SUB
beWed abindance of Adje&ives, fignifying a Number of
peole agreeing in fome common Attribute; as, the Learned,
the Gear, the Devout, the Brave,- the Dilfolute, W5c. But
Jf is here to be regarded ; fit we don't fay the Eloquent,
j we lky the Learned; but Elegant Writers, &ic, 'Tis
Cf onm, and the Ear alone, that are to decide about thefe
pifrences.
'gain, Adjee&ives taken fubflantively, for other Things
befide Men, are either fo efed, to fignify a Numbor or Set
of Things that have fome common Quality; or to exprefs
an abfira& Quality. In both which, as in thofe of Men,
there are fome authorized by Cuftom, and others form'd
every Day on their Model.
'With regard to which laft, Ufe, again, and the Ear, are to
decide. Here All the Adjealives of Colours, are ufedfubflan-
tively; as the White, Black, Green, f c. Some of thofe
of Qualities; as the Cold, &)c. Thofe of Time; as the Pall,
Prelent, Future: And many of other Matters5 as the Agree-
able, the Sublime, the Principal, &ec. Nor is it only in the
Pofitive, but alfo in the Comparative and Superlative
Degrees, that Adjectives are ufed fubjantively i as, The
better of the two: DTe bejt of it, &x.
SUBSTITUTE, a Perfon appointed to officiate for an-
other, in cafe of Abfence, or other legal Impediment.
In the French Law, the Trocurears, or Proaors, are
obliged to name two of their Brethren for Subflitutes, whofe
Names are wrote after theirs in the Lifii; to receive Signi-
ficaeions and Summons's made in their Abfence.
The Word is form'd from the Latin, fub, under, and
flatuo, Iappoint, eflablifh.
SUBSTITUTE, in Medicine, aDrug, or Remedy that may
be ufed in lieu of another; or that fupplies the Place of an-
other of like Virtue, which is not to be had; call'd alfo a
Succedaneurn. See SUCCEDANEUM.
The Root of the great Centaureum, and Sometimes
Monk's Rhubarb, are ufed as Subflitutes to Rhapontic.
SUBSTITUTION, in Grammar, the ufing of one
Word for another; or a Mode, State, Manner, Perfon or
Number of a Word for that of another. This the Gram-
snarians otherwife call SyllepJis. See SYLLEPSIS.
SUBSTITUTION, in the Civil Law, a Difpofition of a
Tecfator, whereby he Subftitutes one Heir to another, who
has only the Ufu-fruit, and not the Property of the Thing
left him.
Subflitution is a kind of Inheritance, call'd Fiduciary, or
Fidei-commiffio, in regard the immediate Inheritor has only
the Ufe or Fruit of the Thing; the Body thereof bein
fiubilituted and affeied to certain Perfons, who are likewif
to have the Ufuifruit in their Times, but never the Property.
In Iome Countries, the Suibjitution is perpetual ; in France,
it only holds to the fourth Generation.
Subflitution aiwers to Remainder, in our common Law.
See REMAINDER.
Among the Romans, there were abundance of thefe Fidu-
ciary Heirs; who enjoy'd Inheritances, till they returned
them  into the Hands of the right Heir; and the Reafon
why they did not likewife reffore the Fruits, or that the
Fruits were not deem'd to make a Part of the Inheritance,
but only of the Thing, was, that the Fiduciary was obliged
to run the Risks, and to fland the Charge of the Culture of
the Land.
SUBSTITUTION, in Algebra,Fra~ions, Uec. is the putting
in the Room of any Quantity in an Equation, fome other
Quantity, which is equal, but exprefs'd after another Man-
ner. See QUANTITY.
SUBSTRACTION, in Arithmetic, the fecond Rule, or
rather Operation, in Arithmetic ; whereby we dedu61 a lefs
Number from a greater, to learn the precife Difrence:
Or, more jufIly, $ubtraffion is the finding of a certain
Number from two Homogeneous ones given; which, with
one of the given Numbers, is equal to the other. See ARITH-
METIC.
The Doflrine of Subftraffion is as follows;
'oftbftradf a lefs Nunraerfrom agreater.
10 Write the lefs Number under the greater, in fuch Man-
rer, as that homogeneous anfiver to homogeneous Figures,
i.e. Unites to Unites, Tens to Ten, &c. as we have direled
under ADDITION. 2f Under the two Numbers,draw a Line.
30 Subflraff, Severally, Unites fiom Unites, Tens from Tens,
Hundreds from Hundreds; beginning at the right Hand, and
proceeding to the Left; and write the feveral Remainders in
their correfpondent Places, under the Line. 40 If a greater
Figure come to be Jidbtrafled from a lefs; borrow an Unite
from the next Left-hand Place; this is equivalent to 1o, and
added to the lefs Number, the Subjiragion is to be made
from the Sum : Or if a Cypher chance to be in the next
Left-hand Place, borrow the Unite from the next further
Place. By thefe Rules, any Number may be fitraffted out
of another greater. For Example 3


