 5th, sth, llth, 
etc., harmonics of the one are respectively identical with 
the 1st, 3d, 5th, 7th, etc., of the other ; while for converse 
reasons it is hardly at all related to its minor second. 
Tones that have but a distant relation to each other, how- 
ever, are often both closely related to a third tone, and 
then, particularly if they are associated together in some 
melodic series, like a scale, may acquire a close relation. 
Thus, the seventh and eighth tones of a major scale have 
a close relation which is indirectly harmonic, but appa- 
rently due to their habitual melodic proximity. The re- 
lation of chords depends primarily on the identity of one 
or more of their respective tones. Thus, a major triad is 
closely related to a minor triad on the same root, or to a 
minor triad on the minor third below itself, because in 
each case there are two tones in common. Thus, the 
tonic triad of a key is related to the dominant and sub- 
dominant triads through the Identity of one of its tones 
with one of theirs. As with tones, chords having but a 
distant relation to each other may acquire a relation 
through their respective close relations to a third chord, 
especially if habitually brought together in harmonic pro- 
gressions. Thus, the dominant and subdominant triads 
of a key have a substantial but indirect relation ; and, 
indeed, a relation is evident between all the triads of a 
key. The relation of keys (tonalities) depends properly 
on the number of tones which they have in common 
though it is of ten held that a key is closely connected with 
every key whose tonic triad is made up of its tones. Thus, 
a major key is most intimately related to the major keys 
of its dominant and subdominant and to the minor key 
of its submediant, because each of them differs from it by 
but one tone, and also to the minor keys of its mediant 
and supertonic, because their tonic triads are also com- 
posed of its tones. Hence a major key and the minor 
key of its submediant are called mutually relative (rela- 
tive major and relative minor), in distinction from the 
tonic major and tonic minor, which are more distantly 
related. When carefully analyzed, the fact of relation is 
6058 
found to be profoundly concerned in the entire structure 
and development of music. It has caused the establish- 
ment of the major diatonic scale as the norm of all mod- 
ern music. It is the kernel of tonality, of harmonic and 
melodic progression, of form in general, and of many ex- 
tended forms in particular. 
10. In law: (a) A fiction of law whereby, to 
prevent injustice, effect is given to an act done 
at one time as if it had been done at a previous 
time, it being said to have relation back to that 
time : as, where a deed is executed and acted 
on, but its delivery neglected, the law may give 
effect to its subsequent delivery by relation 
back to its date or to its execution, as may be 
equitable. (6) Suggestion by a relator; the 
statement or complaint of his grievance by one 
at whose instance an action or special proceed- 
ing is brought by the state to determine a ques- 
tion involving both public and private right. 
11. In arch., the direct dependence upon one 
another, and upon the whole, of the different 
parts of a building, or members of a design. 
Abellan relation, a relation expressed by certain iden- 
tical linear equations given by Abel connecting roots of 
unity with the roots of the equation which gives the val- 
ues of the elliptic functions for rational fractions of the pe- 
riods. Accidental relation, an indirect relation of A to 
C, constituted by A being in some relation to B, and B being 
in an independent relation to C. Thus, if a man throws 
away a date-stone, and that date-stone strikes an invisible 
genie, the relation of the man to the genie is an accidental 
one. Actual relation. See actual. Aggregate rela- 
tion, (a) A relation resulting from a disjunctive con- 
junction of several relations, such that, if any of the latter 
are satisfied, the aggregate relation is satisfied. (6) Same 
as composite relation (a). [This Is the signification attached 
to the word by Cayley, contrary to the established ter- 
minology of logic.] AliO relation, a relation of such a 
nature that a thing cannot be in that relation to itself : as, 
being previous to. Aptltudlnal relation. See aiititudi- 
nal. Categories of relation. See category, I. Com- 
posite relation, (a) A relation consisting in the simul- 
taneous existence of several relations. (6) Same as ag- 
gregate relation (a). [This is the signification attached 
to the phrase by Cayley, in opposition to the usage of 
logicians.] Confidential, cyclical, discriminant re- 
lation. See the adjectives. Definite relation, a rela- 
tion unlike any relation of the same relate to other corre- 
lates. [This is Kempe's nomenclature, but is objection- 
able. Peculiar relation would better express the idea. ] 
Distributively satisfied composite relation. See 
distributiaely. Double relation, dual relation, rela- 
tion between a pair of things, or between a relate and a 
single correlate. Dynamic relations. See dynamic. 
