ARITHMETIC 
 Da/z^ SILVERSMITH 
 
 William Jockin 
 
 D.VAN NO STRAND COMPANY 
 
 NEW YORK 
 
FRANKLIN INSTITUTE LIBRARY 
 
 PHILADELPHIA, PA. 
 
 REFERENCE 
 
The Arithmetic 
 
 of the 
 
 Gold and Silversmith 
 
 PREPARED FOR THE USE OF JEWELERS, FOUNDERS, MER- 
 CHANTS, ETC., ESPECIALLY FOR THOSE ENGAGED IN 
 THE CONVERSION AND ALLOYING OF GOLD 
 OR OTHER METALS, THE MIXING OF 
 VARIOUS SUBSTANCES, ETC. 
 
 BY 
 
 WILLIAM JOCKIN 
 
 NEW YORK 
 
 D. VAN NOSTRAND COMPANY 
 
 23 MURRAY AND 27 WARREN STREETS 
 1906 
 
CONTENTS 
 
 PAGE 
 
 Preliminary Definitions 1 
 
 Fineness of Gold 6 
 
 Weights 8 
 
 Simple Proportions 9 
 
 Percentage 13 
 
 Examples 18 
 
 Problems of Conversion and Alloying 20 
 
 Examples 25 
 
 Examples of the 1000 Part Scale 28 
 
 Examples of all kinds 40 
 
 Melting Points of Metals 44 
 
 Examples for Exercise 51 
 
 European Laws Relating to Fineness of Gold and 
 
 Silver 55 
 
u J 
 
PREFACE 
 
 Many works on goldsmithing have been written 
 for the practical jeweler, furnished with tables and 
 recipes for making alloys of gold and silver. Such 
 tables and recipes, however, do not answer all ques- 
 tions which may arise in alloying or calculating the 
 value of gold. Among other serious drawbacks, the 
 tables and recipes being restricted, the artisan is 
 often compelled to make a choice between such as 
 do not exactly suit his needs. Again, the constant 
 use of and reliance on them make his mathematical 
 knowledge dull, which we can see from his strange 
 questions made in this regard, and still more from 
 the incorrect answers given to him by men who 
 should know better. 
 
 A mere elementary knowledge of arithmetic is 
 amply sufficient to solve the most comphcated 
 problems in alloying and conversion which occur 
 in the work-shop. 
 
 On investigating the matter, the writer has found 
 a scarcity of treatises on this subject, and hence the 
 necessity for a special manual which will teach the 
 workman, who has a knowledge of elementary 
 arithmetic, to easily solve all questions of conver- 
 sion and alloying which may present themselves 
 in his trade. 
 
vi PREFACE 
 
 Such knowledge is of importance not only to 
 every jeweler, but also to all who have to alloy with 
 baser metals, or mix different substances, dry or 
 liquid, and for that purpose I have compiled a series 
 of the most simple and useful rules. As there is no 
 necessity of a manual on the rules of elementary 
 arithmetic, it being supposed that every man who 
 nowadays learns a trade has a knowledge of them, 
 they are explained here only synoptically, my aim 
 being to show how to take advantage of that knowl- 
 edge of arithmetic to solve all the so-called difficult 
 problems in conversion. 
 
 Wm. Jockin. 
 
PRELIMINARY DEFINITIONS 
 
 1. The correct solving of problems in alloying 
 requiring no special knowledge of mathematics, 
 and being of great importance to every person who 
 has to do with it, there should not be a single one 
 who makes an alloy of gold, etc., by guesswork. 
 One of the reasons why so many are at a loss to make 
 the required calculations, although they no doubt 
 possess the necessary knowledge of arithmetic, may 
 be the fact that the primary school books generally 
 contain problems having reference only to articles 
 of commerce, and rarely speak about technical sub- 
 jects such as alloys, or the value of gold or other 
 alloys. In later days some find it difficult to apply 
 the arithmetical rules learned in school to problems 
 of conversion of metals and the Uke, especially when 
 they contain the Asiatic word karat, which sounds 
 so very mysterious and of which many do not under- 
 stand the correct meaning. We will try to enhghten 
 them. 
 
 2. Karat. This word, when expressing the fine- 
 ness of gold, as in all questions pertaining to the 
 problems, means nothing else but 'part. Thus if 
 we say 14-part or 14-karat gold, it is exactly the 
 same thing, if we have in mind or using the 24-karat 
 scale. It represents no weight. 
 
 The reason why, by preference, the word karat is 
 still used, is to clearly designate what scale of fine- 
 
2 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 ness we are using, there being two different scales 
 adopted in the goldsmith's trade. 
 
 Karat, when used in the valuation of precious 
 stones, expresses a weight which in the United 
 States is 3.2 grains; in London, 3.17; in Paris, 3,18. 
 
 3. Scales of Fineness. Only two scales are used in 
 the jewelry trade, to express the fineness of gold, 
 although a scale might be imagined to consist of as 
 many parts as desired. The only science in the use 
 of different scales is, as we shall see later, to find 
 what ratio a certain number of parts of one scale is 
 to that of another. 
 
 4. One of these scales, the oldest, supposes pure 
 gold to consist of 24 equal parts, generally called 
 karats; the karat is subdivided into 32 grains fine, 
 so that the pure gold is composed of 768 degrees of 
 purity. 
 
 Pure silver is supposed to consist of 12 equal parts, 
 karats, each one subdivided into 24 equal parts also 
 called grains fine, so that pure silver is composed of 
 288 degrees of purity. 
 
 This subdivision of fineness of gold is still generally 
 used by jewelers in the United States and England, 
 while that of the silver is practically obsolete. 
 
 By the modern scale, now used alike for gold and 
 silver, the precious metals are supposed to consist 
 of 1000 parts of purity. The degree of fineness of 
 their respective gold and silver coins is determined 
 by all governments by the modern scale. Both 
 scales are here graphically illustrated: scale A the 
 1000 parts, and B the 24 parts or karat scale. 
 
1-5 
 
 "-5 
 
 o - 
 
 I I 
 
 <V tn *) 
 
 Oi rt N 
 
 N OJ to 
 
 a I I 
 
 K <0 <A 
 
 vO ve K K N CO CO 
 
 CO 
 
 « (0 5) 
 
 II n 
 
 II 
 
 N e< w N 
 
 'S^J-irVJ SHXVJ10JXXN3MX 
 
 KARATS oi- PARTS of JCARAT-S CA.LE 
 
 II II II U II II II II II II U K » <> II II « " <■ " ') II " 'I 
 
 a<0^*^m^^Q<o^^■om«y<aooNlr>'OSJS^S^l^2^i 
 SC)Oioo«QNkN««'0<0"0'»'»"5<ONK«y>>'K 
 
 I>ECTMAL SCALE. 
 
4 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 5. The smallest subdivisions of A in the illustra- 
 tions are hundredths of thousand, and those of B 
 are of the full karat. The equivalent of one scale 
 to another can be seen approximately enough to 
 give at the first glance an idea of their respective 
 fineness. The illustration is not made to serve as 
 a guide for comparisons, but merely to inculcate the 
 proper idea what scale, fineness, karats, and parts 
 mean. 
 
 6. The illustration further shows 24 ingots repre- 
 senting different grades of fineness. The black 
 parts of the ingots indicate the amount of pure gold 
 contained in each of them, the clear white parts 
 represent the amount of alloy (in gold, any baser 
 metal than gold). In the estimation of its worth 
 the alloy is considered to have no value. 
 
 7. The upper ingot thus shows pure gold, i.e. gold 
 of 24 karats or 1000 parts fine, as written in the 
 columns on the left side. There is not a single part 
 of alloy in such gold. The one underneath contains 
 23 karats of gold and 1 part of alloy. 
 
 8. It is a pecuharity of the scale B that we say 
 karats of gold and parts of alloy, not karats of alloy. 
 However, by using scale A we say parts of gold and 
 parts of alloy. The third ingot contains 22 karats 
 of gold, 2 parts of alloy, or, according to scale A, 
 916.66 parts of gold, and 83.33 of alloy, and so forth. 
 
 9. Arithmetical Signs. Although we suppose most 
 every jeweler to remember the signs of arithmetic, 
 nevertheless it will do no harm to explain them 
 here in brief. 
 
PRELIMINARY DEFINITIONS 
 
 5 
 
 The sign + is called plus, and signifies addition. 
 Thus 7 + 3 is 10. 
 
 The sign — is called minus, and signifies subtrac- 
 tion. 
 Thus 7-3 is 4. 
 
 The sign X signifies multiplication. 
 Thus 7X3 is 21. 
 
 The sign -r- signifies division. Division is also 
 represented by placing the divisor under the divi- 
 dend, in the form of a fraction. 
 
 Thus7-f-3, or I is 2^. 
 
 The sign = is that of equality, and denotes that 
 two quantities between which it is placed are equal 
 to each other. 
 
 Thus 7 + 3 = 10; 7-3 = 4; 7x3 = 21, etc. 
 
 The signs : :: : denote proportion. Thus 4:2::6:3 
 is to be read, as 4 is to 2, so is 6 to 3 ; the signs placed 
 in this order indicate that 4 stands in the same ratio 
 to 2 as 6 stands to 3. Many use the sign = (of 
 equality) for the sign :: (double colon). 
 
 The sign ? represents the unknown quantity, some- 
 times called the fourth term. Often the letter x is 
 used instead of the query sign (?), or even a simple 
 dash. Thus 4:3 ::6:?, or 4:3 = 6:x, wherein ? and x 
 represent the unknown or fourth term. 
 
 The sign % signifies per cent, by the hundred, and 
 %o per mil, by the thousand. Thus 3% means 3 
 parts of every 100 parts; 3%o means 3 parts for 
 every 1000 parts. 
 
6 
 
 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 FINENESS OF GOLD 
 
 10. We presuppose every man who attempts 
 alloying gold to thoroughly understand the methods 
 of testing its fineness, a chemical process, the descrip- 
 tion of which hardly belongs to the subject of arith- 
 metic and is therefore omitted here. 
 
 11. Gold Coin, which is extensively used in the 
 alloying of gold, has the following value and legal 
 weight : 
 
 United States Gold Coins 
 
 
 Diameter. 
 
 Thiclsness. 
 
 Legal Weight. 
 
 Grains. 
 
 Grams. 
 
 Dollar $1.00 
 
 Quarter Eagle. ... 2.50 
 Three Dollars .... 3.00 
 
 Half Eagle 5.00 
 
 Eagle 10.00 
 
 Double Eagle . . . .20.00 
 
 Inch. 
 
 0.55 
 
 0.75 
 
 0.8 
 
 0.85 
 
 1.05 
 
 1.35 
 
 Inch. 
 
 0.018 
 0.034 
 0.034 
 0.046 
 0.060 
 0.077 
 
 25.8 
 64.5 
 77.4 
 
 129 
 
 258 
 
 516 
 
 1.672 
 4.179 
 5.015 
 8.359 
 16.718 
 33.436 
 
 United States coin gold contains 900 parts of pure 
 gold and 100 parts of alloy. Its value is that of 
 pure gold only ; the cost of the alloy and of the coinage 
 being borne by the Government. 23.22 grains of 
 pure gold is worth $1.00, so that 1 grain is worth 
 4.3 cent. 
 
