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ALL
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ALL
Quantities mixed, tbo unequally. Multiply the Total of
the Mixture by the leaft Value, fubtraet the ProduS from the total Value ; and the Remainder is the firft Dividend : Then take the faid leaft Value from the grcateft valued Ingredient, and the Remainder is the firft Divifor. The Quotient of this Divifion fhevvs the Quantity of the high- eft-pric'd Ingredient, and the other is the Complement to the Whole. And when more Ingredients than two are in the Compofition, the Divifors are the fevers! Remains of the leaft Value, taken from the other : The Dividends are the Remains left upon the Divifions, till none remain there ; which will be one fhort of the Number of Ingredients : and this defective Ingredient is to be fupplied as a Comple- ment ; and in Divifion, no more muft be taken in every Quotient, than that there may remain enough for the other Divifors ; and the laft to leave nothing remaining. See Di- vision. .
Alligation Alternate, is when the Rates or Qualities of divers Simples are given ; and the Quantity of each is required neceffary to make a Mixture of the given Rate or Quality.
Alligation Alternate, mews the due Proportion of feveral Ingredients ; and counter-changes the Places of fuch Excef- fes or Differences as arife between the mean Price and the Extremes ; afcribirig that to the greater Extreme, which pro ceeds from the letter ; and contrarily.
The Rules which obtain in Alligation Alternate, are as follow.
Every greater Extreme to be linked with one leffer.
If either of the Extremes be fingle, and the other Ex- tremes plural ; the fingle Extreme to be linked to all the reft.
If both greater and leffer Extremes be not plural, they may be linked fo diverfly, that feveral Differences may be taken, and a Variety of Anfwers be made to the Queftion, yet all true : But if one of the Extremes be fingle, there can be but one Anfwer.
The Numbers being linked, take the Difference of each from the mean or common Price ; and place this difference againft the Number it is linked to, alternately.
Every Number linked with more than one, muft have all the Differences of the Numbers it is linked to, fet againft it.
Thofe Differences refolve the Queftion, when the Price of every of the Ingredients is given without their Quantities ; and the Demand is to mix them fo as to fell a certain Quantity at a mean Rate.
But when the Quantity of one, with the Price of all the Ingredients is given ; and the Demand is to know the Quantities of the other Ingredients ; then, the Rule of Three is to be ufed.
And when the Price of every Ingredient is given, without any of their Quantities, and the Demand is to make up a certain Quantity to be fold at a mean Rate ; then all the Differences added together will be the firft Number in the Rule of Three ; the whole Quantity to be mixed the fe- cond Number ; and each Difference apart the feveral third Numbers : And fo many Sorts mixed, fo many Operations of the Rule of Three. See Rule of Three.
We fhall add an Example, wherein both the Kinds of
Alligation have place. Suppofe a Mixture of Wine of
119 Quarts, required to be made of Wines of the following Prices 7 d. 8 d. i$d. and I'jd. per Quart ; and fo, as that the Whole may be afforded at izd. per Quart.
Having linked 8 to 14, and 7 to I 5, and counterchang'd their Difference from the common Price, 12 d. the Sum of their Difference is found to be 14 ; by which dividing 119, the Quotient is 8f 4 -, or 8;, or for conveniency in Opera- tion, *f.
Quarts. 8?» ^4-;==-J = I7
14S3 -i.J+4= 6 !-=34
7?4 -tJ-f-3 = ! T=*5r
15S 5 i i+5 = 't = 4*i
ALLIOTH, in Aftronomy, a Star in the Tail of the Great Bear, whofe Obfervarion is much ufed at Sea. See Star.
Its Longitude, Latitude, &c. fee among the reft of Ur- sa Major- To find the Latitude, or Elevation of the 'Pole by this Star. See Latitude, and Pole.
ALLOCATION, Allocatio, the admitting, or allow- in" of an Article in an Account ; and palling it as fuch. See Account.
The Word is form'd of the Latin Alloco.
Allocation is alfo an Allowance made upon an Ac- count ; ufed in the Exchequer. See Allocatione.
ALLOCATIONE Facienda, a Writ direfted to the LordTrcafurer and Barons of the Exchequer, upon the Com-
plaint of fome Accountant ; commanding them to allow him fuch Sums as he hath in execution of his Office lawful- ly expended.
ALLODIAL, Allodian, in antient Cuftoms.. Terra
Allodia, or Allodial Land, is that whereof a Perfon has the abfolute Property ; or which he holds without pay- ing any Service or Acknowledgment to any Superior Lord. See Property, $$c.
