Question 7. Suppose it were required to mix Malaga at 7 s. 6 đ. the Gallon, with Canary at 6 s. 9 d. the Gallon, Sherry at 5 s. the Gallon, and White Wine at 4s. 3 d. the Gallon; fo that the whole Mixture may be go Gallons; to be fold for 6 s. the Gallon: How much of each fort will compofe that Mixture? Mean Rate 72 d. Then 60 90: :) [ Malaga 90 } { 21 Sherry 6012 21: 31/ 9 : 13- 60 their Sum. the Gallons of Malaga. Canary. 12 Sherry 6018 Or thus, 72 Canary 81 (21 White 51 9 9:13 2 S Malaga. Sherry. White Wine. Either of thefe Ways do equally answer the Queftion, as may be eafily tried by Alligation Medial. As before, &c. Note, The Work of thefe Proportions may be much shortened (especially when there are many Ingredients to be mixed) if you obferve the fame Method as was propofed in the Rule of Fellowship, page 99, &c. I have made Use of the very fame Examples both in Alligation Medial, and Alternate, throughout the three Cafes; being, as I prefume, much better than if they had been different ones; because the Learner may (if he confiders them a little) eafily perceive, not only the Difference between the two Rules, but also wherein the the chief Difference of each Cafe in the Alternate Rule depends, &c. Not but that I could have inferted many various Examples, as also the Manner of compofing Medicines, &c. which, for Brevity fake, I have omitted, and refer thofe 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 Answers 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 Queftions are capable of, nor perhaps thofe 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 Metals and their Specífick Gravities, &c, Sect. 1. Of Gold and Silver. PURE 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 waste but a very little by being in the Fire any reafonable 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. And altho' moft Places differ more or lefs in the Quantity of such Allay, yet in England it is generally agreed on, that, Standard Standard for old. 22 Caracts of Fine Gold, and 2 Caracts of Copper, being melted together, fhall be efteemed the true Standard for Gold Coin, &c. (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. 24 Whence you may obferve, that a Caract is not any certain Quantity or Weight, but Part of any Quantity or Weight; and the Minters and Goldsmiths divide it into 4 equal Parts, which they call Grains of a Caract; also 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 lefs 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 Caracts and Grains of a Caract in Gold, and by Penny-weights in Silver; and is thus difcovered: The Goldsmiths or Refiners, &c. take a small 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 Joft nothing of it's firft Weight, they conclude it is Fine Gold, but if the Lofs be Part, they call it 23 Caracts Fine, or one Caract better than Standard: If it have loft Parts, it is 22 Caracts fine, or Standard: If Parts, it is faid to be 21 Caracts fine, or rather one Caract worse than Standard, and fo 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 several Perfons, till that Appearance; and then by a Jury of 24 able Goldsmiths, in the Prefence of the faid Lords, every Piece is most 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. EXAMPLE 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 II 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 Question. Firft 787 Oz. 14 Pwt. 6 Grains 378102 Grains. And 12 Oz. 240 Pwt. = Then, As 240: 226: 378102: 356046=741 Oz. 15 Pwt. 6 Grains, the fine Silver in that Ingot. Which at 5s. Id. the Ounce, amounts to 190l. 1 s. 6d. and near à Half-penny. be EXAMPLE 2. If an Ingot of Gold weighing 115 Oz. 13 Pwt. 18 Grains, of a Grain worfe than Standard: How much Standard Gold is there in it, and what comes it to at 3. 115. an Ounce? First 115 Oz. 13 Pwt. 18 Grains 55530 Grains Troy. Again, 2313,75 × 22 = 50902,5 ought to be the fine Gold in that Ingot, if it had been Standard: But But 59902,5 144,60937559757,890625 is the Quantity of fine Gold according to the Queftion. Therefore 50902,5: 50757,899625: 55530: 55372,244, &c. Grains 115 Qz. 7 Prut. 4,244, &c. Grains Troy, being the Quantity of Standard Gold in that Ingot, as was required. Next for the Value of it at 3. 11s, per Ounce; 1 Oz. = 480 Grains; and 34 415. = 715. Confequently 480: 71 :: 55372,244, &c.: 8190,4777, &c. = 4091. 10 s. 5 d. very near; being the Value of that Ingot, as was required. Or the last Question may be otherwife wrought thus; 115 Oz. 13 Pwt. 18 Grains 115,6875. And of a Grain of a Caract is (viz. the of 4.) Then 222121,9375. Confequently 22: 21,9375: 115,6875: 115,358842, & = 115 Oz. 7 Pwt. 4,244 Grains, &c. as before. Next for the Value; as 1 : 3,55:: 115,358842: 409,523889 =4091. 10s. 5 d. very near: as before. I Sect. 2. The Specifick Gravity 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 feveral 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 Altead, 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 100. Oil go. These seem to be taken from those of Van Etten's, with fome Additions only. 3. The ingenicus 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. Bras 1890. Iron 1680. Tin 1554. 2 4. lo ་ |