FINENESS OF GOLD 
 
 7 
 
 Value of Gold based upon the United States 
 Gold Coin 
 
 Karats 
 Fine. 
 
 Thousandths 
 Fine. 
 
 23.22 grains = 1.504665 grams 
 
 1 grain 
 
 1 gram 
 
 1 grain 
 
 1 gram 
 
 1 gram 
 
 1 pennyweight 
 
 1 decigram 
 
 1 decigram 
 
 24 
 24 
 24 
 1 
 1 
 
 1 
 1 
 
 1000 
 1000 
 1000 
 
 12. Gold Coins of Foreign Countries. Austria, 
 quadruple ducat and the ducat, 986 fine; ten-crown 
 pieces, 900 fine. 
 
 France, 5, 10, 20, 50 and 100 franc pieces, 900 fine; 
 155 pieces of 20 francs weigh 1 kilogram. 
 
 Great Britain, sovereign, pound sterling, 20 shill- 
 ings, 916.66 fine (22 karats). 
 
 Germany, all gold coin 900 fine. 
 
 Russia, I imperial or 5 roubles before the year 
 1886, also 3 roubles, 916.66 fine (22 kt.). After 1886, 
 imperials (10 roubles) and J imperials (5 roubles), 
 900 fine. 
 
 Spain, 20 and 10 pesetas, 900 fine. 
 
 From the foregoing we see that the modern gold 
 coin of the United States and the great powers is 
 established upon the thousand part scale. 
 
8 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 WEIGHTS 
 
 13. In the United States and England and her 
 possessions, troy weight is used for gold and silver; 
 it consists as follows: 
 
 Troy Weight (United States and British). 
 24 grains=l pennyweight (dwt.). 
 20 pennyweight (480 grains)-! ounce (oz.). 
 12 ounces (240 pennyweights, or 5760 grains) = 
 1 pound (lb.). The latter is only imaginary. 
 
 14. Avoirdupois or Commercial Weight (United 
 States and British). 
 
 27.34375 grains=l dram. 
 16 drams = 1 ounce 
 16 ounces = 1 pound 
 
 = 437t grains. 
 
 = 256 drams =7000 grains. 
 
 A troy pound = 0.82286 avoirdupois pound. 
 
 An avoirdupois pound = 1.21528 troy pound. 
 
 A troy oz. = 1.09714 avoirdupois oz. 
 
 An avoirdupois oz. = 0.911458 troy oz. 
 
 The grain of the troy, apothecaries' and avoirdu- 
 pois weights is equal. 
 
 15. Metric Weights. The gram is the basis of 
 the French weights, and is the weight of a cubic 
 centimeter of distilled water at its maximum 
 density. 
 
SIMPLE PROPORTIONS 9 
 
 1 milligram =yoVogni- =0.015432 grains. 
 1 centigram = S^- =0.15432 grains. 
 1 decigram - to g^. = 1.5432 grains. 
 1 gram 15.432 grains. 
 
 1 decagram = 10 gms. - 1.54.32 grs. = 
 
 0.022046 lb. av. 
 
 1 hectogram- 100 gms. = 1543.2 grs. = 0.22046 lb. av. 
 1 kilogram = 1000 gms. = 15432 grs. = 2.2046 lb. av. 
 
 These weights are used indiscriminately for gold, 
 apothecaries' and commercial calculations. 
 
 SIMPLE PROPORTIONS 
 
 16. To the category of simple proportions, also 
 called single rule of three, belong all problems in 
 which three quantities are proportionally combined 
 in order to find the fourth one, or in other words, 
 all problems which can be solved by simple propor- 
 tion. By this rule questions of conversion from 
 one scale to another can be readily solved. 
 
 17. Ex. To how many parts of the modern scale 
 corresponds an ingot of gold 22 karats fine? 
 
 Explanation. Here we have three known quan- 
 tities of which two numbers (24 and 1000) are in 
 ratio, and it is required to find the proportional ratio 
 of which only one quantity (22) is given. It is evi- 
 dent that 24 karats contain more thousandths than 
 22 karats, and consequently the answer sought must 
 be less. We thus have the following proportion: 
 
 karats parts 1000X22 
 
 24 : 22 :: 1000 : ? = — — — = 916.66 parts. 
 
10 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 18. Although karats are subdivided into grains 
 fine (4), those who make use of the old scale find it 
 more practical to express fractions of karats by- 
 decimals. As a difference of from 1 to 3 thousandths 
 of fineness can hardly be detected with certainty in 
 testing gold, the laws of most governments allow 
 such difference in the statements of fineness of manu- 
 factured gold articles, and therefore fractions of luViF 
 parts are generally omitted. We therefore can write 
 as the answer to the foregoing problem either 916, 
 or, as the fraction 0.66 is more than half a unit, we 
 write 917. 
 
 19. Ex. If a watch chain 14 karats fine contains 
 336 grains of pure gold, how much should it con- 
 tain if it were of 18 karats? 
 
 Ans. In this problem we have the reverse of the 
 foregoing, as the greater the fineness of the gold the 
 more pure gold it must contain. Consequently we 
 have the following proportions: 
 
 karats grains 
 
 14 : 18 :: 336 : ?= -432 grains. 
 
 14 
 
 The proportion of Ex. 17 may be interpreted thus: 
 Greater : less : : greater : less. 
 In the present one it is. 
 
 Less : greater : : less : greater. 
 
 From which we conclude, that in order to obtain 
 the correct answer, if the unknown or fourth term 
 is to be less than the third term, we multiply the 
 latter with the smaller and divide by the greater of 
 
SIMPLE PROPORTIONS 
 
 11 
 
 the known ratio; if the unknown term is to be greater 
 than the third term, we multiply the latter with the 
 greater and divide by the smaller term of the known 
 ratio, as shown in the foregoing examples. 
 
 20. Ex. A formula for an easy flowing gold 
 solder was recommended to T.M.K. It is composed 
 as follows: fine gold 155 grs., fine silver 210 grs.; 
 copper, 60 grs.; brass, 45 grs. However, before 
 using it on gold works of low karats, he wants to 
 know exactly of what fineness his solder is. How 
 can he find that? 
 
 Ans. Being given: 
 
 Alloy 
 Silver 210 grs. 
 Copper 60 grs. 
 Brass 45 grs. 
 
 Total 315 grs. + 155 grs. of gold = 470 grs. 
 
 Here, 470 grains the total weight, stands in ratio 
 with 24 parts, the total of the scale of fineness; then 
 we find the proportional of 155 grains, the gold 
 contained in the solder. Consequently we have the 
 following simple proportion: 
 
 24X155 
 
 470: 155:: 24:?: 
 
 470 
 
 7.84 karats fineness of the solder. 
 
 21. Ex. How much gold should the above 
 formula contain, to make solder of 6 karats fine? 
 
 Ans. We know that 6 kt. gold contains 18 parts 
 of alloy; consequently, if those 18 parts weigh 315 
 
12 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 grains, we find the proportional of 6 by the follow- 
 ing simple proportion: 
 
 18 : 6 :: 315 : ?= ^^^^^ ^ j^q^ gj-g jg amount of 
 18 ^ 
 
 fine gold required to make the solder 6 kt. fine. 
 
 22. Simplification. In most problems, familiar 
 to the student, he can dispense with writing down 
 the proportion, and solve it by using the following 
 simple reasoning : 
 
 23. Ex. If a 14 kt. gold article contains 60 grains 
 of pure gold how much should it contain if it were of 
 18 kt? 
 
 Explanation. If 14 karats or parts contain 
 
 60 grains of pure gold, 1 karat or part will contain 
 
 ■J5 part of 60 grains or f |; and if 1 part contains f |, 
 
 18 parts or karats must contain 18 times f | (1 part) 
 
 60X18 
 or — — — = / ^.14. 
 14 
 
 As multiplying or dividing both terms of a fraction 
 by the same number does not change the value of 
 the fraction, we can still more simplify the present 
 formula by dividing the numerator and denominator 
 by 2. Hence : 
 
 30 
 
 00X18 
 
 7 
 
 = 77.14. 
 
 24. Ex. If in 16 kt. gold we have 380 grains of 
 pure gold, what is the weight of the alloy? 
 
PERCENTAGE 
 
 13 
 
 Am. 
 
 16 kt. (parts) = 380 grs. 
 1 kt. (parts) -=-W grs. 
 
 1 190 
 
 8 kt. i^,rts) = ^J^ = ^-^ = m><l = m^rs. 
 Id / 
 2 1 
 
 190 grains is the weight of the alloy. 
 
 PERCENTAGE 
 
 25. Many commercial transactions are made by 
 estimating their results to the number 100. It is 
 on that base that interest and value of money, loss 
 and profits, discount, insurance, commission, etc., 
 are calculated. In the jeweler's trade it is often 
 used in estimating the fineness of gold, and in follow- 
 ing recipes, alloys, or mixtures, when it is required 
 to add or subtract a certain percentage from certain 
 quantities, etc. It is practically nothing but a rule 
 of three, which according as the question has been 
 posed may offer some difficulty to the beginner, 
 which we will try to elucidate as follows: 
 
 26. Ex. It is required to find 9% of 429 grains. 
 
 9x429 
 
 Operation. 100 : 429 :: 9 -^^^^ =38.61. 
 
 It being required to take 9% from 429, we have 
 the proportion, as 100 is to its rate 9%, so must be 
 429 to its proportional rate, which we have found 
 to be 38.61; but if the question had been put up thus: 
 
14 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 27. What becomes of the number 429, after hav- 
 ing subtracted 9%? 
 
 we would again as above find the 9% of 429 and 
 then subtract 38.61, which would be 390.39; but 
 the solution can be obtained directly by subtracting 
 the rate of per cent from 100, then make the follow- 
 ing proportion : the number 100 is to 100 less 9% (a 
 smaller number) as is 429 to the proportional, con- 
 sequently also a smaller number. Hence, 
 
 42Q vQl 
 
 100 : 91 : : 429 : ? = - 390.39. 
 
 100 
 
 It is entirely indifferent how we write the propor- 
 tion, or where we place the unknown term, provided 
 we keep in mind the rule of proportion: greater, 
 less, greater, less; or, less, greater, less, greater, 
 according to circumstances. Thus we can make 
 the proportion as follows: 
 
 The greater unsubtracted number, 429, is to the 
 smaller unsubtracted number, 100, as is the unknown 
 subtracted number, ?, to the subtracted number, 91. 
 We have here : 
 
 429:100:: ? : 91. 
 
 greater: less :: greater : less 
 
 Because the unknown term must be greater than 
 the third term, according to 19 we multiply the 
 third term, 91, with the greater, 429, and divide by 
 the smaller term, 100, of the known ratio. Hence, 
 
 390.39. 
 
 100 
 
PERCENTAGE 15 
 
 28. A number of which 9% has been subtracted 
 is 390.39; what was the number? 
 
 Explanation. This question is the reverse of 
 the foregoing, and we therefore reverse the pro- 
 portion, which becomes : 
 
 . ^ o 390.39X100 
 91 : 100 :: 390.39 : ?= =429. 
 
 u X- 
 
 The first term of the proportion is 100 less its 
 rate; hence 91 is to the number 100, as is 390.39 
 to the required proportional. We have here, less, 
 greater, less, greater. We can equally well make 
 the proportion thus: 
 
 100X390.39 , 
 91 : 390.39 :: 100 : ?= = 429, as above. 
 
 less: greater :: less : greater 
 
 29. If instead of subtracting the rate of per cent 
 of a number, it must be added, we can as in 27 solve 
 the question in two different ways, either by first 
 finding the 9% of that number and then add it to 
 the number, or directly, by adding the rate of per 
 cent to 100 and make a proportion accordingly. 
 