Such an Inheritance is Allodial, i. e. not fubjecf to any Charge, Service, t£e. See Free Land.
In this Senfe, Allodial ftands oppofed to Feudal, or Bene- ficiary. See Fee, Benefice, &c. — See alfo Allodium.
ALLODIUM, Allode, Allodus, or Alleud, Land held of a Man's own Right. — Bollandus explains Allodium to be c Prt£diu?n, feu qtidevis poffefjh libera jurifque proprii & non in Fcudam Clientelari onere aceepta. See Allodial.
After the Conqueft of the Gauls, the Lands were divided in two manners, viz. into Benefices, Beneficia 5 and Allodia.
Benefices, coniifted in Lands given by the King to his Officers and Soldiers ; either for Life, or for a Time fixed. See Benefice.
Allodes, or Attends, were fuch Lands as were left in Pro- perty to the antient Poffeffors. — The 6zd Title of the Salic Law, is, 2)c Aliodis ; where the Word fignifies Hereditary Lands, or thofe derived from a Man's Anceftors. Whence, Allodittm and 'Patrimcnium are frequently ufed indifcrimi- nately. Sec Patrimony.
In the antient Capitulars of Charlemaign and his Succef- fors, we find Allode conftantly oppofed to Fee 5 but, toward the Period of the fecond Race of Kings, it loft the Prero- gative 5 the Feudal Lords obliging the Proprietors of Allo- dial Lands to hold of them for the future. The fame Change alfo happened in Germany, &c. See Tenure.
The Ufurpation of tke Feudal Lords over the Allodial Lands, went fo far, that they were almoft all either fubjecV ed to 'em, or converted into Fees : Whence the Maxim, Nulla Terra fine %)omino, No Land without a Lord.
The Origin of the Word is infinitely controverted. CaJJi- neuve fays, it is almoft as obfeure as the Head of the Nile. Few of the European Languages, but one Etymologift or other has derived it from.
ALLONGE, in Fencing, a Thruft, or Pafs at the Ene- my. See Pass, Guard, 0£c.
The Word is French, form'd of the Verb Allonger, to lengthen out a thing by piecing another to it.
ALLOTTING, or Allotment of Goods, in Matters of Commerce, is when a Ship's Cargo is divided into feveral Parts, to be bought by divers Perfons, whofe Names are wrote on as many Pieces of Paper, which are apply'd by an indifferent Perfon to the feveral Lots or Parcels ; by which means, the Goods are divided without Partiality ; every Man having the Parcel which the Lot with his Name on, is appropriated to.
ALLOT, or Allay, in Matters of Coinage, ?3c. a Pro- portion of a bafer Metal, mingled with a finer, or purer. See Metal, Mixture, £J?c.
Such is the Quantity of Copper mingled with Gold, in the Coining of Species of that Metal. See Gold, Money, cifc.
The Intention of Alloy, is to give the Gold a due hard- nefs, that it may not wafte with wearing ; and to increafe its Weight, fb as to countervail the Charges of Coinage. See Seigneurage.
Gold that has more of this, than it ought to have ; is faid to be of a coarfer or greater Alloy, or below Standard. See Standard.
The Proportion of Alloy for Gold ufed in our Mints, is about a 1 2th Part. See Coining.
The Word feems derived from the French, Loy, Law j in regard the Alloy is fix'd by Law.
ALLUM, or Alum, Alumen, a kind of Mineral Salt, of an acid Tafte, leaving in the Mouth a Senfe of Sweetnefs accompany'd with a confiderable Degree of Aftringency. See Salt.
The antient Naturalifts allow of two forts of Alluni ; the one Native, the other Factitious. — The Natural is found in the Ifland of Milo, being a kind of whitifh Stone, very light, friable and porous 5 and ftreak'd with Filaments reiembling Silver.
The Facfirious Allum, is prepared in different manners, according to the different Materials whereof it is made.
Allum is of divers Kinds, Red, Roman, Citron, 'Pitt- mofe, Saccharine, and •Burnt. The three laft of which, are not proper native Allmns.
England, Italy, and Flanders, are the Countries where the Allum is principally produced. — The Engl/fb Allum, "'" led alfo Roche-Allum, Allumen Rupemn, is made from a bleuifh mineral Stone, frequent in the Hills in Torkfoire and Lancafhire. This Stone they calcine on a Hearth or Kiln ; then fteep it fucceflively in feveral Pits of Water : then boil it for about 24 Hours : Laftly, letting it ftand for about two Hours j the Impurities fubfide, and leave a pure Liquor j which, removed into a Cooler, and ibme Urine added to it,
begins,
