I 11 K 



402 



T H 



by u tint in the cut ; and the copying-rail, which extends 

 ttif whole \viilth ol" tin- machi: -.1 intervals 



..f \vliirli is si To these 



rods, and consequently to the copping-rail and bobbins 

 supported by them, ;i . citiciilni 



parted through the connecting pie ;n the 



MOt lever 11. which i> pr- bj mo- 



tion adjustable friction-roller /.from an ei 



trie or hemrt wheel m. Thus by (lie eomhim il rotatory 



motion of the spindle and flyer, and rising and falling 



motion of the bobbin, the thread is ;it once twisted and 



wound regularly upon the bobbin*, \vhieli may K- easily 



removed when full. [I :l the cou- 



'.y which motion is communicated to various 



. liine. and it is sufficient to add that, by 



the relative sizes of some ofthe toothed wheels 



liich the moving-power is di>trihuted from the main 



. the spindle-, winch always revolve much faster than 

 the rollers, may he made to do so t 



so as to impart a greater or li of twist to the 



thread. 



Silk thread i*, according to Dr. Ure, commonly t 

 in length* of from lilty to a hundred feet, with band-reels 



-hat similar to those employed in rope-making. 

 (Anderson, Hist/try of r<, //,/, nv, vol. iv., pp. 70:!-4 ; 

 Dr. I're's I'.ittnn Manufacture if (imit Uritdiv, vol. ii., 

 pp. 226-2U : Di'-t. "f'.lrts; &C.) 



THREATS AN'l) THREATENING LKTrKHS. By 

 the criminal law of England, threats of personal violence, 

 or any other threats by \vhich a man of ordinary firmness 

 and prudence may be put in fear, and by means of which 

 money or other property is extorted from him, amount to 

 the crime of robbery. [RoBBBBY.] And by the statute 

 7 Will. IV. & 1 Viei.. c. 7, sect. 7, a person demanding 

 by menaces any property of another with intent to steal 



ame, is declared to be guilty of felony, and is liable to 

 imprisonment for any term not exceeding three 

 Besides these offences, it is a misdemeanor at common 

 law to threaten another in order to deter him from 

 doing some lawful act, or to compel him to do an un- 

 lawful one, or to extort money or goods from him, or 

 to obtain any other benefit to the person who makes the 

 threat. 



The offence of sending or delivering letters or wi-i' 

 threatening to kill or injure the person to whom they are 



or delivered, or to burn his house, or to accuse him of 

 some heinous crime for the purpose of extorting i 

 was formerly Considered to be high treason -lat.SHen. 

 V., c. 6) ; and under the stat. 9 Geo. I., c. 22, continued 

 for more than a century to be punishable as a capital 

 felony. By the stat. 4 Geo. IV., c. 54, s. 3, it v 

 to be desirable that a less punishment should be substituted 

 for that of death ; and it was enacted that, 'if any i 

 shall knowingly and wilfully send or deliver any writinir. 

 with or without any name or signature subscribed thereto, 

 or with a fictitious name or signature, threatening to kill 

 or murder any person, or to burn or destroy his house, out- 

 house, barns, or stacks of corn or grain, hay or straw, the 



ler shall be guilty of felony, punishable with trans- 

 portation for life, or not less thrui seven years, or im;- 

 ment for any term not exceeding seven years." By a more 



it statute, 7 .V s Geo. IV., c, 2'.), Met. H. it is" enacted 

 that, 'if any person shall knowingly send or deliver any 

 l.tiei or writing, demanding of any person with menaces. 

 and without any reasonable or probable cause, any chattel, 

 money, or valuable security : or if any person shall accuse. 

 or threaten to accuse, or shall knowingly send or deliver 

 any letter or writing accusing or threnteiiini; to accuse. 

 any person of any crime punishable by law with death, 

 transportation, or pillory, or of any assault with intent to 



mil any rape, or of any attempt or endeavour to com- 

 mit any rape, or of any infamous c>nne tin- meaning o 

 which term is specially defined in the !Mh sei 

 same statute), with a view or intent to extort or train from 

 mich person any chattel, money, or valuable sccuritv . 

 such offender shall he guilty of felony, and shall be 

 punishable with transportation for life or not lex* than 

 even years, or with imprisonment not exceeding four 

 yearn, with or without whipping. 



