

FACTORIALS 



the Cads* are mode to incline inward* from the vertical 

 lifts; as, for iwUnor. in toe rrthco..n, tl..- tempi.- n( lUcchiw at 

 Bon*, UM Bath* of Diocletian, and UM temple of Vesta t Tiv,,li. The 

 farts* of UM architraves of the temple of Man t'ltor. ami of the K..nim 

 , incline outward* ; but the optical effect Urn* |ir.luel U w 

 iiBtslttfii <nrjr that it may almost be considered to be indispensable 

 thai UM more general ml* should be observed. 



. i* a mercantile agent who buy* and sell, on behalf of 

 other*, usually being intrusted with poeMaakm of the goods, to deal 

 with them in hit own name, and to receive and give receipt* for the 

 money. Mid U remunerated for hi* tervicet by a percentage ou the 

 tranaaotioo. A broker acu at a middleman only, having no poeaet- 

 aion of the gooda, and properly negotiating the buxineta in the name 

 only of hi* principal ; the price doet not pass through hit handt, but 

 be too i* remunerated for hit atsktt nno by percentage on the 



Xu amall thare of the butmetn of the mercantile world is carried 

 on through the medium of factort, living at a distance from their 

 principal*; whom for their own interest they keep duly informed of 

 the aUte and prospect. of the market in their immediate dittrict; 

 and from whom they accordingly receive consignments, often remit- 

 ting their acceptance* for the tame in advance, on the expectation that 

 future amle* will put them in aufficient funds to retire their accept- 

 ance* when due. At these transaction* multiply, the relation of 

 principal and agent become* more complicated in interest, and a clear 

 and complete statement of credito and debits on hit principal's account 

 it one of the most astntitl dutiet of the factor, which a court of 

 equity will compel him to render, if need be, and for wont of which, 

 when refuted, an action for damages will lie against him at common 

 law. 



The law givet him a lieu upon the property in hw hands for the 

 general balance, composed of advances, expencet, and commission, due 

 from hit principal ; and the produce of tales, at well as the goods 

 before tale, are subject to this lien. Ho may therefore think it 

 prudent for hit own behalf to effect an insurance on the projwrty of 

 the principal in hit handt ; and unless he is expressly forbidden he 

 may insure in hit principal'! name, and at hit expense; but if the 

 principal requires him to do so, it then becomes bit duty, and neg- 

 ligence at to that might leave him answerable for the consequencea of 

 accidental fire, lie hat an interest obviously in keeping the property 

 safe. The Uw imposes on him the duty of exercising ordinary care 

 and diligence for its protection, but if there is no failure therein upon his 

 part, he it not liable for damage hnp|>ening to it through violence or 

 accident, at by robbery, or fire, which n prudent, careful man under 

 ances could 



the circu 



not have prevented. 



In his transactions about the goods of hit principal in tho market be 

 is bound by the usage of trade, when that is not expressly negatived 

 by hit instruction*. If it is not usual therefore to sell ou credit, and if 

 he yet doet to, he it answerable for the consequences of this deviation 

 from his authority. In other respectt he it Iwund to exercise 

 ordinary skill, caution, and diligence, in the discharge of his duties 

 at factor. 



By the common Uw of this country the factor hat no authority to 

 pledge the goods of hit principal. The disadvantage of this rule with 

 regard to a class of agentt who are in the <Uily habit of binding thcm- 

 telves by their acceptances in favour of the principal, in dependence 

 upon the market and their ability to realise the goods in time to meet 

 the billt at maturity, became to obvious, that the British legislature 

 twice interfered by statute, the 6 Uo. IV. c. 94, and tho 6 & Viet. 

 c. 89, to place these agents, in this respect, upon a footing suitable to 

 the necessities of trade and the dictates of prudence. The results of 

 this legislation now are, that a factor may pledge goods or documents 

 of UUe in hit possession for advances to himself, with security to the 

 Under, provided the advance*, which must not include an antecedent 

 debt, were boo* fide, and that the lender had no notice of the pledge 

 being contrary to the factor's authority, or made twU jfefa in Aspect 

 of his principal If the loan i* made on a written contract to deposit 

 pods, a pledge in accordance therewith it protected, unless the lender 

 have notice of the factor's want of authority priorto tho receipt of the 

 goods; and em an antecedent debt it a good consideration for the 

 pUdgD- to the extent of the factors lien against the principal, if the 

 pledgee at the time did not know of the factort agency. Goods or 



^T U * ^ U lV P ?" dy L on ****" "*' * r "P Uc ty othCT good" 

 or documents of title i. the hands of the pledgee, subi.it to theW 

 tinuing hen. Documents of title are now^aid to be intrusted to the 



55&5^^f -iltollta *" I' |W| 8 *& whether they come immc- 

 disUly from the owner or in virtue of his having had possession of the 

 good, or of tome other document, of title beforV 



" n " ction "^ tut the Purchaser 

 hi "> >t to pay the money to the 



'hL . 'T Si D l" lrch "-. pt in to far at the 

 * hat a ben upon the money aguntt hit principal. In the absence 



* " to the 1 ctor g&<Uscharg.ofthe 



the name of the principal, of taking 



in * to*****- 53 



the opinion that be it a 



princi|ia], and with a view to a right of set-off which tl. 