 1st method : 
 
 9X429 
 
 100 : 429 ::9 :?= ^^^ = 38.61 38.61 
 
 467.61 
 
 2d method : 
 
 109X429 
 
 100 : 429 :: 109 :? = — =467.61; 
 
 42Q y 1 09 
 
 or, 100 : 109 : : 429 : ? = = 467.61. 
 
16 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 30. After having added 9% to a number it has 
 become 467.61; what was that number? 
 
 Explanation. As 467.61 represents the number 
 which we want to know plus the 9%, the first term 
 of the proportion will be 100 plus the 9%, which is 
 109; consequently we will have: 
 
 109 : 100 :: 467.61 : 1 =™<102 = 429; 
 
 greater : less :: greater : less ^09 
 
 or which is the same, 
 
 467,61:109:: ? : 100=M><i!!^1.429. 
 
 109 
 
 31. From the above questions we can establish 
 the following general rules, taking 9% only as an 
 example. 
 
 (1) If required to find what a number will be 
 after adding 9%, the ratio will be 100 : 109, less : 
 greater. 
 
 (2) If what it was before having added 9%, the 
 ratio will be 109 : 100, greater : less. 
 
 (3) If what it will be after having subtracted 
 9%, the ratio will be 100 : 91, greater: less. 
 
 (4) If what it was before having subtracted 9%, 
 the ratio will be 91 : 100, less : greater. 
 
 32. Simplification. The foregoing operations can 
 be simplified by a judicial placing of the decimal 
 point in all multiplications and divisions; that is, if 
 we remember that in multiplying a number by 10, 
 100, 1000, etc., we have only to add respectively 
 one, two, three zeros, etc., to the number, as for 
 instance 9X10 = 90, 9X100 = 900, 9X1000 = 9000. 
 
PERCENTAGE 17 
 
 If the number has a decimal fraction, as for in- 
 stance 390.39, when multiplying it by 10 no zero 
 is added, as that would not change the value of the 
 number; in this case the decimal point is removed 
 one place to the right, thus: 390.39x10 = 3903.9. 
 When multiplied by 100 the point is moved two 
 places to the right, as 390.39X100=39039, when 
 multiplied by 1000 it is moved three places to the 
 right, but as there are only two figures after the point 
 and its displacement for one figure, as we have seen, 
 is equal to the addition of a zero to an integral num- 
 ber, we add one zero after having moved the point 
 two figures to the right; thus 390.39X1000 = 390390. 
 
 33. Dividing by 10, 100, 1000, etc., is a similar 
 operation, but is done in a reversed manner; i.e., in- 
 stead of moving the decimal point to the right it is 
 moved to the left; thus 390.39^10 = 39.039; 390.39^ 
 100 = 3.9039; 390.39^1000 = 0.39039, etc. If in the 
 integral number there are not figures enough to 
 remove the decimal point, an equivalent number of 
 zeros are placed between the point and the first 
 figure; thus, 390.39^10,000 = 0.039039. 
 
 34. Applying these rules to the foregoing ex- 
 amples, we have: 
 
 If as in 26, to find 9% of 429; simply 0.09X429 = 
 38.61. 
 
 If as in 27, what becomes of the number 429, after 
 having subtracted 9% ? Ans. 4.29 X 91 = 390.39. 
 
 If as in 30, a number of which 9% has been sub- 
 tracted is 390.39; what was that number? Ans. 
 39039^91 = 429. 
 
18 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 If as in 29, after having added 9% to a number it 
 has become 467.61, what was that number? Ans. 
 46761-^109 = 429. , 
 
 EXAMPLES 
 
 35. How much is 90% of 129 grains? 
 Explanation. We are looking for percentage of 
 
 129, which number, being greater than 100, will of 
 course produce a greater unknown fourth term. To 
 obtain this according to 19, we multiply the third 
 term, 90, with the greater and divide by the smaller 
 term of the known ratio (100:129), which we do thus: 
 0.90X129 = 116.1, or which is the same, 90x1.29 = 
 116.1, or, 90X129 = 11610, and then placing the 
 decimal point, which gives 116.1. 
 
 It does not matter, as shown above, whether we 
 multiply or divide first, neither does it matter by 
 which one of the multiplicants we place the decimal 
 point, if only we observe where it ought to be in the 
 product after the multiphcation is finished (see 32). 
 
 36. How much is 10% of 129 grains? 
 
 Ans. -\Y- = 12.9, or, we write directly 12.9 (see 32). 
 
 Verification. 129X90% = 116.1 
 129X10%= 12.9 
 
 100% = 129 
 
 37. How much is 15% of a half eagle whose 
 weight is 129 grains? Ans. 129X0.15 = 19.35 grs. 
 
 38. Per mil, %q. The same rules can be followed 
 in calculations of per mil (%o). 
 
EXAMPLES 
 
 19 
 
 39. Ex. How much is 9%o of the number 4650? 
 Explanation. We first find how many times 
 
 1000 is contained in the number 4650. This division 
 we do according to rule 33 by placing a decimal 
 point to the left, then multiply the quotient by 
 the rate. Hence: 
 
 4.650X9 = 41.85 
 
 40. Ex. How much is 9%o of the number 763? 
 Ans. iVVo =P-763 X 9 = 6.867 
 
 41. Ex. How much is 24%^ of the number 3205? 
 Ans. 3.205x24 = 76.92 
 
 42. Ex. How much is 24%^ of the number 850? 
 Ans. 0.850x24 = 20.4 
 
 43. From the fact that the karat scale stands to 
 the modern scale as 24 : 1000 or 24%o, the above 
 operations can be followed in problems where it is 
 required to convert fineness of the modern scale into 
 the karat scale. 
 
 44. Ex. What fineness in karat represents an 
 article of gold 500 fine? 
 
 Ans. 0.500X24 = 12 kt. 
 
 45. Ex. What is the equivalent in karats of 735, 
 875, and 900 gold? 
 
 Ans. 0.735 X 24= 17.64 kt. 
 
 0.875X24 = 21 kt. 
 0.900X24 = 21.6 kt. 
 
 The equivalent of 735 is 17.64 kt.; 875 = 21 kt.; 
 900 = 21.6 kt. 
 
20 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 46. The problem of converting the fineness of the 
 karat scale into the modern scale being a reversed 
 question, the operation must consequently also be 
 reversed; i.e., instead of dividing the number of 
 which the equivalent is sought, by 1000, it is mul- 
 tiplied by the latter number, and instead of being 
 multipUed by the rate 24%^, it is divided by that 
 rate. 
 
 47. Ex. What is the equivalent in thousandths 
 of 12 kt., 17.64 kt., 21 kt., 21.6 kt., and 14 kt. gold? 
 
 Ans. HV-=-500, 1-W- = 735, 
 
 1 -0^00 _ 875^ 2 i_6^o 0 _ 900, 1 4_o^oo _ 533 33^ 
 
 The equivalent of 12kt. = 500, of 17.64 = 735, of 
 
 21 = 875, of 21.6 = 900, of 14 = 583i 
 
 PROBLEMS OF CONVERSION AND ALLOYING 
 First Kind 
 
 48. Problems of the first kind are those in which 
 the weight and the fineness of the articles being 
 given, it is desired to know what the fineness of the 
 ingot will be when those articles have been melted 
 together. 
 
 49. To obtain the solution of such problems, we 
 must multiply the weight of the objects by their 
 de gree of fineness, then divide the sum of the products 
 by the total weight of the objects which are used in 
 the melting. The same formulas are applicable to 
 all problems of alloying and mixtures, other than 
 
PROBLEMS OF CONVERSION AND ALLOYING 21 
 
 gold and silver, and their weight may be equivalent 
 to measure, fineness, price, etc. For instance : 
 
 50. Ex. A wine merchant mixes 50 gallons of 
 wine at 50/ the gallon with 25 gallons at 80/: how 
 much a gallon will the mixed wine cost? 
 
 Ans. 50 gal. at 50/= 2500 
 25 gal. at 80/= 2000 
 75 gal. mixed wine cost 4500/. 
 
 One gallon will cost 4500^75=60/. 
 
 51. Ex. A grocer mixed 150 pounds coffee at 30/ 
 with 60 pounds at 24/: how much will the mixed 
 coffee cost per pound? 
 
 Ans. 150 lb. at 30/= 4500/ 
 _601b. at24/= 1440/ 
 210 lb. mixed coffee cost 5940/ 
 
 One pound mixed coffee cost 5940^210=28.29/. 
 
 52. Ex. A founder has melted together 360 
 pounds of copper and 70 pounds of tin. The copper 
 cost 25/ and the tin 52/ a pound: what is the price 
 of one pound of the alloy? 
 
 Ans . 360 lb. of copper at 25/ = 9000/ 
 701b. of tin at 52/ = 3640/ 
 
 4301b. of alloy cost 12640/ 
 One pound of alloy cost 12640^430 = 29.395/ 
 or nearly 29|/. 
 
 53. Ex. A jeweler melts together 2 ounces of 
 gold 10 kt. fine, and 1 ounce of gold 14 kt. fine: 
 of what fineness will be the alloy? 
 
22 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 It must be observed that the word alloy means 
 baser metal, and also a mixture of metals, which 
 latter it expresses here. 
 
 Ans. 2 oz. of gold 10 kt. fine = 20 
 1 oz. of gold 14 kt. fine= 14 
 
 3 oz. 34 
 Alloy = 34 -:-3= llj karats fine. 
 
 The preceding examples have shown that, in 
 order to solve problems of conversion, we must con- 
 sider the karats expressing fineness as if they express 
 price, which in reality is the same thing, as the finer 
 the gold the higher is its value or price, then multiply 
 the karats by the weight of each article of gold, and 
 divide the sum of the products by the total weight 
 of the alloy. 
 
 54. Ex. Three qualities of gold are molten to- 
 gether, 350 grs. 18 kt. fine, 240 grs. 14 kt. fine, and 
 45 grs. 20 kt. fine : of what fineness will be the alloy 
 of gold? 
 
 Ans. 350x18= 6300 
 
 240X14= 3360 
 45X20= 900 
 
 635 10560 
 1 = 10560^635=16.63, nearly 16f kt. fineness of 
 the alloy. 
 
 55. H.K. has 2 half eagles, 1 ounce and 4 dwt. of 
 18 kt., and 2^ ounces of 10 kt. gold. If he melts 
 that together what will be the fineness? 
 
PROBLEMS OF CONVERSION AND ALLOYING 23 
 
 Ans. United States coin gold containing 90% of 
 pure gold is equal to 24X0.9 = 21.6 karats fine. 
 
 2 half eagles = 258 grs.X 21.6= 5572.8 
 1 oz. + 4 dwt. = 576 grs. X 18 - 10368 
 2Joz. =1200 grs.X 10 = 12000 
 
 2034 27940.8 
 Fineness will be = 27940.8 ^2034= 13.245 = 13 and 
 nearly j. 
 
