happens when there is an odd number of ingredients or when the number of prices above the space is not the same as the number below. Example 1. Spirits at 12s. per gallon are to be mixed with sweet water at 9d. per gallon so as to reduce the price to 10s.-find the proportions. 128.91 10s. Proportion 37: 8. is./2 Example 2. Teas at 5s., 4s. 2d., 3s. 6d., 2s. 4d. are to be mixed so as to bear a price of 38. 9d. Example 3. 1 at 3s. 9d. 40 at 150s. 1 at 3s. 9d. Whiskies at 25s., 22s., 20s., 18s., 10s. per gallon are Example 4. Coffees at 2s., 1s. 10d., 1s. 8d., 1s. 4d., 1s. are mixed C. S ༤༠ T 6+4 6+2 4+2 4 6 6 at 1s. 8d. 10 at 1s. 4d. (5) (6) 2 at 1s. =10s. 22 at 33s. 1 at 1s. 6d. When some of the ingredients of given prices are limited in quantity-to find quantities of the re LIMITED INGREDIENTS. 121 maining ingredients of given prices to join with the fixed quantities so that whole mixture may have given price. (1) If one ingredient is limited. Use linkages and then proportion. (2) If more than one ingredient is limited. Convert the given limited ingredients into a mixture of given weight and price by the method of A. Then for this and the remaining quantities use linkages and finally proportion. Example 1. 8 lbs. tea at 4s. 2d., others at 3s. 6d., 2s. 4d., to mix at 3s. Example 2. 4 lbs. coffee at 1s. 10d., 6 lbs. at 1s. 4d.,-others at 1s. 8d., 1s. 3d., to mix at ls. 5d. D. Given prices of ingredients to find quantities to form a given weight of mixture at given price. Use linkages and then proportion. Example. Currants at 18., 10d., 6d., 4d.—240 lbs. at 8d. required. 12 42 of 240=80 at 1s. =960d. The proportions and price of any mixture being thus determined the retailer has only to increase the price per measure or weight by the profit he thinks fair to get the selling price of the mixture-the profit being a percentage or otherwise as the retailer thinks right. Alcohol Strengths. 5. Proof Spirit is that which weighs 1 of an equal measure of water-both being at 51° F. By volume or measure it contains 57.06 p.c. of pure alcohol-at 60° F. its specific gravity is 920. The terms proof, over proof (o.p.), under proof (u.p.) are used to indicate alcoholic values. Proof=1. The o.p. strengths are added to, the u.p. strengths are taken from this as decimals. 25 o.p.=1·25. 20 u.p. = '80. In mixtures the rules are derived from simultaneous equations or indeterminate equations as in the case of ordinary ingredients. Use the method of linkages and (if necessary) then proportion. Example 1. To mix two spirits, one 20 o.p., the other 10 u.p., so as to result in a mixture 5 o.p. 1.05 1.20.15. .. Proportions are 1 to 1. Proof. = 1 gallon at 20 o.p.1.20 proof galls. 1 gallon at 10 u.p. 90 proof galls. =2.10 proof galls. =2 galls. 5 o.p. Example 2. How many gallons at 6 u.p. are required to reduce 24 gallons 60 o.p. to 5 o.p.? 1.05 1.60 11. Proportions 1 to 5. .. necessary quantity is 94/55. Proof. 24 gallons at 60 o.p. 38-40 galls. proof. 120 gallons at 6 u.p.112.80 galls. proof. THE FINENESS OF METALS. 123 Example 3. With spirit 25 o.p. how much water must be mixed to make a mixture 10 u.p.? Example 4. What is strength of a mixture of 9 galls. 25 o.p. and 6. In Goldsmiths' and Silversmiths' work, according to law, the oz. Troy and decimals of the oz. are only to be employed, and fineness is to be reckoned in millièmes (thousandths). The old way of estimating the fineness of gold was by carats-18 carats out of 24 being the standard. The old way of estimating the fineness of silver was by ozs. and dwts. These methods are still employed, the weights being expressed in ozs. and grains. Millièmes are increasingly used, as their simplicity and convenience are appreciated. The rules for Alloys are particular cases of mixtures. 1°. To find the proportions of two metals of differing fineness to produce when mixed an intermediate fine ness. Divide difference of higher and required fineness by difference of required and lower fineness. For more than two metals use linkages. 2o. To make a compound of given weight and fineness. Find proportions of the metals by 1° or linkages. If the total weight required is given we can find the weight of each metal necessary. If the weight of one metal is given we can find the weights of the others and thus the total weight. Example. Mix golds 900 and 925 fine so as to make 625 ozs. 916 fine. Ratio= 916-900 = 10. .. 18 of 625=400 ozs., 2% of 625=225 ozs. EXAMPLES. 1. How much plain water must be added to 1 gallon of spirit or wine (1) at 12s. to make a profit of 3s. 6d. or a profit per gallon of 3d.? (2) at 11s. 9d. to make a profit of 2s. 3d. or a profit per gallon of 1s. 5d.? (3) at 10s. to make a profit of 5s. or a profit per gallon of 3s.? (4) at 15s. 6d. to make a profit of 7s. 3d. or a profit per gallon of 9d.? (5) at 11s. 6d. to make a profit of 4s. 2d. or a profit per gallon of 9d.? 2. How much sweet water at 9d. per gallon must be added to 1 gallon of spirit (1) at 13s. 9d. to make a profit of 2s. or a profit per gallon of 5d.? (2) at 10s. 3d. to make a profit of 3s. 7d. or a profit per gallon of 1s. 1d.? (3) at 12s. 6d. to make a profit of 5s. 6d. or a profit per gallon of 28. 3d.? 3. Find profit from mixing (1) 9 gallons of water, (2) 13 gallons of inferior spirit at 1s. 2d., (3) 12 gallons of sweet water at 8d., with 1 gallon of wines at 15s. 4d., 13s. 7d., 12s. 9d., 17s. 8d., 11s. 6d. 4. Find price of following mixtures (1) coffees 17 lbs. at 10 d., 13 at 1s. 3 d. (2) teas 12 lbs. at 2s. 4d., 5 at 3s. 7d., 11 at 4s. 1d., 16 at 3s. (3) spirits 10 galls. at 11s. 9d., 12 at 10s. 3d., 18 at 9s. 6d. |