NOTE 2. A little skill is necessary in order to obtain integral answers.

NOTE 3. In working the examples, we can begin with any of the quantities. If when we come to the last quantity, we have already too much of that which is of the same nature as this last, that is, gain or loss, we must change the quantities already taken so that there will be a balance of a nature opposite to the last.

114. A farmer wishes to mix corn worth $0.70 a bushel with rye worth $0.75, barley worth $0.60, and oats worth $0.45 to make a mixture of 60 bushels worth $0.65 a bushel. How many bushels of each kind may he take?

therefore, he must take of 60 bushels, or 12 of corn, 12 of barley, and 12 of oats, and of 60 bushels, or 24 of rye.

Ans. 12 bushels of corn, 12 of barley, 12 of oats, and 24 of rye. 115. A farmer has cows worth $ 35, $ 42, $ 48, $ 50, and $ 55 a head. What number of each may he sell without loss at an average price of $45 a head?

116. How many pounds of wool worth, respectively, 30, 35, and 40 cents a pound, can be mixed with 40 pounds worth 45 cents, to make a mixture worth 38 cents a pound?

117. How many ounces of gold 700, 840, 900, and 1000 fine, respectively, can be taken to form a mass of 8 ounces 880 fine?

118. How many sheep worth, respectively, $1.50, $ 2, $ 2.75. $ 3, and $ 4 apiece, can be taken to make a flock of 300 worth $2.50 apiece?

600. Gauging is finding the capacity of a cask in gallons.

Rule.

Add to the head diameter from 0.5 to 0.7 (according as the staves are curved little or much) of the difference between the bung and head diameters to obtain the mean diameter. Multiply the square of the mean diameter in inches by the length of the cask in inches, and this product by 0.0034.

601. The Tonnage of a Vessel is her capacity, and is determined by measurement.

The tonnage of all vessels built or owned in the United States is registered at a Custom House in tons of 100 cubic feet each; this is called register tonnage.

The rule for finding the register tonnage is prescribed in the customs laws, and is made very elaborate and exact to apply to the varying forms of steam and sailing vessels. The following rule is found to give very nearly the government tonnage for hulls of vessels.

Rule.

Multiply together the length in feet on the upper deck, the inside main breadth, and the depth at midship from upper deck to the ceiling in the bottom of the hold, and divide this product by 100; then multiply the result by 0.8 for sailing ships of full form, 0.7 for ships of present usual form, 0.65 for steam vessels and clippers of two decks or 0.68 for those of three decks, 0.5 for yachts above 60 tons, 0.45 for small yachts.

NOTE. In determining the carrying capacity of vessels 40 cubic feet, that is, the volume of a ton weight of water, is considered a ton, an allowance of about 20% being made in the measurement for space taken up by beams, knees, etc.