 56. Ex. We have 150 grs. of 8 kt. gold, 35 grs. 
 of 10 kt., 200 grs. of 14 kt., 75 grs. of 17 kt. to be 
 melted together. What will be the fineness of the 
 alloy? 
 
 Ans. 150X 8=1200 
 
 35X10= 350 
 200X14 = 2800 
 75X17=1275 
 
 460 grs. = 5625 
 Alloy = 5625-- 460 grs. = 12.23 or 12, and nearly 
 I kt. fine. 
 
 Problems of the Second Kind 
 
 57. Problems of the second kind are those of 
 which the fineness or value of the various gold 
 articles is given, and of which we want to know 
 what quantity we must take to obtain an alloy of 
 certain fineness or a mixture of a certain value. 
 
 58. To solve problems of this kind we must first 
 observe how much lower in fineness or value will be 
 
24 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 the alloy than the articles of a higher fineness or 
 price, and how much finer or more valuable it will 
 be than the articles which are lower in fineness or 
 cheaper. We must then take of these latter a certain 
 quantity to equalize the loss made upon those of a 
 higher fineness or price. 
 
 59. In such cases where the required degree of 
 fineness is the mean between the articles of higher 
 and lower fineness, we can equalize by taking as 
 much from one article as from the other. But if 
 the required fineness is nearer to that of the article 
 of lower fineness than to those of higher fineness, we 
 must take more from the former (the lower) and 
 less from the latter (the higher). From which we 
 infer that the quantities which we must take are in 
 an inverse ratio between higher and lower fineness. 
 This can be summed up as follows: Take the differ- 
 ences between the required fineness and the articles of 
 higher fineness, and also between the required fineness 
 and the articles of lower fineness; the former indi- 
 cate how many units we must take from the articles 
 of lower fineness, and the latter indicate how many 
 units we must take from those of higher fineness. 
 In other words, they tell us in what proportion the 
 articles must be mixed. 
 
 60. This kind of problems is of an indefinite 
 variety, i.e., they admit of many different solutions, 
 for the resultant proportion may be multiplied by 
 any required number (according to circumstan- 
 ces). 
 
EXAMPLES 
 
 25 
 
 EXAMPLES 
 
 61. A jeweler has 9 kt. and 18 kt. gold with which 
 he desires to make 14 kt. gold : in what proportion 
 must he take of each? 
 
 18 5 difference 
 
 9 4 difference 
 
 According to the above rule he must take the 
 differences between 14 and 9 which is 5, and between 
 14 and 18 which is 4, and place them in a reversed 
 order; those differences then tell him that he must 
 take 5 parts of the 18 kt. gold, and 4 parts of the 
 9 kt. gold. 
 
 62. To prove that our calculation is correct we 
 verify according to Rules 48 and 49 as follows : 
 
 5partsatl8kt.= 90 
 4 parts at 9 kt. = 36 
 
 9 parts = 126 
 
 One part or alloy = 126 ^ 9 - 14 kt. 
 
 Which proves that he must take in the ratio of 
 5 from the higher and 4 from the lower gold. This 
 proportion is equal to 10: 8, to 15: 12, to 20: 16, etc., 
 from which we see that problems of that kind are 
 indefinite (see 60). 
 
 63. Jeweler X has some 12 kt. gold which he wishes 
 to convert into 14 kt. gold, using 18 kt. to do it. 
 He asks a friend how this can be calculated. 
 
 Desired fineness 14 
 
26 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 The friend says that he cannot do it and that in 
 order to convert qualities of gold such as 12 kt. and 
 18 kt. into 14 kt. gold he must know quantities, and 
 have stated on paper how many pennyweights he 
 wishes to convert. 
 
 Rules 57, etc., show that this is not necessary, and 
 that a correct answer can be given by means of a 
 few figures, namely: 
 
 Desired fineness 14^^^ ^ 
 (12 4 
 
 which says that in order to make 14 kt. gold we must 
 take 2 parts of the 18 kt. gold and 4 parts of the 
 12 kt. gold. As stated before (6o and 62), the pro- 
 portion is exactly the. same if we take 1 part to 2; 
 3 to 6; 4 to 8, etc. 
 
 64. We can verify the above according to rules 
 48 and 49. 
 
 2 parts at 18kt. = 36 
 4 parts at 12kt. = 48 
 
 6 parts = 84 
 
 Alloy =-V-= 14 kt. 
 
 65. How many per cent of alloy must be added 
 to a five-dollar piece in order to make 18 kt. gold? 
 
 Ans. According to 46 and 47 we find the equiva- 
 lent of 18 karat in thousandths to be: J-||-^ = 750, 
 750%o gold contains 250 %o of alloy, or, 75% gold 
 contains 25% of alloy; coin gold, or 900%^ gold 
 contains 100%o of alloy, or, which is the same, 90% 
 gold contains 10% of alloy. Consequently, the dif- 
 ference of alloy between coin gold and 18 kt. gold 
 
EXAMPLES 
 
 27 
 
 is of 15%. But let us not confound. It does not mean 
 that 15% of the weight of the coin must be added. 
 To find this we make the following proportions : 
 
 75:90=25:?= ?^ = 30 
 
 3 
 
 which says, if for 75 parts of fine gold we must have 
 25 parts of alloy, then for 90 parts of fine gold there 
 must be 30 parts of alloy in order to make 18 kt. 
 gold. Now, 100 parts of coin gold being composed 
 of 90 pure gold and 10 alloy, we must add 20 parts 
 of alloy, or 20%, in order to convert it to 18 kt. 
 gold, and consequently, to a five-dollar piece, weigh- 
 ing 129 grs., the addition will be, 1.29X20-25.8 grs. 
 
 66. Ex. A jeweler has coin gold and 14 kt. gold 
 to make 18 kt. gold: how much, or in what propor- 
 tion, must he take of each? 
 
 Ans. First, we find the equivalent in karats of 
 900 gold (coin gold), see 43, etc., which is 0.900x24- 
 21,6 kt.; then we have: 
 
 Desired fineness 18^^^^ t ^ 
 (14 3.6 
 
 From which we see that he must take 4 parts of coin 
 
 gold, and 3.6 parts of the 14 kt. gold, or, which is 
 
 the same, 20: 18, or, 40:36, etc. 
 
 Verification, according to 48 and 49: 
 
 4 parts at 21.6= 86.4 
 
 3.6 parts at 14 = 50.4 
 
 7.6 parts = 136.8 
 
 Fineness of alloy = 136.8 ^7.6= 18 kt. 
 
28 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 67. Ex. A grocer has coffee at 30/ and at 22/ 
 a pound, which he wants to mix in order to sell the 
 mixture at 26/ a pound: how much must he take 
 of each quality? He also wants to make a mixture 
 with coffee at 30/ and at 23/ a pound, to sell it at 
 28/ a pound: how much must he take of each? 
 
 Ans. The price as explained in 57, etc., is treated 
 in the same way as the fineness of gold or carats, 
 and consequently we have: 
 
 2fiS30 4 (30 5 
 
 (22 4 (23 2 
 
 which says that for the first mixture he must take 
 4 parts of each, or equal parts, and for the second 
 mixture, or coffee at 28/, he must take 5 parts of 
 coffee at 30/, and 2 parts of coffee at 23/. 
 
 EXAMPLES OF THE 1000 PART SCALE 
 
 68. A jeweler has gold of 950 and of 800; he would 
 like to make with it gold of 900 fineness: what pro- 
 portions must he take? 
 
 Ans. 
 
 Desired 900 
 
 100 difference 
 50 difference 
 
 He must take in the proportion of 100 of the 950 
 and 50 of the 800 gold, or (which is the same) 2 to 1. 
 Verification. 
 
 2 parts at 950 = 1900 
 Ipart at 800= 800 
 
 3 2700 
 Alloy = -^3 ~ = 900, the desired fineness. 
 
EXAMPLES OF THE 1000 PART SCALE 29 
 
 69. Ex. We have gold containing yo^oo =0.005 
 of copper, and some containing -^q%% = 0.2 of copper: 
 what proportions must we melt in order to get an 
 ingot containing i^^o=0.01? 
 
 Ans. J 0.005 0.19 
 
 ^0.2 0.005 
 
 We take in a proportion of 0.19 of the 0.005 and 0.005 
 of the 0.2. 
 
 70. It is easier not to use decimal fractions when 
 expressing the fineness, especially when there is no 
 doubt about the scale we are using. The foregoing 
 example could be written thus: 
 
 ^200 5 
 
 in a proportion as 190 to 5, which is the same as 0.19 
 to 0.005 or foVo to -Joo- 
 
 71. Ex. (of the karat scale). We want to make 
 21 kt. gold by using 18 and 22 kt. gold: what pro- 
 portions must we take of each? 
 
 Ans. (22 3 
 
 "^^18 1 
 
 3 parts of the 22 kt., and 1 part of the 18 kt. gold. 
 
 72. Ex. A wine merchant has wine at 50/ and 
 at 75/ a gallon: how must he mix them to get wine 
 at 60/ a gallon? 
 
 Ans. „A75 10 
 
 ^^150 15 
 
 He must mix in the ratio as 10 : 15, or 2 : 3, etc. 
 
30 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 Verification . 2 X 75 = 1 50 
 3X50 = 150 
 
 5 300 
 1 gal. = ^P = 60/ 
 
 73. If we desire to make an alloy of a certain 
 weight and of a certain fineness, of articles of dif- 
 ferent fineness, we must first find the ratio of the 
 articles; next we make a proportion of which the 
 first term is the sum total of the numbers of the ratio ; 
 the second term, one of the numbers of the ratio; 
 and the third term, the total weight of the ingot : the 
 answer will state how much must be taken of each 
 article. The same rule is apphcable to all kinds of 
 mixtures, if for instance the fineness is considered 
 as price, the weight as measure or quantity. The 
 following examples will explain this: 
 
 74. Ex. A jeweler has 12 kt. and 18 kt. gold 
 with which he wants to make 340 grs. of 14 kt. gold : 
 how much of each quality of gold must he take? 
 
 Desired fineness 14 
 
 6, sum of the numbers 
 of the ratio. 
 
 Having the ratio 4 : 2, we only need by a simple 
 proportion to determine how much of each quality 
 of gold must be taken for the alloy. Hence: 
 
 6 : 4-340 : ?-226§ grs. of the 12 kt. gold 
 and consequently, 
 
 340-226§ =113i of the 18 kt. gold. 
 
EXAMPLES OF THE 1000 PART SCALE 31 
 
 75. Ex. A grocer has coffee at 30/ a pound and 
 at 22/ a pound: how much must he mix of each 
 quahty to obtain 150 pounds at 26/ a pound? 
 
 (20 4 
 
 Mean price 26 1 g 
 
 10 sum of the terms 
 of the ratio. 
 
 Then we have the proportion : 
 
 10 : 4=150 :?=^!^^^-601b. at 20/. 
 10 
 
 and 150-60 = 90 at 30/. 
 
 Verification. 
 
 60X20=1200 
 90X30 = 2700 
 150 3900 
 l = -3_9_Q_o.^26/ price of 1 lb. of the mixed coffee. 
 
