Ullaging

Ullaging is the art of finding what quantity of liquor is contained in a cask when partly empty and it is considered in two positions: first, as standing on its end, and secondly, lying on its side.

To find the contents of ullage by the sliding rule. — By one of the preceding problems find the whole contents of the cask; then set the length on N. to 100 on S. S. for a segment standing, or set the bung diameter N. to 100 on S. L. for a segment lying; then against the wet inches on N. is a number on S. S. or S. L. to be reserved. Next set 100 on B. to the reserved number on A., then against the whole contents on B. will be found the ullage on A.

The diagonal rod. — The diagonal gauging rod is 4 feet long and .4 of an inch square. The four sides of it contain different lines, the principal one of which is a line for imperial gallons for gauging casks. The use of the principal line is to determine the contents of a cask of the most common form, by merely measuring with the rod the diagonal extending from the bung-hole to the opposite side of the head; that is, to the part where the staff opposite to the bung-hole meets the head; then the number on the rod at the bung-hole on the principal or first side is the number of gallons in the content of the cask.

Gauging (part 3)

Dr Hutton’s general rule for finding the contents of casks
Add into one sum 39 times the square of the bung diameter, 25 times the square of the head diameter, and 26 times the square of the product of the two diameters; then multiply the sums by the length and the product again by .00031 4/9 for the contents in gallons

EXAMPLE

What are the contents of a cask whose length is 40 inches, and the bung and head diameters 32 and 24?
Ans 93.4579 gallons

32 × 32 = 1,024; 1,024 × 39 = 39,936
24 × 24 =   576;   576 × 25 = 14,400
32 × 24 =   768;   768 × 26 = 19,968
                              ------
                              73,304
                                  40
                           ---------
                           2,972,160
                          .00031 4/9
                           ---------
                             93.4579

I have to say, I’ve never seen a mixed decimal and fraction like .00031 4/9.

Short rules for finding the contents of plank and deals

To find the contents of 2-inch plank, multiply ⅙ of the length by the breadth. To find the contents of 3-inch deal, multiply ¼ of the length by the width. For 4-inch deal multiply ⅓ the length by the breadth.

  1. What are the contents of a deal 3 inches thick, 18 feet long, and 16 inches wide?
    18 ÷ 4 = 4½, 4½ × 16 = 72 feet. Ans
  2. In a plank 30 feet long and 16 inches wide, how many feet? 30 ÷ 6 = 5, 16 × 5 = 80 feet Ans
  3. What are the contents of a plank 24 feet long and 18 inches wide? 24 ÷ 6 = 4, 4 × 18 = 72 feet Ans
  4. What are the contents of a deal 24 feet long, 10 inches wide, and 4 inches thick? 24 ÷ 3 = 8, 8 × 10 = 80 feet Ans
  5. What are the contents of a deal 3 inches thick, 40 feet long, and 9 inches wide? 40 ÷ 4 = 10, 10 × 9 = 90 feet Ans

Triangles

To find the area of an equilateral triangle, having the side. — multiple ¼ of the square of the side by the square root of 3.

Having the area of a square, to find the side of an equilateral triangle equal in area to the square. RULE. — Divide the area by the square root of 3, and multiply the quotient by 4, and the square root gives the side.

Having the circumference of a circle, to find the side of the inscribed equilateral triangle RULE. — Multiply the circumference by .2756646, and the product is the side.

An equilateral triangle is one whose sides are all equal. The line drawn from the vertex perpendicular to the base is the altitude of the triangle. An isosceles triangle is one which has two of its sides equal. A scalene triangle is one which has its three sides unequal. A right angled triangle is one which has a right angle.

To find the area of a triangle. — Multiply the base by half the altitude, and the product will be the area. Or, add the three sides together, take half that sum, and from this subtract each side separately then multiply the half of the sum and these remainders together and the square root of this product will be the area.

To drive the cockroaches out of a house

One half pound of borax will drive the cockroaches out of any house.

A large handful of the powder to 10 gals. of water, will effect a savings of fifty per cent. in soap. It is an excellent dentifrice, and the best material for cleaning the scalp.

This is one of the rare bits of advice in this book that isn’t prima facie awful: I agree that borax is good for killing roaches, and of course it is an effective cleaner. As to all the other stuff, I was surprised at the idea of using it as toothpaste, but apparently it’s not a completely outrageous idea.

Form of an inland draft, with acceptance

$550.00
BOSTON, June 12, 1872

Six months after date, pay to the order of George Just, five hundred and fifty dollars for value received, and place the same to my account.

THOMAS PAY
to MR L. T. DELIVER. Merchant, Boston.

I had to look up “inland draft”. According to A Complete System of Practical Book Keeping in Four Sets of Books, it is “a written order from a party called the Drawer, addressed to another party called the Drawee, both in the same country, requiring the latter to pay his order, at a specified time, a certain amount in money or other property.”

American champagne

Good cider (crab-apple cider is best) 7 gals., best fourth proof brandy 1 qt., genuine champagne wine 5 qts., milk 1 gal., bi-tartrate of potassa 2 oz.; mix, and let stand a short time, bottle while fermenting. An excellent imitation.

Where do I even start with this? Offending purists with this violation of Appellation d’origine contrôlée? More adulterating of good ingredients? Milk?

Scarlet red

Take soft water sufficient to cover the cloth you wish to color, bring it to a boil, in a brass or copper kettle; then add 1½ oz. of cream tartar for every pound of cloth; now boil a minute or two, and then add 2 oz. of powdered lac, and 3 oz. of madder compound; the lac and compound must be previously mixed in a glass or earthen bowl; boil five minutes; now wet the cloth in warm water and wring and put in the dye; boil the whole an hour, take out the goods and rinse in clear cold water.