Enharmonic relation. See enharmonic. Exterior re- 
lations. See ezterinr. Extrinsic relation, a relation 
which is established between terms already existing. 
False or inharmonic relation, in music. See false. 
In relation to, in the characters that connect the sub- 
ject with the correlate which is the object of the prepo- 
Bition to : as, music in relation to poetry (music in those 
characters that connect it with poetry). Intrinsic re- 
lation. See intrinsic. Involutorial relation. See t'n- 
vcHutorial. Irregular relation, a relation not regular. 
Jacobian relation, the relation expressed by equat- 
ing the Jacobian to zero. K-fOld relation, a relation 
which reduces by k the number of independent ways in 
which a system of quantities may vary. Legal rela- 
tion, the aggregate of legal rights and duties character- 
izing one person or thing in respect to another. Omal 
relation, a relation expressed by a system of linear equa- 
tions. [With Legendre, omal means having the differen- 
tial coefficient constantly of one sign ; but Cayley uses 
the word as a synonym of hmnal'iidal or linear.] Order 
of a relation, in math. See order, 12. Parametric 
relation, a relation involving parameters, or variables 
over and above the coordinates. Plural relation, a rela- 
tion between a relate and two or more correlates, as when 
A aims a shot, B, at C. Predicamental relation, a 
relation which comes under Aristotle's category of rela- 
tion. Prime relation, a relation not resulting from the 
conjunction of relations alternatively satisfied. Real 
relation, a relation the statement of which cannot be 
separated into two facts, one relating to the relate and the 
other to the correlate, such as the relation of Cain to Abel as 
his killer. For the facts that Cain killed somebody and that 
Abel was killed do not together make up the fact that 
Cain killed Abel : opposed to relation of reason. Regu- 
lar relation, a relation of definite manifoldness. [So de- 
fined by Cayley ; but it would have been better to denomi- 
nate this a homoplasial relation, reserving the term regular 
relation for one which follows one law, expressible by gen- 
eral equations, for all values of the coordinates this mean- 
ing according better with that usually given to regular.] 
Relation of disquiparance, a relation which confers 
unlike names upon relate and correlate. Relation of 
equiparance, a relation which confers the same relative 
name upon relate and correlate : thus, the being a cousin of 
somebody is such a relation, for if A is cousin to B, B is 
cousin to A. Relation of reason, a relation which de- 
pends upon a fact which can be stated as an aggregate of 
two facts (one concerning the relate, the other concerning 
the correlate), such that the annihilation of the relate or 
the correlate would destroy only one of these facts, but 
leave the other intact : thus, the fact that Franklin and 
Rumford were both scientific Americans constitutes a 
relationship between them with two correlative relations ; 
but these are relations of reason, because the two facts 
are that Franklin was a scientific American and that 
Rumford was a scientific American, the first of which 
facts would remain true even if Rumford had never ex- 
isted, and the second even if Franklin had never existed. 
Resultant relation, a relation between parameters 
involved in a superdeterminate relation. Self-relation, 
(a) A relation of such a sort that a thing can be in that 
relation to itself: as, being the killer of; but better (6) 
a relation of such a sort that nothing can be so related 
to anything else, as the relations of self-consciousness, 
relative 
self-depreciation, self help, etc. Superdeterminate 
relation, a relation whose manifoldness is as great as or 
greater than the number of coordinates. Transcen- 
dental relation, a relation which does not come under 
Aristotle's category of relation, as cause and effect, habit 
and object. =Syn. 1. Narration, llecital, etc. See account. 
3. Attitude, connection. 6. Affiliation. S and 7. Re- 
lation, Relative, Connection. When applying to family af- 
filiations, relation is used of a state or of a person, but in 
the latter sense relative is much better ; relative is used 
of a person, but not of a state; connection is used with 
equal propriety of either person or state. Relation and 
relative refer to kinship by blood ; connection is increas- 
ingly restricted to ties resulting from marriage. 6. Kin- 
dred, kin. 
relational (re-la'shon-al), a. [< relation + -al.~\ 
1. Having relation or kindred. 
We might be tempted to take these two nations for re- 
lational stems. Tooke. 