 76. In such instances where articles of gold of 
 more than two grades of fineness are being melted 
 together, and two or more of them be of a higher 
 and one of a lower fineness, or two or more be of a 
 lower and one of a higher fineness, or in short, an 
 equal or unequal number of the articles be of a higher 
 or lower fineness than that which we desire to ob- 
 tain by the melting, we must take the differences in 
 the same manner as explained above, observing, 
 however, that the number of the differences which we 
 place after those of higher fineness be equal to the 
 number of the differences which are placed after 
 
32 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 the lower fineness, whatever their number may be. 
 The following examples will make this more clear: 
 
 77. Ex. H. K. has some 18, 12, and 9 kt. gold : 
 how much must he take of each to make 14 kt. gold? 
 
 The differences between the articles of lower fine- 
 ness 14 and 12, 14 and 9, have been placed after the 
 articles of higher fineness 18, and the difference 
 between 14 and 18 has been placed after the 12 and 
 9 ; so that the gold of lower fineness and the gold of 
 higher fineness each have two differences. The cal- 
 culation shows that in order to obtain 14 kt. gold, 
 H. K. must take 7 parts of the 18 kt., 4 parts of the 
 12 kt., and 4 parts of the 9 kt. gold. 
 
 Vekification : 
 
 7x18-126 
 4X12= 48 
 4X9 = 36 
 
 15 210 
 Alloyage = -\V-=14kt. 
 
 78. Ex. A jeweler has 20, 18, 14, and 12 kt. gold 
 which he wants to convert into 14 kt. gold : in what 
 proportion must he take of each? 
 
 Ans. 
 
 2 + 5=7 
 
 4 
 
 4 
 
 Ans. 
 
 2 
 
 2 
 
 6 + 4 = 10 
 
EXAMPLES OF THE 1000 PART SCALE 33 
 
 He must take 2 parts of the 20 kt., 2 of the 18 kt., 
 10 of the 12 kt., and as the mixing of gold of the 
 same fineness does not change the latter, he can add 
 as much of the 14 kt. gold as he desires. 
 
 79. Ex. E. Z. has 20, 18, 16, and 9 kt. gold, with 
 which he wants to make 14 kt. alloy : what propor- 
 tion must he take of each? 
 
 Ans. 
 
 14 
 
 20 5 
 
 18 5 
 
 16 5 
 
 9 2 + 4 + 6-12 
 
 In order to obtain an alloy of 14 kt. fine he must 
 take in the ratio of 12 parts of the 9 kt., 5 parts of the 
 16 kt., 5 parts of the 18 kt., and 5 parts of the 20 kt. 
 gold. 
 
 8o. Ex. 0. K. has 21, 19, 12, and 8 kt. gold, 
 with which he desires to make an alloy 14 kt. fine ; 
 what proportion must he take of each? 
 
 Ans. 
 
 14 
 
 21. 
 19. 
 12. 
 
 He must take 6 parts of the 21, 2 parts of the 19, 
 5 parts of the 12, and 7 parts of the 8 kt. gold. 
 
 It must be observed that here the differences have 
 been exchanged between the extremes of fineness 21 
 and 8, as also between the intermediates 19 and 12. 
 
34 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 8i. If we proceed according to rule 76, the opera- 
 tion will be as follows: 
 
 Here the differences between the desired fineness 
 14, and the articles of higher fineness 21 and 19, have 
 been placed after the articles of higher fineness 21 
 and 19. We have thus obtained the numbers 8, 8, 
 12, 12, or if reduced, 2, 2, 3, 3, which answer the 
 question as well as the numbers obtained through 
 the foregoing operation, 6, 2, 5, 7, which is another 
 proof that the problems of the second kind are of 
 an unlimited solution. 
 
 82; Let us verify both solutions. 
 
 14 
 
 21 
 19 
 12 
 8 
 
 6 + 2- 8 
 
 6 + 2- 8 
 
 7 + 5 = 12 
 7 + 5 = 12 
 
 (80) 
 
 6X21 = 126 
 2X19= 38 
 5X12= 60 
 7X 8= 56 
 
 20 
 
 280 Alloy 
 
 ^2V = 14kt. 
 
 (81) 
 
 8X21 = 168 
 8X19=152 
 12X12 = 144 
 12X 8= 96 
 
 40 
 
 Hence both are correct. 
 
 560 Alloy 
 
 -V/=14 kt. 
 
 83. Ex. Jeweler Q. has a lot of old gold articles 
 
i 
 
 EXAMPLES OF THE 1000 PART SCALE 35 
 
 of different fineness, 6, 10, 12, 14, 18 and 20 kt., of 
 which he wants to make gold 15 kt. fine; what pro- 
 portion must he take of them? 
 
 20 
 
 1+3+5+9=18 
 
 18 
 
 1+3+5+9=18 
 
 14 
 
 5 + 3= 8 
 
 12 
 
 5+3= 8 
 
 10 
 
 5 + 3= 8 
 
 6 
 
 5 + 3= 8 
 
 The differences between the mean 15, 20, and 18, 
 the higher, have been placed after each of the gold 
 of lower fineness, and the differences between the 
 mean 15 and the articles of lower fineness have 
 been placed after the articles of higher fineness. 
 Thus we have obtained the proportion 18 parts 20, 
 18 parts 18, 8 parts 14, 8 parts 12, 8 parts 10, 8 parts 
 6kt. gold. 
 
 84. The case might present itself where gold of 
 two or more grades of fineness is to be melted to- 
 gether and that a given quantity of a certain fine- 
 ness is to be put in the alloy. In that case, we first 
 find in what ratio the mixture must be made accord- 
 ing to the above rules, then by means of the ratio 
 we have thus obtained, we make a simple propor- 
 tion of which the third term is that of the given 
 quantity of the gold of certain fineness which is to 
 be put in the alloy. The following problem is of 
 that kind: 
 
36 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 85. Ex. P. has several gold watch chains of 
 14 kt., weighing 4 dwts., of which he wants to make 
 18 kt. gold, by adding 21 kt. gold, how much must 
 he take of the latter? 
 
 Ans. -,oU4 3 
 
 He must take in the ratio of 3 : 4, and by means 
 of this ratio we make the following simple propor- 
 336x4 
 
 tion: 3:4 = 336:a:= -^ = 448 grs. of the 21 kt. 
 
 3 ^ 
 
 gold are needed for the conversion into 18 kt. gold. 
 Verification. 
 
 336 grs. at 14 kt. - 4704 
 448 grs. at 21 kt. = 9408 
 
 784 14112 
 Alloy = i|ip = 18 kt. 
 
 86. If the weight of articles of different fineness 
 of gold, which are to be melted in an alloy, is given, 
 and we want to know what proportion must be taken 
 from gold of other grades of fineness, in order to 
 obtain an alloyage of given fineness, we should first 
 find the mean fineness of the articles of which the 
 weight is given, then find in what ratio the other 
 articles must be mixed by comparing their respective 
 fineness, and the found mean fineness of the articles 
 of which the weight is determined, with the fineness 
 we expect to obtain by the melting. When this 
 ratio Jias also been found, a simple proportion or 
 single rule of three is made of which the third term 
 
EXAMPLES OF THE 1000 PART SCALE 37 
 
 will be the total weight of the articles which are 
 required to be mixed in the alloy, and the fourth term 
 will give the solution. 
 
 87. Ex. A jeweler has 236 grs. 9kt. and 462 grs. 
 14 kt. gold : how much 20 kt. gold must he add to 
 make 16 kt. gold? 
 
 Ans. 236 X 9=2124 
 
 462X14=6468 
 
 698 8592 
 
 An alloy of the given quantities would he = ^Q%^^'= 
 12.30 kt. This known, it reduces the problem to : 
 he has gold of 12.30 kt. and of 20 kt. with which 
 to make 16 kt. gold. We have then : 
 
 ..U2.30 4 
 
 ^^^20 3.7 
 
 which says that he can make 16 kt. gold by taking 
 4 parts of 12.30 kt., and 3.7 parts of 20 kt.; but he 
 has 698 grs. at 12.30 kt., how much of the 20 kt. 
 must he add to them? 
 
 The following simple proportion will give the 
 answer: 4 : 3.7 = 698 : a; = 645 grs. 
 
 Verification. 
 
 236 grs. at 9 kt. = 2124 
 462 grs. at 14 kt. = 6468 
 645 grs. at 20 kt. = 12900 
 
 1343 21492 
 Alloy = -\V5V-= 16 kt. 
 Hence the foregoing calculation is correct. 
 
38 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 88. In problems of the kind which we are actually 
 explaining, the given quantities might be combined 
 thus, that each one of them in turn becomes an un- 
 known quantity; nevertheless the solutions will be 
 based upon the same principles as those we have 
 already demonstrated. 
 
 89. Ex. By melting together gold of two dif- 
 ferent grades of fineness an alloyage of a total weight 
 of 536 grs. and 14 kt. fine has been obtained; one 
 part of the gold consisted of 220 grs. of 12 kt. fine : 
 what was the weight and fineness of the other part 
 of gold? 
 
 Ans. It is evident that if we subtract from the 
 total of the alloy the weight of the known gold, and 
 if from the total of karats we subtract the total 
 of karats of that known part of gold which has been 
 melted in the alloy, the differences will express 
 respectively the weight of gold and the total of 
 karats which have been added, from which we then 
 obtain the grade of fineness. Hence: 
 
 536 grs. of 14 kt. = 7504 
 
 220 grs. of 12 kt.- 2640 
 
 316 4864 
 which shows that 316 grains of a total of 4864 have 
 been added; its fineness therefore was %yV"= 15.39 kt. 
 
 90. If it be required to know the ratio of the 
 different metals contained in a certain quantity of 
 ingot, we must take each quantity of which the ingot 
 is composed as a numerator of the fractions, which 
 
EXAMPLES OF THE 1000 PART SCALE 39 
 
 each will have the total sum of the mixed quantities 
 for denominator; then we take the part expressed by 
 those fractions from the given quantity of which 
 we want to know the ratio. 
 
 91. Ex. 5 dwts. of gold, 7 dwts. of silver, and 2 
 dwts. of copper have been melted together: in what 
 proportion are those metals represented in 1 dwt. 
 of the ingot? 
 
 Ans. 5 dwts. gold = i\ of 24 grs. = 8.57 grs. 
 7 dwts. silver = = | of 24 grs. = 12 grs. 
 2 dwts. copper =3-^ = } of 24 grs.= 3.43 grs. 
 14 24.00 grs. 
 
 In 24 grains or 1 dwt. of this ingot are contained 
 8.57 grs. of gold, 12 grs. of silver, 3.43 grs. of 
 copper. 
 
 92. The same rules which have been given here 
 for the conversion of gold, as before stated, are also 
 appHcable to silver, and the alloying of other metals 
 and the mixing of liquid or dry substances. They 
 also serve to solve questions where it is required to 
 find the mean of different quantities, whatever be 
 their nature, as for instance the mean of the salaries 
 of workmen, the mean of the work done by several 
 workmen, the mean of time required for work per- 
 formed by several men, etc. The following examples, 
 comprising questions of all kinds, which can be 
 easily solved by the rules we have explained, will 
 soon familiarize the student with their appUca- 
 tion. 
 