TUKKK. un.K OF, the technical name of the rule 

 in arithmetic by which, three quantities beini: given, the 

 first and second ol one kind, a fourth is found such that 

 the four afc in proportion, or that the first is the arne 



multiple, part, or part*, of i which the third is of 



.rth. 



Ill the earliest mod, -, arc fimiu'. the explana- 



tory headings of this piuve-vs from which the denomina- 

 tion nil- </ //</ has been formed by sbbicviation. 

 most all such . : >m the time uhcll 



systems of commercial arithmetic began to be written, that 

 is, about the beginning of the sixteenth century, i; 

 that time. - nncd 



demonstrations from full definitions ; and it was not ji: 



iry to provide the simple :' :;ding a fouith 



'tional to three ifiven numbers with a 

 or to divide the I from oth< 



ever was done by trail : daily practice, vvli 



parated the rule of three from the other pa: 1 

 and called it th an older term, 



than //'///<;.(. Bishop T 

 his chapter on the . 



:in eomni' this iiKUinii: 



omnium re iae detiibus notis quartum i 



noticiam eu - ah Anthmeticis traditui. 



'in niiri'iim voeat ; quia 1 



reirulis velut c;eteri.s metallis auruill pra-stct.' H 

 Recoiile i 154<) calls it the ' feate of the rule of pi' 

 tions, whiche for his excclleneic is called the gulden rule.' 

 Humphrey Baker l.'ii'J uses the phrase rule of three,' and 

 sayt that 'the philosophers did name it the golden rule.... I nit 

 nowe in these' latter daies, by us it is called the rule of 

 three.' 



The immense variety of questions which are to be solved 

 by finding a fourth proportional del. --iticatiun: 



but they may all be reduced to one form, though it may 

 in particular eases not be the mode of reduc- 



tion. That form is : A produces B ; what will ( 

 It may be that it is money which produces iroo.i- 

 whicli produce money, or money which produces im. 

 or money of one country which produces money of another, 

 or time which produces distance travelled. Xc. ice. X.-. 

 The difficulty to beginners is the reduction of the question 

 given to the above simple form, which must be done 

 what is i or used to be, called the nt/itrtiii'iit of I he 

 question can be made, namely, the writiiiir down the 

 numbers A, B, C, in the proper order, with the mar 

 proportion between them : 



A : B : : C : the answer requiied. 

 It is proper enough to say that this is a question of pro- 

 'ii when numbers only are considered: but absurd 

 when the things represented by the numbers are used in- 

 stead of the numbers. Thus, if fi pence buy 10 apples, 

 7 pence will buy 14 apples, and the number S is t 

 In is to 14, or 5 in the ,-aine fiaction of 7 as 10 is of 14. 

 But it is absurd to say that ") pence bear the same propor- 

 tion to 10 apples that 7 pence bear to 14 apples: simply 

 because ."> pence are not any assignable traction of 10 

 apples. That there is a ri'lutmn i.s true : but that relation 

 is not proportion. Thus, it is not absurd to say, in the 

 common language of the rule. As ~> pence are to 10 

 apples, so are 7 pence to 14 apples; for the tiisl 

 to the second in the same relation as the third to tin- 

 fourth: ;"> pence must, at all rates, do as much I 

 i>urchase of 10 apple* , towaids that ol 1 1 a; 



With this understanding there is no objection to the 

 mon mode of statement, and the proof of the rule is H 

 lows: If A of the fn>t produce H of the second, then, at 

 the same rate of production, 1 of the first must produce. 



n 



-T- of tlie second ; whence C of the first must produce 



II CB 

 C X -7-, or -j- of the second. 



The importance of the mle of tin, I arithme- 



ticians to attach two other rules to it : the inverse rule of 

 three i called by Heeorde. Uakcr. N;e.. the // : and 



the double rule of three. Some of the writers of Cocker'*, 

 school, apparently by an abbreviation of his un; 

 that the rule of tlircc inverse is used ' when less i, 

 more and more requires less;' meaning that ' 

 the third of the given numbers, UM less will be the an 



and i-i' r VtrtH. Thus, suppose that K)/. ha- been lent me 

 for :t months, and I want to know how loin; I ouirht to 

 lend a given sum : other than Ml. in retmii : i \ idently the 

 more I lend, the less the time for which I 01 Lrht to lend 



it. If the sum be !>/., then 8 months is to the tin 



