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the chief Difference of each Cafe in the Alternate Rule depends, &c. Not but that I could have inferted many various Examples, as alfo the Manner of compofing Medicines, &c. which, for Brevity, fake I have omitted, and refer those that defire to fee into that Bufinefs to Sir Jonas More's Arithmetick, wherein he will find it largely handled. And fo I fhall conclude with Alligation Alternate, which altho' it gives true Anfwers to Questions of that Kind, with fome little Variety, according as the Ingredients are more or lefs in Number; as appears by the foregoing Examples; yet it will not give all the Anfwers fuch Questions are capable of, nor perhaps those which fuit beft with the prefent Occafion: Nor can this Imperfection be remedied by common Arithmetick; but by an Algebraick Way of arguing it may; whereby all the poffible Anfwers to any Queftion may be clearly and easily discovered; as fhall be fhewed further on in the Second Part.

CHAP. X.

Of Petals and their Specifick Gzavities, &c.

Sect. 1. Of Gold and Silver.

OURE Gold, free from Mixture with other Metals, ufually called Fine Gold, is of fuch a Nature and Purity that it will endure the Fire without wafting, although it be kept continually melted: and therefore fome of the ancient Philofophers have fuppofed the Sun to be a Globe of liquid or melted Gold.

Silver having not the Purity of Gold, will not endure the Fire like it: Yet Fine Silver will wafte but a very little by being in the Fire any reasonable time; whereas Copper, Tin, Lead, &c. will not only wafte, but may be calcined or burnt to a Powder.

Both Gold and Silver in their Purity, are fo very flexible or foft (like new Lead, &c.) that they are not fo useful either in Coin, or otherwife (except to beat in Leaf-Gold or Silver) as when they are allay'd, or mixed and hardened with Copper or Brafs. And altho' moft Places differ more or lefs in the Quantity of fuch Allay, yet in England it is generally agreed on, that,

Standard

Standard for Gold.

zz Carracts of Fine Gold, and 2 Carracts of Copper, being melted together fhall be efteemed the true Standard for Gold Coin,

(The French and Spanish Gold being very near of the fame Standard.) That is, if any Quantity or Weight of Fine Gold, be divided into Twenty-four equal Parts, and 22 of thofe Parts be mixed with 2 of the like Parts of Copper; that Mixture is called Standard Gold.

Whence you may obferve, that a Carract is not any certain Quantity or Weight, but 4 Part of any Quantity or Weight; and the Minters and Goldfmiths divide it into 4 equal Parts, which they call Grains of a Carract; alfo they fubdivide one of those Grains, into Halves, Quarters, &c.

Standard for Silver.

Eleven Ounces and Two Penny-weight of Fine Silver, and Eighteen Penny-weight of Copper being melted together, is esteemed the true Standard for Silver Coin, called Sterling Silver. And fo in Proportion for a greater or leffer Quantity; which is a lefs Proportion of Allay for Silver, than the other is for Gold.

Note, When either Silver or Gold is finer than Standard, it is called Better; if coarfer, it is called Worfe; and that Betterness or Worfeness, is reckoned by Carracts and Grains of a Carract in Gold, and by Penny-weights in Silver; and is thus discovered: The Goldsmiths or Refiners, &c. take a fmall Quantity of fuch Gold as they intend to try (which they call making an Assay) and weigh it very exactly, then they put it into a Crucible, and melt it in a strong Fire, fo long, that if there be any Copper, or other Allay mixt with it, that Allay may be confumed or burnt away: When it is cold they weigh it very exactly again, and if it have loft nothing of it's firft Weight, they conclude it is Fine Gold, but if the Lofs be 2 Part, they call it 23 Carracts Fine, or one Carract better than Standard: If it have loft Parts it is 22 Carraets fine, or Standard: If Parts, it is faid to be 21 Carracts fine, or rather one Carract worse than Standard, and so in Proportion as it happens to be better or worse.

In the fame Manner they make their Affay on Silver, only they compute it's Lofs by Penny-weights, &c.

The Author of the Prefent State of England, mentioned before (page 32.) fays,

• That

That the English Coin may want neither the Purity nor 'Weight required, it is moft wifely and carefully provided, that once every Year the chief Officers of the Mint appear before the • Lords of the Council in the Star-Chamber at Westminster, with fome Pieces of all Sorts of Monies coined the foregoing Year, 'taken at Adventure out of the Mint, and kept under feveral Locks, by feveral Perfons, till that Appearance, and then by a Jury of 24 able Goldsmiths, in the Prefence of the faid Lords, every Piece is moft exactly weighed and affay'd.'

This, if it were conftantly practifed, would keep our Coin to it's true Standard, &c.

Many pretty Questions may be started concerning the Fineness of Gold and Silver, &c.