40 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 EXAMPLES OF ALL KINDS 
 
 93. Ex. A jeweler has 240 grs. 12 kt., and 312 
 grs. 18 kt. gold, which he melts together, of what 
 fineness will be the alloy? 
 
 Ans. Applying rules 48 and 49, 
 240X12 = 2880- 
 312X18=5616 
 552 8496 
 Alloy = V5¥-= 15.39 kt. 
 Or if we want to express its fineness in grains we must 
 multiply 8496 kt. by 32 grains and divide the pro- 
 
 8496x32 
 
 duct by the weight 552, which is = 492 grs. 
 
 n 552 
 tine. 
 
 94. Ex. I. L. M. & Sons ask, Which is the best 
 alloy you know of in preparing gold for ring making? 
 
 They received from a friend the following formulas : 
 Nine karats. — To 1 ounce of standard or coin 
 
 gold, add 1 ounce, 8 dwts., and 21 grs. of alloy, § of 
 
 copper, and | of silver. 
 
 Ten karats. — To 1 ounce of standard or coin gold, 
 
 add 1 ounce and 4 dwts. of alloy, f of copper, and ^ 
 
 of silver. 
 
 Twelve karats. — To 1 ounce of standard or coin 
 gold, add 16 dwts. and 6 grs. of alloy, § of copper, 
 and ^ of silver. Let us verify the above formulas : 
 
 9 karats: AUoy ^^[^ 
 
 1 oz. or 480 grs. of coin gold contain 10% = 48 grs. 432 
 1 oz, 8 dwts. and 21 grs. of alloy = 693 grs. 
 
 Total of alloy = 741 grs. 
 
EXAMPLES OF ALL KINDS 
 
 41 
 
 Hence the proportion: If 9 parts (kt.) are to repre- 
 sent 432 grains, how many grains must then repre- 
 
 432 X 15 
 
 sent the 15 parts of alloy? 9: 15 = 432: = 
 
 720 grs. should be the total of alloy contained in 
 this gold; consequently the recipe contains 21 grains 
 of alloy too much. 
 
 10 karats: AUoy 
 1 oz. or 480 grs. of coin gold contain 10% = 48 432 
 1 oz. and 4 dwts. of alloy =-576 
 
 Total of alloy = 624 grs. 
 432 X 14 
 
 Hence: 10 : 14=432 : x = — — — =604.8 grs. should 
 
 be the total of alloy contained in this gold; conse- 
 quently the recipe contains 19.2 grains of alloy too 
 much. 
 
 12 karats: Aiioy ^^^l 
 
 1 oz. or 480 grs. of coin gold contain 10% = 48 432 
 16 dwts. and 6 grs. of alloy = 390 
 
 Total of alloy = 438 grs. 
 Hence if 12 parts of gold weigh 432 grains, the 12 
 parts of alloy must have the same weight, conse- 
 quently the recipe contains 6 grains of alloy too 
 much. 
 
 95. In countries which have severe laws concern- 
 ing the accurate statement of fineness of gold, an 
 addition of too much alloy may have serious conse- 
 quences. Let us see how much extra profit has been 
 made by selling a gold article weighing 1173 grains 
 
42 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 for 9 kt. gold when it contains 21 grains of alloy 
 more than required. 
 
 The extra profit having been made only upon 
 21 grains in seUing them for 9 kt., we must find how 
 much pure gold they should have contained, and this 
 multiplied by the price of gold is the amount of extra 
 profit. Therefore : 
 
 kts. grs. 21 y Q 
 
 24:9-21 :x = —^ -7.87 grains; 
 
 24 ^ 
 
 then 7.87X4.3 = 33.84/ or about 34/ extra profit. 
 
 96. Ex. What is the loss in selling a gold article 
 of 6 kt. fine which contains 50 grains of pure gold 
 too much? 
 
 Ans. We first find, as in the foregoing example, 
 how much pure gold those 50 grains should have 
 contained in being sold for 6 kt. gold. Hence, 
 
 50 Yfi 
 
 24 :6-50 :x = ^^=: 12.50 grs. 
 
 24 ^ 
 
 Consequently the loss was 50 — 12.50 = 38.5 grs. of 
 pure gold at 4.3/= 165.55 = 11.65 and i/. 
 
 97. Ex. How much gold and how much alloy is 
 contained in a gold watch chain 583 fine, weighing 
 15 dwts. and 10 grs.? 
 
 Ans. 15 dwts. + 10 grs. = 370 grains. 
 
 370 V "^83 
 
 Then, 1000 : 583 = 370 : x= =215.71 grs. 
 
 1000 
 
 or, in applying rule 33 we simply write: 0.583X370 = 
 215.71 weight of the gold, and 370-215.71 = 154.29 
 grains weight of the alloy. 
 
EXAMPLES OF ALL KINDS 43 
 
 98. Ex. A jeweler has gold 750 and 950 fine, 
 which he wants to use to make gold 900 fine, in what 
 ratio must he take? 
 
 ^ . onnS^SO 
 
 Desired fineness 900 < _^ 
 ( 750 50 
 
 He must take in the ratio as 150 parts to 50 or as 3 : 1. 
 
 99. Ex. Express in karats gold fine 588, 330, 
 450, 725, and 950 (see 38, etc.). 
 
 Ans. 0.588x24=14.11 kt. 
 
 0.330X24= 7.92 kt. 
 0.450x24=10.8 kt. 
 0.725X24 = 17.4 kt. 
 0.950X24 = 22.8 kt. 
 
 which says that 588= 14.11 kt.; 330 = 7.92 kt.; 450 = 
 10.8 kt. ; 725 = 17.4 kt. ; 950 = 22.8 kt. 
 
 100. Ex. How many thousandths of gold are 
 contained in 13 karats gold and how many of alloy? 
 
 Ans. (See 46.) 
 l5J)^oo = 542 of gold, and 1000-542 = 458 of alloy. 
 
 101. Ex. A jeweler has three kinds of gold 
 which he wants to melt together. He has 250 grs. 
 900 fine, 325 grs. 800 fine, and 50 grs. 950 fine: of 
 what fineness will be the alloy? 
 
 Ans. 250 at 900=225000 
 
 325 at 800 = 260000 
 50 at 950= 47500 
 625 532500 
 Alloy = = 852 fine. 
 
44 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 102. Ex. Find the value of a gold watch chain 
 18 kt, fine weighing 2^ ounces. 
 
 Ans. 2i oz. = 1200 grs. total weight; pure gold = 
 
 24 : 18=1200 = 900 grs.; value = 900 
 
 24 
 
 grs. X 4.3/ = 3870/ or $38.70. 
 
 MELTING POINTS OF METALS 
 
 103. The exact melting points are quite uncer- 
 tain and sometimes differ greatly, even of metals 
 belonging to the same category according to different 
 authorities, as shown by the following table : 
 
 METALS 
 
 Melting Points 
 in 
 
 Degrees Centigrade 
 
 Authority 
 
 Platinum 
 
 1460-2534 
 
 Various 
 
 Palladium 
 
 1360-1950 
 
 
 Nickel 
 
 1371-1600 
 
 u 
 
 
 1250- 1587 
 
 <( 
 
 Gold 
 
 1035 
 
 Violle 
 
 <( 
 
 1035-1142 
 
 Various 
 
 (( 
 
 1142 
 
 Daniell 
 
 (( 
 
 1240 
 
 Riemsdijk 
 
 <( 
 
 1425 
 
 Daniell 
 
 
 950-1398 
 
 Various 
 
 
 916 
 
 Deville, Becquerel 
 
 <( 
 
 940 
 
 Deville 
 
 « 
 
 954 
 
 Violle 
 
 << 
 
 954-1042 
 
 Various 
 
 <( 
 
 1040 
 
 Riemsdijk 
 
 It 
 
 1042 
 
 Daniell 
 
 Aluminium 
 
 600-850 
 
 Various 
 
 
 342-450 
 
 
 
 320-335 
 
 (I 
 
 Tin 
 
 220-246 
 
 
MELTING POINTS OF METALS 
 
 45 
 
 This table shows us which metals to melt first, 
 when alloying, so as not to scald or burn the metals 
 having a much lower melting point. 
 
 104. Thermometer readings. To change de- 
 grees of Centigrade to the corresponding degrees 
 of Fahrenheit, we multiply the centigrade reading 
 by 9, and divide the product by 5, then add 32° to 
 the quotient. Thus: 
 
 105. To change degrees of Fahrenheit to the cor- 
 responding degrees of Centigrade the operation must 
 be reversed. We subtract 32° from the Fahrenheit 
 reading, multiply by 5, then divide by 9. Thus: 
 
 1895° Fah. = (1895-32) X 5 -^ 9= 1035° C. 
 
 106. The exact melting points of the constituent 
 metals of an alloy and solders being given, we could 
 easily find the mean melting point of such alloy or 
 solder, but as the physical properties and fusibihty 
 of the alloys are quite different from those of the 
 constituents, they cannot be determined accurately 
 in advance by mathematical formulas. In nearly 
 all cases the fusing point of an alloy is lower than the 
 mean of its constituent metals, and in some in- 
 stances, as in the so-called fusible alloys, it is lower 
 than that of either. Experiments have been made 
 and tables compiled of alloys composed of two 
 metals only, but as the varieties and proportions 
 increase immensely in alloys composed of three or 
 
 1035° C = 
 
 1035X9 ' 
 . 5 
 
 + 32° = 1863 + 32° = 1895° Fah. 
 
46 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 Gold 
 % 
 
 
 Silver 
 
 % 
 
 100 
 
 + 
 
 0 
 
 80 
 
 + 
 
 20 
 
 60 
 
 + 
 
 40 
 
 40 
 
 + 
 
 60 
 
 20 
 
 + 
 
 80 
 
 0 
 
 + 
 
 100 
 
 more metals, no reliable table of the fusing points of 
 such alloys has yet been made up, especially not of 
 alloys having high melting points. 
 