2. Indicating or specifying some relation : used 
in contradistinction to notional : as, a relational 
part of speech. Pronouns, prepositions, and 
conjunctions are relational parts of speech. 
relationality (re-la-sho-nal'i-ti), n. [< rela- 
tional + -%.] The state or property of having 
a relational force. 
But if the remarks already made on what might be 
called the relationality of terms have any force, it is obvi- 
ous that mental tension and conscious intensity cannot be 
equated to each other. J. Ward, Mind, XII. 56. 
relationism (re-la'shon-izm), . [< relation + 
-isw.] 1. The doctrine that relations have a 
real existence. 
Relationism teaches . . . that things and relations con- 
stitute two great, distinct orders of objective reality, in- 
separable in existence, yet distinguishable in thought. 
F. E. Abbot, Scientific Theism, Introd., II. 
2. The doctrine of the relativity of knowledge, 
relationist (re-la'shon-ist), n. [< relation + 
-ist.] If . A relative ; a relation. Sir T. Browne. 
2. An adherent of the doctrine of relationism. 
relationship (re-la'shon-ship), n. [< relation -f 
n.] 1. The state 'of being related by kin- 
, affinity, or other alliance. 
Faith is the great tie of relationship betwixt you [and 
Christ). Chalmers, On Romans viii. 1 (ed. R. Carter). 
Mrs. Mugford's conversation was incessant regarding 
the Ringwood family and Flrmln's relationship to that 
noble house. Thackeray, Philip, xxl. 
2. In music, same as relation, 8. Also called 
tone-relationship. 
relatival (rel-a-ti'val or rel'a-tiv-al), a. [< 
relative + -o/J Pertaining to relative words 
or forms. 
Conjunctions, prepositions (personal, relative, and in- 
terrogative), relatival contractions. 
E. A. Abbott, Shakespearian Grammar (cited in The 
[Nation, Feb. 16, 1871, p. 110). 
relative (rel'a-tiv), a. and n. [< ME. relatif, 
< OF. (and FV) relatif = Pr. relatiu = Sp. Pg. 
It. relativo,< LL. relativus, having reference or 
relation, < L. relatus, pp. of referre, refer, re- 
late: see refer, relate.) I. a. 1. Having rela- 
tion to or bearing on something; close in con- 
nection ; pertinent ; relevant ; to the purpose. 
The devil hath power 
To assume a pleaaing shape ; yea, and perhaps . . . 
Abuses me to damn me. 111 have grounds 
More relative than this. Shak., Hamlet, ii. 2. 638. 
2. Not absolute or existing by itself ; consid- 
ered as belonging to or respecting something 
else ; depending on or incident to relation. 
Everything sustains both an absolute and a relative 
capacity : an absolute, as it Is such a thing, endued with 
such a nature ; and a relative, as It is a part of the uni- 
verse, and so stands in such a relation to the whole. 
South. 
Not only simple ideas and substances, but modes also, 
are positive beings : though the parts of which they con- 
sist are very often relative one to another. 
Locke, Human Understanding, II. xxvi. 6. 
Religion, it has been well observed, Is something rein- 
tine to us ; a system of commands and promises from God 
towards us. J. H. Newman, Parochial Sermons, i. 317. 
3. In gram., referring to an antecedent; intro- 
ducing a dependent clause that defines or de- 
scribes or modifies something else in the sen- 
tence that is called the antecedent (because it 
usually, though by no means always, precedes 
the relative) : thus, he who runs may read ; he 
lay on the spot where he fell. Pronouns and pro- 
nominal adverbs are relative, such adverbs having also 
the value of conjunctions. A relative word used without 
an antecedent, as implying in itself its antecedent, is often 
called a compound relative : thus, who breaks pays ; 1 saw 
where he fell. Relative words are always either demon- 
stratives or interrogatives which have acquired seconda- 
rily the relative value and use. 
4. Not intelligible except in connection with 
something else ; signifying a relation, without 
stating what the correlate is: thus, father, bet- 
ter, west, etc., are relative terms. 
Profundity, in its secondary as in Its primary sense, is a 
relative term. Macaulay, Sadler's Ref. Refuted. 
