the chief Difference of each Cafe in the Alternate Rule depends, &c. Not but that I could have inserted many various Examples, as also the Manner of composing Medicines, &c. which, for Brevity, fake I have omitted, and refer those that defire to fee into that Business to Sir Jonas More's Arithmetick, wherein he will find it largely handled. And so I shall conclude with Alligation Alternate, which altho' it gives true Answers to Questions of that Kind, with fome little Variety, according as the Ingredients are more or less in Number; as appears by the foregoing Examples; yet it will not give all the Answers such Questions are capable of, nor perhaps those which suit best with the present Occafion: Nor can this Imperfection be remedied by common Arithmetick; but by an Algebraick Way of arguing it may; whereby all the possible Answers to any Question may be clearly and easily discovered; as shall be shewed further on in the Second Part.

CHAP. Χ.

Of Betals and their Specifick Gravities, &c.

Sect. 1. Of Gold and Silver.

PURE Gold, free from Mixture with other Metals, usually called Fine Gold, is of fuch a Nature and Purity that it will endure the Fire without wasting, although it be kept continually melted: and therefore fome of the ancient Philosophers have supposed 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 waste but a very little by being in the Fire any reasonable time; whereas Copper, Tin, Lead, &. will not only waste, but may be calcined or burnt to a Powder.

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

Standard

Standard for Gold.

22 Carracts of Fine Gold, and 2 Carracts of Copper, being melted together shall be esteemed 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 those Parts be mixed with 2 of the like Parts of Copper; that Mixture is called Standard Gold.

Whence you may observe, that a Carract is not any certain Quantity or Weight, but 24 Part of any Quantity or Weight; and the Minters and Goldsmiths divide it into 4 equal Parts, which they call Grains of a Carract; also they subdivide 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 so in Proportion for a greater or lesser Quantity; which is a less 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 Worseness, 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 small Quantity of fuch Gold as they intend to try (which they call making an Affay) and weigh it very exactly, then they put it into a Crucible, and melt it in a strong Fire, so 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 first Weight, they conclude it is Fine Gold, but if the Loss be 24 Part, they call it 23 Carracts Fine, or one Carract better than Standard: If it have loft4 Parts it is 22 Carracts fine, or Standard: If Parts, it is said 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 Loss by Penny-weights, &c.

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

• That

1

That the English Coin may want neither the Purity nor • Weight required, it is most wisely 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 • some Pieces of all Sorts of Monies coined the foregoing Year, taken at Adventure out of the Mint, and kept under several • Locks, by several Persons, till that Appearance, and then by a 'Jury of 24 able Goldsmiths, in the Presence of the faid Lords, every Piece is most exactly weighed and assay'd.'

6

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

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

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 Put. For 11 Oz. 2 Put. 222 Put. the fine Silver in 12 Oz. of Standard. But 11 Oz. 6 Pwt. = 226 Put. the fine Silver in 12 Oz. accordingto the Question.

First 787 Oz. 14 Put. 6 Grains = 378102 Grains.
And 12 Oz. = 240 Pwt.

Then, As 240 : 226 :: 378102 : 356046 = 741 Oz. 15 Put. 6 20 Grains the fine Silver in that Ingot.

Which at 5 s. 1 d. the Ounce, amounts to 1901. 1s. 6d. and near a Half-penny.

If an Ingot of Gold weighing 115 Oz. 13 Pwt. 18 Grains; be of a Grain worse than Standard: How much Standard Gold is there in it, and what comes it to at 31. 11 s. an Ounce?

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

1

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

But

But 50902,5-144,60937550757,890625 is the Quantity of fine Gold according to the Question. 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. 115. per Ounce; Oz. = 480 Grains; and 31. 115. = 71 s. Consequently 480:71:: 55372,244 &c. : 8190,4777 &c. = 409 1. 105. 5d. very near; being the Value of that Ingot, as was required.

Or the last Question may be other wife wrought thus; 115 Oz. 13 Pwt. 18 Grains = 115,6875. And of a Grain of a Carract is is (viz. the of 4) Then 22-21 = 21,9375. Consequently 22 : 21,9375 :: 115,6875 : 115,358842 . = 115 Oz. η Pwt. 4,244 Grains, &c. as before.

Next for the Value; as 1 : 3,55 :: 115,358842: 409,523,889 = 4091. 105.54 d. very near: as before.

Sect. 2. The Specifick Gravity of Petals, &c.

ITake an Enquiry made about the different Gravities, or Weights of Metals, and other Bodies, to be (not only a Work of Curiosity, but also) of very good Use upon many Occafions. Therefore several Authors have given us such Proportions, or Difference of their Weights, as they are said to have one to another; supposing every one of them to be of the fame Magnitude or Bigness. Some of which I shall here insert.

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 Alsted, in his Encyclopædia, printed 1649, hath them thus: Gold 1875. Quicksilver 1500. Lead 1165. Silver 1040. Copper 910. Iron 806. Tin 750. Honey 150. Water 100. Oil 90. These seem to be taken from those 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. Quicksilver 2850. Lead 2415. Silver 2170 Brass 1890. Iron 1680. Tin 1554.

4. In the Philosophical Transactions, (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 Brass 8349 Caft Brass 8100. Steel 7852. Iron 7643. Tin 7321 Pump-water 1000.

These laft Proportions being approved of and published by Order of the Royal Society seem to be unquestionably true: Nevertheless, because they differ so much from the before-mentioned, (and those from one another) I have for my own Satisfaction made several Experiments of that Kind: And have (Iprefume) obtained the Proportions of Weight that one Body bears to another of the same Bulk or Magnitude, as nicely as the Nature of such Matter, which may be contracted or brought into a lesser Body (viz. either by Drying, or Hammering, or otherwise) will admit of; which are as followeth:

Sound Dry Oak,

Oil Olive,

0,489008 = 0,536569

0,491591 = 0,539345