 107. Table of Alloys of Gold and Silver according 
 to Erhard and Schertel: 
 
 Melting Point 
 in 
 
 Degrees Centigrade 
 
 1075 
 
 1045 
 
 1020 
 
 995 
 
 975 
 
 954 
 
 108. Table of Alloys of Silver and Copper accord- 
 ing to W. Roberts: 
 
 Silver Copper Melting Point 
 
 % % Degrees Centigrade 
 
 100 + 0 1040 
 
 92.5 + 7.5 931 
 
 82.1 + 17.9 886 
 
 79.8 + 20.2 887 
 
 77.4 + 22.6 856 
 
 75 + 25 850 
 
 71.9 + 28.1 870.5 
 
 63 + 37 847 
 
 63 + 37 847 
 
 60 + 40 857 
 
 57 + 43 900 
 
 54.1 + 45.9 920 
 
MELTING POINTS OF METALS 47 
 
 Silver Copper Melting Point 
 
 % % Degrees Centigrade 
 
 50 + 50 941 
 
 45.9 + 54.1 961 
 
 25 + 75 1114 
 
 0 + 100 1330 
 
 1 09. The melting point of silver in the above 
 tables 107 and 108 being widely different, we have 
 made the following table which will combine them: 
 
 Gold 
 
 Silver 
 
 Melting Points, Degrees Centigrade 
 
 % 
 
 
 
 Mean of the 
 
 Mean of 
 
 Mean of the 
 
 Mean of 
 
 
 % 
 
 Constituents 
 
 Alloys 
 
 Constituents 
 
 Alloys 
 
 100 
 
 + 
 
 0 
 
 1075 
 
 1075 
 
 1075 
 
 1075 
 
 90 
 
 + 
 
 10 
 
 1062 
 
 1060 
 
 1071 
 
 1068 
 
 80 
 
 + 
 
 20 
 
 1050 
 
 1045 
 
 1068 
 
 1062 
 
 70 
 
 + 
 
 30 
 
 1038 
 
 1033 
 
 1064 
 
 1058 
 
 60 
 
 + 
 
 40 
 
 1026 
 
 1020 
 
 1061 
 
 1054 
 
 50 
 
 + 
 
 50 
 
 1014 
 
 1008 
 
 1058 
 
 1050 
 
 40 
 
 + 
 
 60 
 
 1002 
 
 995 
 
 1054 
 
 1046 
 
 30 
 
 + 
 
 70 
 
 990 
 
 985 
 
 1051 
 
 1045 
 
 20 
 
 + 
 
 80 
 
 978 
 
 975 
 
 1047 
 
 1043 
 
 10 
 
 + 
 
 90 
 
 966 
 
 965 
 
 1043 
 
 1042 
 
 0 
 
 + 
 
 100 
 
 954 
 
 954 
 
 1040 
 
 1040 
 
 no. Table of Different Alloys. 
 
 Lead 
 Parts 
 
 
 Tin 
 Parts 
 
 1 
 
 + 
 
 1 
 
 1 
 
 + 
 
 2 
 
 1 
 
 + 
 
 3 
 
 1 
 
 + 
 
 4 
 
 1 
 
 + 
 
 5 
 
 2 
 
 + 
 
 1 
 
 2 
 
 + 
 
 8 
 
 Melting Point 
 Degrees Centigrade 
 
 Authority 
 
 194 Kupfer 
 
 ,210. 
 
48 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 Lead Tin Melting Point Authority 
 
 Parts Parts Degrees Centigrade 
 
 3 -f 1 282 Pillichody 
 
 3 + 2 246 Kupfer 
 
 4 + 1 292 Pillichody 
 
 4 + 3 236 
 
 5 + 7 184.5-181.9 Various 
 
 25 + 1 558 Tomlinson 
 
 10 + 1 541 
 
 5 + 1 511 
 
 1 + 6 381 
 
 1 + 5 378 
 
 5 + 3 + 8 bismuth 94° Cent, alloy of Darcet. 
 
 2 + 9 + 1 zinc 168° Cent. 
 
 111. How can we calculate the mean of the melt- 
 ing points of metals? 
 
 Simply by following the rules 48, etc. 
 Ex. Give the mean melting point of an alloy of 
 80% gold at 1075° and 20% silver at 954°. 
 
 Ans. 80x1075-86000 
 20 X 954-19080 
 100 105080 
 Mean = ^-Yo "o - = 1050.8° 
 
 112. Therefore, the mean of the above alloy 
 should have been 1050°, but according to authorities 
 this alloy is in realty 5° lower or 1045° C (see table, 
 107). 
 
 Ex. How can we find the equivalent of this num- 
 ber 1045°, if instead of 954° the melting point of 
 silver be taken as 1040°? 
 
MELTING POINTS OF METALS 49 
 
 Ans. We first find what the mean melting point 
 would have been in this case, and then find the pro- 
 portional of that mean melting point. Thus: 
 
 80x1075-86000 
 20X1040 = 20800 
 
 Too 106800 
 Mean=i-\V/- = 1068° 
 
 Then: 
 
 1045X1068 
 
 1050 : 1068= 1045 : x = — — = 1062° 
 
 1050 
 
 113. Having the melting point of the percentage 
 of gold and silver and of the percentage of silver and 
 copper contained in an object of gold, we could find 
 that of the object itself by taking the mean of those 
 two melting points; but, as has been stated above, 
 nothing definite being as yet known about the phys- 
 ical changes in alloys composed of three or more 
 metals, no reliable results can thus be obtained by 
 calculation, and consequently the tables given by 
 some writers on goldsmithing, which quote the 
 exact melting points of gold of the different karats 
 with the precision of one single degree, cannot be 
 trusted. 
 
 114. An example of that kind is the following, 
 taken at random: 
 
 B. K. C. asks for a good formula for 10 kt. gold 
 solder. His adviser tells him to take 140 grs. fine 
 gold; 70 grs. fine silver; 75 grs. copper. Let us 
 verify. 
 
50 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 We see at a glance that the solder is composed 
 about half and half, i.e., half of gold (140 parts) and 
 half of alloy (145 parts), consequently that the solder 
 is nearly 12 kt. fine. It is evident from the tables 
 that the gold having a much higher melting point 
 than the silver or copper, that point must increase 
 in alloys containing a greater percentage of gold, and 
 consequently, that the gold article, of 10 kt. fineness, 
 will melt before the solder of 12 kt. fineness flows. 
 Therefore the advice is not recommendable. The 
 solder should always be made of a safe amount lower 
 in fusibihty than the gold article to be soldered, as 
 shown by the following formulas recommended by 
 Schlosser : 
 
 Hard solder for 18 kt. gold: take 9 parts of 18 kt. 
 gold, 2 parts of silver, and 1 part of copper. 
 
 Soft solder for 18 kt. gold: take 12 parts of 18 kt. 
 gold, 7 parts of silver, and 3 parts of copper. 
 
 Solder for 14 kt. gold: take 3 parts of 14 kt. gold, 
 2 parts of silver, and 1 part of copper. 
 
 115. Find the fineness of the above solders. 
 
 Ans. Hard solder for 18 kt. gold. 18 kt. gold con- 
 tains If f of gold, and 31 X i of alloy, consequently 
 we have in the 9 parts of 18 kt. gold: 
 
 9xf-=-V-= 
 9Xi=| - 
 
 6.75 parts of gold, and 
 2.25 parts of alloy. 
 
 That makes 6.75 parts of gold and 2.25 + 2+1 = 5.25 
 
MELTING POINTS OF METALS 51 
 
 parts of alloy in the solder. Its fineness is found by 
 the following proportion: 
 
 24X6.75 
 
 12 : 6.75 = 24 : X = = 13.50 kt. 
 
 Fineness of the hard solder for 18 kt. gold is 13| kt. 
 
 Soft solder for 18 kt. gold. 12x| = 9 parts of gold, 
 and 12Xi = 3 parts of alloy are contained in the 12 
 parts of 18 kt. gold. Therefore the solder will con- 
 tain 9 parts of gold, and 3 + 7 + 3 = 13 parts of alloy, 
 a total of 22 parts. Hence : 
 
 24 vQ 
 
 22 :9 = 24 :a;=-— — -9.8kt. 
 22 
 
 Fineness of the soft solder for 18 kt. gold is 9.8 kt. 
 
 Solder for 14 kt. gold. 14 kt. gold contains 1 1 = iV 
 of gold, and | | = i2 alloy, consequently 3 parts of 
 14 kt. gold contains 3X^2 = ^-'^^ parts of gold, and 
 3X^2 ="1-25 parts of alloy. The solder, therefore, 
 contains 1.75 parts of gold and 1.25 + 2+1 = 4.25 
 of alloy, a total of 6 parts. Hence: 
 
 6: 1.75 = 24 ::r=5i^ii:^ = 7kt. 
 
 6 
 
 Fineness of solder for 14 kt. gold is 7 karat. 
 
 EXAMPLES FOR EXERCISE 
 
 116. A melts together gold 325 grs. 900 fine; 
 230 grs. 800 fine, and 45 grs. 950 fine: what will 
 be the fineness of the alloy? Ans. 865 parts. 
 
 117. To make type metal 15 lbs. of lead, 4 lbs. of 
 antimony and 1 lb. of tin have been used. Sup- 
 
52 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 posing lead to cost 13/, antimony 15/, tin 52/, 
 what will 1 lb. of the alloy cost? Ans. 15.35/. 
 
 ii8. To make an experiment, we want to have 
 seawater containing 6 lbs. of salt per 100 pints, but 
 the water we get from the sea contains 9 lbs. per 100 
 pints: how much water must be added to give the 
 desired proportion? Ans. 50 pints. 
 
 HQ. We had 400 grains of gold which we knew 
 was 14 kt. fine, we melted it with 500 grains of 
 gold, of which fineness we were not certain, but 
 expected the alloy to become 18 kt. fine; we ob- 
 tained 16 kt. instead. Of what fineness were those 
 500 grains? Ans. 17.6 kt. 
 
 120. A merchant has coffee at 40/, 35/, 33/, 30/ 
 24/, and 18/ a pound; he wants to obtain a mixture 
 of 300 lbs. ; taking 50 lbs. of each quahty, what will 
 a pound of the mixture cost? Ans. 30/. 
 
 121. Find the equivalent of in karats, and of 
 13| karats in thousandths. Ans. 10.46 kt., 562.5. 
 
 122. How much water must be added to 45 
 gallons of wine at 60/ to make wine at 50/ a gallon? 
 
 Ans. 9 gals. 
 
 123. How much 18 kt. gold must be added to 
 650 grs. 9 kt. gold to make 12 kt. gold? 
 
 Ans. 325 grs. 
 
 124. A grocer has 350 lbs. of coffee at 30/, 450 
 lbs. at 28/, 500 lbs. at 22/, and 640 lbs. at 18/. His 
 customers generally ask for coffee at 26/ a pound, 
 therefore he wants to mix them. Before mixing he 
 
EXAMPLES FOR EXERCISE 53 
 
 first wants to make one mixture of 280 lbs. by 
 taking from the 30/ and 22/ qualities to sell it at 
 23/ a pound. He asks (1) how many pounds of 
 each he must take for the first mixture; (2) how 
 much per pound the second mixture will cost. 
 
 Ans. (1) 35 lbs. at 30/ and 245 lbs. at 22/; 
 (2) 25.41/. 
 
 125. A jeweler has gold of different degrees of 
 fineness, 20 grams 650 fine, 24 grams 725 fine, 18 
 grams 800 fine, 15 grams 900 fine. He wants to 
 make two alloys of gold of different fineness. One, 
 by taking from the two lowest, 18 grams 700 fine. 
 Find; (1) how much of each must be taken for the 
 first alloy; (2) and of what fineness the second alloy 
 will be. 
 
 Ans. (1) 12 grams at 725, 6 grams at 650; 
 (2) 808.5 parts fine. 
 
 126. A contractor receives $2700 a week to pay 
 his workmen, which is at the mean rate of $3 a day. 
 He pays them 2 at $8, 50 at $4, 30 at $3, 25 at $1, 
 28 at 75/, and 15 at 50/ a day. Find how much 
 profit the contractor makes a day. Ans. $90.5. 
 
 127. A jeweler has been paid at the rate of 51 
 dwts. 12 kt. fine for a gold article which he has 
 made. He used for it 4 dwts. 18 kt., 5 dwts. 14 kt., 
 12 dwts. 12 kt., and 30 dwts. 9 kt. fine; how much 
 has he overcharged his customer, supposing the value 
 of 1 dwt. 1 kt. gold to be 4/? Ans. $2.24. 
 