[blocks in formation]

If an Ingot of Silver weighing 787 Oz. 14 Pwt. 6 Grains, be 11 Oz. 6 Pwt. fine; How much fine Silver is there in it, and what amounts it to, at 5 s. 1 d. the Ounce?

This Ingot is better than Standard by 4 Pwt. For 11 Oz. 2 Pwt. 222 Pwt. the fine Silver in 12 Oz. of Standard. But 11 Oz. 6 Pwt.226 Pwt. the fine Silver in 12 Oz. according to the Queftion.

15

Firft 787 Oz. 14 Pwt. 6 Grains

And 12 Oz. 240 Pwt.

378102 Grains.

Then, As 240: 226: 378102: 356046 741 Oz.
Pwt. 6 Grains the fine Silver in that Ingot.

Which at 5 s. 1 d. the Ounce, amounts to 190l. 1 s. 6d. and near a Half-penny.

[blocks in formation]

If an Ingot of Gold weighing 115 Oz. 13 Pwt. 18 Grains; be of a Grain worfe than Standard: How much Standard Gold: is there in it, and what comes it to at 3 l. 11 s. an Ounce?

Firft 115 Oz. 13 Pwt. 18 Grains 55530 Grains Troy.
Then 24) 55530 (2313,75 = a Carract of that Quantity.
And 4) 2313,75 (578,4375a Grain of that Carract.
Confequently 4) 578,4375 (144,609375 of a Grain.

Again, 2313,75 x 22 50902,5 ought to be the fine Gold in that Ingot, if it had been Standard :

But

But 50902,5144,60937550757,890625 is the Quantity of fine Gold according to the Queftion. Therefore 509025: 50757,890625 :: 55530: 55372,244, &c. Grains = 115 Oz. 7 Pwt. 4,244 &c. Grains Troy, being the Quantity of Standard Gold in that Ingot, as was required.

Next for the Value of it at 31. 11 s. per Ounce; r Oz. 480 Grains; and 3 l. 11 s. = 71 S. Confequently 480:71 :: 55372,244 c.: 8190,4777 &c. 409 l. 10 s. 5 d. very near; being the Value of that Ingot, as was required.

13

Or the laft Queftion may be other wife wrought thus; 115 Oz. Pwt. 18 Grains 115,6875. And of a Grain of a Carract is (viz. the 4 of 4) Then 222121,9375. Confequently 22: 21,9375 :: 115,6875: 115,358842 &c. =115 Oz. 7 Pwt. 4,244 Grains, &c. as before.

Next for the Value; as : 3,55 :: 115,358842: 409,523,889 =4097. 105.5 d. very near: as before.

Sect. 2. The Specifick Gavity of Metals, &c.

Take an Enquiry made about the different Gravities, or Weights of Metals, and other Bodies, to be (not only a Work of Curiofity, but alfo) of very good Ufe upon many Occafions. Therefore several Authors have given us fuch Proportions, or Difference of their Weights, as they are faid to have one to another; fuppofing every one of them to be of the fame Magnitude or Bignefs. Some of which I fhall here infert.

1. Henry van Etten, in his Mathematical Recreations, printed Anno 1633, fets down the Proportion of their Weights thus; Gold 1875. Lead 1165. Silver 1040. Copper 910. Iron 810. Tin 750. Water 100.

2. One Alfted, in his Encyclopædia, printed 1649, hath them thus: Gold 1875. Quickfilver 1500. Lead 1165. Silver 1040 . Copper 910. Iron 806. Tin 750. Honey 150. Water roo. Oil go. Thefe feem to be taken from thofe of Van Etten's, with fome Additions only.

3. The ingenious Mr Oughtred, in his Circles of Proportions, printed Anno 1660, hath their Proportions (according to the Experiments of one Marinus Ghetaldi, in his Tract called Archimedes Promotus) thus: Gold 3990. Quickfilver 2850 ̊. Lead 2415`. Silver 2170. Brafs 1890. Iron 1680, Tin 155.4.

4. In the Philofophical Tranfactions, (Number 169 and 199) there is an Account of a great many Experiments of this Kind; from whence I collected these following, viz. Gold 18888 Mercury 14019. Lead 11343. Silver 11087. Copper 8843 Hammered Brafs 8349. Caft Brafs 8100. Steel 7852. Iron 7643. Tin 7321. Pump-water 1000.

Thefe laft Proportions being approved of and published by Order of the Royal Society feem to be unquestionably true: Neverthelefs, because they differ fo much from the before-mentioned, (and thofe from one another) I have for my own Satisfaction made feveral Experiments of that Kind: And have (I prefume) obtained the Proportions of Weight that one Body bears to another of the fame Bulk or Magnitude, as nicely as the Nature of fuch Matter, which may be contracted or brought into a leffer Body (viz. either by Drying, or Hammering, or otherwife) will admit of; which are as followeth :

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