LIM 



LIM 



vantage, unless in small quantities. Fea- 

 thers, however, may be very convenient- 

 ly 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 perfect glass, if they be mixed to- 

 gether in equal portions, provided the cal- 

 careous 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-tfone. 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 ig- 

 nition in lime-kilns, for the purpose of 

 making mortar. See LIME ; also MOR- 

 TAR. 



LIMEUM, in botany, a genus of the 

 He ptandria Digynia class and order. Na- 

 tural order of Holoracex. Portulacex, 

 Jussieu. Essential character : calyx five- 

 leaved ; petals five, equal ; capsule globu- 

 lar, 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 quan- 

 tity to which a variable one continually ap- 

 proaches ; in which sense the circle may 

 "be said to be the limit of its circumscrib- 

 ed and inscribed polygons. In algebra, 

 the term limit is applied to two quanti- 

 ties, 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, whereby their solution is 

 much facilitated. 



Let any equation, as x3 p x 3 X 9 

 r = o be proposed ; and transform it into 

 the following equation : 



""' -r- 3 e y z -}- 3 e 1 y -f- 



;;f/J^n 



-\-qy-\-qe f ws 

 rj 



Where the values of y are less than the 

 respective values of x, by the difference e. 

 If you suppose e to be taken such as to 

 make all the coefficients of the equation 

 of y positive, viz. el p e 3 - -f- q e r, 3 e 1 

 2p e -f- q, 3 e, p ; then, there being no 

 variation of the signs in the equation, all 

 the values of y must be negative ; and 

 consequently the quantity e, by which the 

 values of x are diminished, must be great- 



er than the greatest positive value of x ; 

 and, consequently, must be the limit of the 

 roots of the equation xi p x 1 -f- Q x 

 r = o. 



It is sufficient, therefore, in order to 

 find the limit, to inquire what quantity 

 substituted for x, in each of these expres- 

 sions .r3 p x 1 + q x r, 3 x* 2 p x 

 -f- <?, 3 x p, will 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 sub- 

 stitute m y, the equation that will arise 

 will have all its roots positive ; because 

 m is supposed to surpass all the values of 

 x, and consequently m x (= y") must 

 always be affirmative. And, by this means, 

 any equation 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 + 

 n the proposed equation shall be trans- 

 formed into one that shall have all its 

 roots affirmative ; for -f- n being greater 

 than any negative value of x t it follows 

 that y = x-\- n 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 e, found as above, which 

 surpasses the greatest root of the equa- 

 tion. But besides these, other limits still 

 nearer the roots may be found ; for the 

 method of doing which, the reader may 

 consult Maclaurin'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 parlia- 

 ment, and, secondly, to make a title to 

 any inheritance, and that is by the com- 

 mon law. 



On penal statutes, all actions, suits, 

 bills, indictments, or informations, for any 

 forfeiture limited to the king, his heirs or 

 successors only, shall be brought within 

 two years after the offence committed, 

 and not after. All such actions, &c. ex- 

 cept the statutes of tillage, which give 

 the penalty to the king and a common in- 

 former, are limited to one year next after 

 the offence committed ; and if not sued 

 for by the informer, they may be sued for 

 by the king, any time within the two years, 

 after that year is ended : and where a 

 shorter time is limited by any penal sta- 

 tute, the prosecution must be within that 

 time 31 Eliz. c. 5. 



All actions of trespass, of assault, bat- 

 tery, wounding, imprisonment, or any of 