 128. A wine merchant has 125 gallons of wine 
 
54 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 at 75/ a gallon: how much water must he add to 
 make wine at 60/ a gallon? Ans. 18f gallons. 
 
 129. A jeweler has 2 oz. 4 dwts. 18 kt. gold: how 
 much alloy must he add to make it 14 kt. fine? 
 
 Ans. 301.71 grains. 
 
 130. Find the price of plumbers' solder per pound, 
 composed of 2 lbs. of tin at 48/ and 1 lb. of lead at 
 12/. Ans. 36/. 
 
 131. Find the price of 1 lb. of spelter solder com- 
 posed of 16 lbs. of copper at 26/, and 12 lbs. of zinc 
 at 9/. • Ans. 18.71/. 
 
 132. Find the fineness of gold composed of 124 grs. 
 of 18 kt. and 350 grs. of 14 kt. gold. Ans. 15.04 kt. 
 
 133. Stereotype metal costing 17.8/ a pound is 
 composed of 48 lbs. of lead at 15/, 1 lb. of tin at 
 49/, and 6 lbs. of antimony. What is the price a 
 pound of antimony? Ans. 35/. 
 
 134. An alloy of gold, weight 13 dwts. and 17 kt. 
 fine, has been composed of 6 dwts. 18 kt., 5 dwts. 
 14 kt., and 2 dwts. of gold, of which it is required to 
 find the fineness. Ans. 11 J kt. 
 
 135. An alloy contains 45% of gold; find the 
 equivalent in twenty-fourths and in thousandths. 
 
 10 8 
 
 Ans. --=3440 0.450. 
 24 
 
 136. An article weighing 16 dwts. contains 65% 
 of gold: (1) of what fineness is the article, and 
 (2) how much pure gold does it contain? 
 
 Ans. (1) ^ = 15.6kt.or^(/^o"o oi'-650; (2) 249.6 
 24 
 
 grams. 
 
EUROPEAN LAWS RELATING TO FINENESS 
 
 OF 
 
 GOLD AND SILVER 
 
 137. The following table of laws has been com- 
 piled by the Swiss Federal Bureau of Gold and Silver 
 Products for the benefit of manufacturers and ex- 
 porters : 
 
 Control 
 
 Fineness of Alloys 
 
 Principal Provisions 
 
 Obligatory. 
 Laws of Aug 19, 
 1865, and May 
 23. 1875 
 
 Optioaal. (Law 
 of June s, 1868) 
 
 Optional- (Law 
 of April s, 1888) 
 
 Obligatory. 
 (Different laws, 
 
 10-1891) 
 Obligatory. 
 ( Law of bru- 
 maire year vi, 1 1 
 Nov. 1797) 
 Law of July 16, 
 
 Optional. (Law 
 of Sept., 1852) 
 
 Optional. (Law 
 of May 3, 1873) 
 
 Gold: 0.920, 0.840, 0.750, 
 0.580. Silver: 0.950, 
 0.900, 0.800, 0.750 
 
 Gold: 0.800, 0.750. Silver; 
 0.900, 0.800 
 
 All fineness to a minimum 
 of 0.585 for gold, and 
 0.826 for silver. 
 Gold: 0.916, 0.833, 0.750, 
 0.625, 0.500, 0.375. Sil- 
 ver: 0.925 
 
 Gold: 0.920, 0.840, 0.750. 
 Silver: 0.950, 0.800. Al- 
 owed for articles to be 
 exported. Gold: 0.583 
 Any fineness for jewelry 
 for all other works the 
 lowest is 0.585 for silver 
 
 Gold: 0.916, 0.833, 0.750 
 Silver: o 934, 0.833 
 
 Gold: 0.900, 0.750, 0.500 
 Silver: 0.950, 0.900, 0.800 
 
 The maker's mark is obli- 
 gatory. 
 
 Works which do not corre- 
 spond to the indicated fine- 
 ness receive the stamp of a 
 lower quality. 
 
 Works must not have any 
 lower mark than the lowest 
 prescribed fineness. 
 The stamp is marked by the 
 jewelers' corporations under 
 control of the State. 
 Works which do not cor- 
 respond to the indicated 
 quality are cut. Special 
 stamps for imported ware. 
 Indications of fineness must 
 be made in thousandths. 
 AH works must be provided 
 with the manufacturers 
 mark and the imperial 
 crown (in the sun sign for 
 gold, and the moon sign for 
 silver; this latter is for- 
 bidden for jewelry. 
 The maker's mark is obli- 
 gatory. Special stamps for 
 imported ware. 
 Works which do not corres- 
 [xmd to the indicated fine- 
 ness receive the stamp of 
 a lower^guality. 
 
56 ARITHMETIC OF GOLD AND SILVERSMITH 
 
 EUROPEAN LAWS RELATING TO FINENESS OF GOLD 
 AND SILVER. — Concluded. 
 
 Control 
 
 Fineness of Alloys 
 
 Principal Provisions 
 
 Obligatory. 
 
 Obligatory. 
 (Rules of Feb. lo, 
 iS86,and Aug. 9, 
 and 25, 1891) 
 Obligatory. 
 (Rules of July i 
 and 13, 1896) 
 
 Obligatory. 
 (Law of March 
 3, 1834 
 
 Obligatory. 
 (Different ordi- 
 nances since 
 1771) 
 
 Obligatory. 
 (Rules of 1759) 
 
 Obligatory for all 
 watch cases that 
 are marked with 
 a legal stamp. 
 Optional for jew- 
 elry which is 
 needed for educa- 
 tional purposes. 
 (Federal law of 
 Dec. 23, 1880) 
 Obligatory 
 
 Gold 
 Silver 
 
 Gold 
 ver: o 
 
 0.750, o 583,0.500 
 : 0.830 
 
 0.750, 0.580. Sil- 
 .800 
 
 Gold: 
 (82), 
 (56)., 
 0.916^ 
 
 Gold: 
 0.580. 
 0.900, 
 
 0.948 (91), 0.854 
 0.7.S0 (72), 0.583^ 
 
 Silver: o 948 (91), 
 \ (88), 0.87s (84) 
 
 0.920, o 840, 0.750. 
 
 Silver: 0.950, 
 0.800, 0.750 
 
 Gold: 0.916, 0.833, 0.750 
 Silver: 0.916, 0.750 
 
 Gold: 0.969, 0.833, 0.750. 
 Silver: o.8i2i 
 
 Gold: 0.750, 0.583. Sil- 
 ver: 0.875, 0.800 
 
 Silver: 0.900 
 
 The indication to fineness 
 and the maker's mark are 
 obligatory. 
 
 The aforesaid qualities are 
 for watch cases. These 
 qualities are higher for 
 other objects. 
 
 No parts of the objects can 
 be lower than the indicated 
 fineness. The stamp indi- 
 cates the fineness by " Zo- 
 lotniks." 
 
 The maker's mark is obli- 
 gatory. 
 
 Divers provisions seldom 
 applied. 
 
 The indications of fineness, 
 the place of stamping, of 
 the year and the maker's 
 mark are obligatory. 
 Works which have not been 
 officially controlled, must 
 not have any other indica- 
 tions than that of their real 
 fineness; if they are marked 
 by such fineness, the ma- 
 ker's mark is obligatory. 
 The law has no final char- 
 acter. 
 
 No limitations for gold. 
 
LIST OF BOOKS 
 
 ON 
 
 JKUatcJ) anD Clock^making: anD B^epair^ 
 im, Clectro^plating, etc* 
 
 BONNEY, G. E. Electroplater's Handbook: a practical man- 
 ual for amateurs and young students in Electro-metallurgy. 
 With diagrams and figures. Fourth edition, enlarged by an 
 appendix on Electrotyping. 12mo, cloth, illustrated, 221 
 pp. $1.20. 
 
 GARRARD, F. J. Watch Repairing, Cleaning, and Adjusting : 
 
 a practical handbook, dealing with the materials and tools 
 used, and the methods of repairing, cleaning, altering, and 
 adjusting all kinds of English and foreign watches, repeaters, 
 chronographs, and marine chronometers. With over 200 en- 
 gravings specially made for this work. 12mo, cloth, illus- 
 trated, 214 pp $2.00. 
 
 HASLUCK, P. N, The Clock- Jobber's Handybook: a prac- 
 tical manual on cleaning, repairing, and adjusting; embrac- 
 ing information on the tools, materials, appliances, and 
 processes employed in clockwork. Fifth edition. 12mo, 
 boards, illustrated, 159 pp $.40. 
 
 The Watch -Jobber's Handybook : a practical manual on 
 
 cleaning, repairing, and adjusting; embracing information on 
 the tools, materials, apoliances, and processes employed in 
 watchwork. Eighth edition. 12mo, boards, illustrated, 144 
 pp $.40. 
 
 HOOD, G. Modern Methods of Horology: a book of prac- 
 tical information for young watchmakers. With engravings 
 and diagrams. 8vo, cloth, illustrated, 253 pp $2.50. 
 
 KEMLO, F. Watch-Repairer's Handbook: being a complete 
 
 guide to the young beginner in taking apart, putting to- 
 gether, and thoroughly cleaning the English lever and other 
 foreign watches, and all American watches. With figures and 
 tables. 12mo, cloth, illustrated, 93 pp $1.25 
 
LIST OF BOOKS -Concluded 
 
 KENDAL, J. F. History of Watches and Other Timekeepers. 
 
 With diagrams and figures. 12mo, cloth, illustrated, 252 
 pp $1.00. 
 
 SAUNIER, C. Treatise on Modern Horology in Theory and 
 
 Practice. Translated from the French by Julien Tripplin, 
 F.R.S.A. and Edward Rigg, M.A. With engravings, and 
 22 colored folding plates. Second edition. Thick 4to, cloth, 
 illustrated, 844 pp $15.00. 
 
 Watch-Maker's Handbook: intended as a workshop com- 
 panion for those engaged in watch-making and the allied 
 mechanical arts. Translated from the French and consider- 
 ably enlarged by Julien Tripplin and Edward Rigg. With 
 diagrams and folding plates. Third edition, revised, with 
 appendix. 12mo, cloth, illustrated, 498 pp $3.00 
 
 URQUHi^RT, J. W. Electro-plating: a practical handbook 
 
 on the deposition of Copper, Silver, Nickel, Gold, Aluminium, 
 Brass, Platinum, etc. With descriptions of the Chemicals, 
 Materials, Batteries, and Dynamo Machines used in the art. 
 Fifth edition. 12mo, cloth, illustrated $2.00 
 
 WATT, A. Electro-plating and Electro-refining of Metals : 
 
 being a new edition of Alexander Watt's " Electro-Deposi- 
 tion." Revised and largely rewritten by Arnold Philip, B.Sc. 
 
 With numerous figures and engravings. 8vo, cloth, illus- 
 trated, 680 pp net, $4.50. 
 
 Electro-metallurgy Practically Treated. Fifteenth edition, 
 
 considerably enlarged. 12mo, cloth $1.00 
 
 FOR SALE BY 
 
 D. VAN NOSTRAND COMPANY, 
 
 Publishers and Booksellers. 
 23 MURRAY & 27 WARREN STREET, NEW YORK. 
 
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