against him, the disclosure of the real principal it not suffered after- 



wards to deprive the other of his right of set-oft: 



The principal may recover against hit factor by action f..i tli. 

 neglect of his duty, or disobedience to his instructions if lost occur 

 thereby, at if he purchases goods at a limited price, and fraudulently 

 sells them again for his own profit. If a factor, without tho orders 

 of his principal, export* goods prohibited by the Customs' Uws, and 

 the tame are seized, the Tost it the factor's; and so, if be pay muey 

 without the direction of his employer, or sells hit goods at an 

 value, or exports goods of an improper quality, he is answerable for 

 the damage. And if a factor exports goods of a different quality ] 

 kind from those he was directed to purchase, or sends them to a place 

 .In i- titan that to which he wot ordered to send them, the merchant 

 may refuse to accept them, and may recover any damage he has sus- 

 tained, in consequence of his neglect, from the factor.. The rights and 

 liabilities of merchant* and factors ore governed by the laws of the 

 place in which they are domiciled, and any contract which may be 

 made by either of them must be governed by the l:i\v of the place 

 where it is mode, and these rules are acted upon by the courts of 

 justice of every civilized nation. Thus, since the passing of the above- 

 mentioned statutes, a foreign merchant cannot recover his goods from 

 the pledgee of his factor in EngUnd, though ho be totally ignorant of 

 the change which has taken place in the law. 



There is another description of factor, who acts under what is called 

 a del credere commission, where, for an additional percentage, he 

 engages for the solvency of the purchasers of the goods consigned to 

 him. This contract, it is evident, arises on the supposition that th* 

 factor being resident among the purchasers, must be better able to 

 judge of their solvency than the princi|Kil, residing in a foreign 

 country. For a long time it was considered that under this arrange- 

 ment those who dealt with the factor were linbU- to him alone, and 

 that he was liable, in the first instance, to his employer; it ha- 

 ever, been decided that the factor stands in the relation of a sun 

 the persons with whom he deals on account of the employ i , and that 

 he is liable to his employer only in case of their default. Del 

 is an Italian mercantile phrase, of the some signification as the English 

 !.:! guarantee, and the Scotch warrandice. 



(See Russell on Factors ; Story on Agency; J<l. nil HaHmfuli ; Sir 

 Win. Jones on Kc ' iley on Prtnciiml . Chittyoii 



Contracts, by J. A. Russell.) 



FACTOR, a name given to any algebraical expression considered as 

 part of a product. Thus, a and a Kc are the actors of the product 

 a (a + x), or a' + aa:. 



Any quantity may be made an apparent factor of any 

 Thus in 



6 is au apparent factor of a. But 4 U not properly called a factor of , 



sj 

 unless it happen that when b is mode 0, T is not thereby made 



infinite. Thus the two equations 



sin x sin x, 



sin x = x x , mnmm & * , 



x .' - 



show x and a- 3 as apparent factors of sin x. But x is a real fact 

 is a fictitious factor. When 



. 

 0, -g- = 1, and ^ = oo . 



FACTOIUALS. The subject treated under this word is one whieh 

 daily becomes of more importance in mathematical analysis, and takes 

 its rise at the commencement of jlgebni. 



WJjt-n we first begin to number, we easily make the transition from 

 integers to fractions, because we ore accustomed to consider ourselves 

 at reckoning simple magnitude, of which each unit can be divided 

 into parts homogeneous with itself. [NUMBKH.] Be the unit what it 

 may, in the oate of simple magnitude, it might as well have U 

 fraction of what it is, so for as the possibility of conceiving and ]>< i 

 forming arithmetical operations it concerned. But when we come to 

 count oyxTo/iod*, not ma'/nitudet, the case is much altered ; we can no 

 longer say at pleasure that we con conceive or introduce fractions. 

 Certainly, at to addition*, we think we need not stop to learn what a 

 fractional number of them means. If, after having thought 

 moment of six addition! of 20 and seven additions of M, we axk 

 selves what ought to be meant by V and a /i// additions of 20, wo 

 imagine that it must necessarily mean tix additions of 2<>, followed by 

 an addition of 10. But this notion, though the most simple, and 

 therefore adopted as a basis, it not necessary. The algebraist knows 

 \ ry well that having proved the equation $(Jc, m) = -r mi> to be true 

 whenever M U an integer, he hot not proved it to be true when mu a 

 fraction : in foot, tXs, m) = x + mb cot 2mr \voul<l equally ati- 

 demonttration, and an infinite number of other solutions might be 

 n .in. .1. 



When we coino to reckon numbers of multiplications, we begin 

 from unity, and my, let a* signify that unity is multiplied n timer. 

 following by a. Now this symbol is, from the beginning, distinctly 



