LIM 
LIM 
corative power with respect to animal oils, 
by combining with the putrid gelatine in 
them ; but its action on them in forming a 
soap is too strong to admit of its being used 
for this purpose with advantage, unless in 
small quantities. Feathers, however, may 
be very conveniently cleaned by steeping 
three or four days in strong lime-water, 
and afterward washing and drying them. 
Though infusible in the strongest heats 
of our furnaces, it is nevertheless a very 
powerful flux with regard to mixtures of 
the other earths. These are all fusible by 
a proper addition of lime. Compounds are 
still more fusible ; for any three of the five 
well-known earths may be fused into per- 
fect glass, if they be mixed together in 
equal portions, provided the calcareous be 
one of them. 
The earthy part of animals is chiefly, if 
not altogether, calcareous: in most cases it 
is united with phosphoric acid, but fre- 
quently with the carbonic. 
LiME-stone. The native indurated car- 
bonate of lime. It is usually more or less 
bluish from iron, and of a granulated frac- 
ture. ; and it is connected with lime by igni- 
tion in lime-kilns, for the purpose of making 
mortar. See Lime ; also Mortar. 
LIMEUM, in botany, a genus of the 
Heptandria Digynia class and order. Na- 
tural order of Holoracae. Portulacese, Jus- 
sieu. Essential character: calyx five-leaved; 
petals five, equal ; capsule globular, two- 
celled. There are three species, all natives 
of the Cape of Good Hope. 
LIMIT, in a restrained sense, is used by 
mathematicians for a determinate quantity 
to which a variable one continually ap- 
proaches ; in which sense the circle may be 
said to be the limit of its circumscribed and 
inscribed polygons. In algebra, the term 
limit is applied to two quantities, one of 
which is greater, and the other less, than 
another quantity ; and in this sense it is used 
in speaking of the limits of equations, where- 
by their solution is much facilitated. 
Let any equation, as a;’ — x qx — 
r = 0 be proposed ; and transform it into 
the following equation : 
— pt/ — 2pey—pe"- I 
+ qy+qe\ 
— r-* 
Where the values of y are less than the re- 
spective values of x, by the difference e. 
If you suppose e to be taken such as to 
make all the coetficients of the equation of 
y positive, viz. e’ — p q e — r, 3e^ — 
2pe-\-q,3e — p; then there being no va- 
riation of the signs in the equation, all the 
values of y must be negative ; and conse- 
quently the quantity e, by which the values 
of X are diminished, must be greater than 
the greatest positive value of a'; and, con- 
sequently, must be the limit of the roots of 
the equation x^ — p x'^-{-q x — r = o. 
It is sufficient, therefore, in order to find 
the limit, to inquire what quantity substi- 
tuted for X, in each of these expressions 
a;’ — px^-\-qx — r, 3 a? — ^ p x^-\-q, 3 x 
— p, wdll give them all positive; for the 
quantity will be the limit required. 
Having found the limit that surpasses the 
greatest positive root, call it m. And if 
you assume y — m — x, and for x substitute 
TO — y, the equation that will arise will have 
all its roots positive ; because m is supposed 
to surpass all the values of x, and conse- 
quently m — X (z=y ) must always be af- 
firmative. And, by this means, any equa- 
tion may be changed into one that shall have 
all its roots affirmative. 
Or, if — n represent the limit of the ne- 
gative roots, then by assuming y = x -j- re 
the proposed equation shall be transformed 
into one that shall have alt its roots affirma- 
tive ; for -|- re being greater than any nega- 
tive value of X, it follows that y=.x + re 
must be always positive. 
What is here said of the above cubic 
equation, may be easily applied to others ; 
and of all such equations, two limits are 
easily discovered, viz. o, which is less than 
the least; and-c, found as above, which 
surpasses the greatest root of the equation. 
But besides these, other limits still nearer 
the roots may be found ; for the method of 
doing which, the reader may consult Mac- 
laurin’s Algebra. 
LIMITATION, a certain time prescrib- 
ed by statute, within which an action must 
be brought, which is generally twofold ; 
first in writs, by several acts of parliament, 
and, secondly, to make a title to any inhe- 
ritance, and that is by the common law. 
On penal statutes, all actions, suits, bills, 
indictments, or informations, for any for- 
feiture limited to the king, his heirs or suc- 
cessors only, shall be brought within two 
years after the offence committed, and not 
after. All such actions, &c. except the 
statutes of tillage, which give the penalty 
to the king and a common informer, are 
limited to one year next after the offence 
committed ; and if not sued for by the In- 
former, they may be sued for by the king, 
any time within the two years, after that 