.3]                     SUB
If it be required, from      9800403459
To Subtrafl                  4743865263
The Remainder will be found  5056538196
For, beginning with the right Hand Figure, and taking 3
from 9, there remains 6 Unites, to be wrote underneath the
Line: Going then to the next Place, 6 I find, can't be taken
from 5; wherefore, from the Place of Hundreds 4, I borrow
one, which is equivalent to Ten, in the Place of Tens; and
from the Sum of this io and S, viz. I, fubtrafling 6, 1
find 9 Tens remaining, to be put down under the Line. Pro-
ceeding to the Place of Hundreds, 2 with the X borrowed at
the lail Place, make 3, which fjbtra Led from d, leave 1.
Again, 5 in the Place of Thoufands, cannot be fizbtratfed
from  ; for which Reafon. taking one from 4, in the Place of
Hundreds 'of Thoufands, into the empty Place of Tens of
Thoufands, the Cypher is converted into Ten Tens of
Thoufands, whence one Ten being borrowed, and added to
the 3, and from the Sum 13 Thoufand, 8 Thoufand being
fubtratfed, we thall have 8 Thoufand to enter under the
Line: Then fubtratfing 6 Tens of Thoufands from 9, there
remain 3. Coming now to take 8 from 4 5 from the 8 further
on the Left, I borrow one, by means whereof, the two
Cyphers will be turned each into 9. And after the like Man-
ner, is the refp of the Subtfratlion eafily perform'd.
If heterogeneous Numbers be to be fubjratfed from each
other; the Unites borrow'dFare not to be equal to Ten; but
to fo many as there go of Unites of the lefs Kind, to con-
flitute an Unite of the Greater. For Example;
1   s.   d.
45   x6  6
27   19  9
17  i6   9
For fince 9 Pence cannot be jubflrafled from !6 Pence; of
the i6 Shillings, one is converted into 12 Pence; by which
means, for 6 we have 18 Pence; whence 9 being fubtrafled,
there remains 9. In like Manner, as 19 Shillings cannot be
fubtratfed from the remaining i5; one of the 4S Pounds is
converted into 20 Shillings, from which, added to the 15,
19 beingfubtratfed; the Remainder is i6 Shillings. Laflly,
27 Poundsfubtrafled from 44 Pounds, there remains 1 7.
If a greater Number be required to be fubtrafed from a
lefs, 'tis evident the Thing is impoffible. The lefs Number,
therefore, in that Cafe, is to be fubtrafed from the greater;
and the Defeff to be noted by the negative Charader. E. gr.
If I am requir'd to pay 8 Pounds, and am only Mailer of 3;
when the Three are paid, there will fill remain 5 behind;
which are to be noted, 5.
Subftraflion is prov'd, by adding the Remainder to the
Subtrahend, or Number to be fubjira fed: For if the Sum
be equal to the Number whence the other is to be fubtrafled,
the Subftraffion is juffly perform'd: For Example;


9800403459
4743865263 Subtrahend


7. S. d.q.
j56    11 3 7
21 17 2 x Subtrahend


- -                     -- -
:5os6538 i96 Remainder  134  14  0
9800403459              156  II  3 4
SUBSTPRACTION, in Algebra, is perform'd by conne&ing
the Quantities with all the Signs of the Subtrahend changed-
and at the fame time uniting fuch as may be united; as is done
in Addition. Thus +7 a rubjiratfed from + 9 a, makes
+ ga- 7aor2a.
In the Subjiraoion of Compound algebraic Quantities; the
Charaiers of the Subtrahend, are to be changed into the con-
trary ones, viz.+ into-; and -into+. See QUANTITY.
Y'o Subfiraff fpecious Numbers, or Quantities from one
another; both thofe affetled with the fame, and thofe
with contrary Characfers.
io If the Quantities defign'd by the fame Letter, have
the fame Signs; and the lefs be to be fubftratled from the
greater; the Subftrafion is perform'd as in common Arith-
metic, e. gr.
5b+4d-f -1b.+4P.-7
2b+d -f      =2J#.+iP.-


3 b 3 d-o


3-+3P. o


2f If a greater Quantity be to be fivb/rafed out of a lefs -
the lefs muff be fubflrafed out of the greater, and to the
Remainder, mull be 'prefix'd the Sign -, if the Quantities
be affeaed with the Sign +; or the Sign +, if they be
affeded with -.
z6a