Part 220

PRACTICAL APPLICATIONS OF CUBIC MEASURE

EXAMPLE: An open tank made of iron 1/4 inch thick, is 4 feet long, 2 feet 6 inches broad, and 2 feet deep, outside measurement. Assuming that iron weighs 7.8 times as much as water, find the weight of the tank.

The external volume of the tank = 2 × 2-1/2 × 4 cubic feet = 20 cubic feet.

Since the iron is 1/4 inch thick, the inside length is 1/2 inch less than the outside, the inside breadth is 1/2 inch less than the outside, and the inside depth is 1/4 inch less than the outside.

Therefore the interior volume

= 29-1/2 × 47-1/2 × 23-3/4 cubic inches

59 × 95 × 95 = ------------ cubic inches 16

= 33279-11/16 cubic inches

Therefore, volume of iron in the tank

= 20 cubic feet - 33279-11/16 cubic inches = 1280-5/16 cubic inches.

But 1 cubic foot of iron weighs as much as 7.8 cubic feet of water, _i. e._, 7.8 × 1000 ounces, or 7800 ounces.

1280-5/16 × 7800 ∴ Weight of tank = ---------------- pounds. 1728 × 16

= 361.199 pounds, _Ans._

EXAMPLE: A wood pile is 8 feet high and 40 feet long. The sticks are 4 feet long. How many cords in it?

SOLUTION: Being 8 feet high, it is 2 cords high. 40 feet in length equal 5 cords in length. Hence, the pile contains 2 × 5 cords, or 10 cords.

To estimate a bin:

(1) Find the number of cubic feet in the bin.

(2) Divide the number of cubic feet by 1-1/4.

(3) The result is the number of bushels.

EXAMPLE: How many bushels will a bin hold, if its inside measurements are, length 20 feet, width 12 feet, depth 8 feet?

SOLUTION: The number of cubic feet in a bin is 8 × 12 × 20, or 1920.

If 1 bushel contains 1-1/4 cubic feet, in 1920 cubic feet there are as many bushels as 1-1/4 is contained times in 1920, or 1536.

WORK:

8 × 12 × 20 = 1920 1920 ÷ 1-1/4 = 1536.

The work may be indicated in this way as well:--

8 × 12 × 20 × 4/5 = 1536.

To get the number of heaped bushels of corn in the ear in a crib:

(1) Multiply the length of the crib in inches by the width in inches.

(2) Multiply the product obtained, by the height of the corn in the crib in inches.

(3) Divide the result by 2748.

EXAMPLE: How much corn in the ear can I put into a crib 12 feet wide, 20 feet long, and 10 feet deep?

SOLUTION: The number of cubic inches in the crib is 144 × 240 × 120, or 4,147,200.

Since 2748 cubic inches hold 1 bushel, 4,147,200 cubic inches hold as many bushels as 2748 is contained times in 4,147,200, or 1509+ bushels.

WORK:

144 × 240 × 120 --------------- = 1509+. 2748

MEASURES OF CAPACITY

Measures used in telling the extent of room in vessels are called _measures of capacity_.

There are two kinds of capacity measures, dry measures and liquid measures.

Dry measures are used to measure grain, seeds, and the like.

Liquid measures are used to measure water, milk, oils, etc.

COMMON LIQUID MEASURE TABLE

4 gills (gi.) = 1 pint (pt.) 2 pints = 1 quart (qt.) 4 quarts = 1 gallon (gal.) 31-1/2 gallons = 1 barrel (bbl.) 2 barrels = 1 hogshead (hhd.)

Gallon Quarts Pints Gills 1 = 4 = 8 = 32

A pint, quart, or gallon, dry measure, is more than the same quantity, liquid measure; for a quart, dry measure, is 1/32 of a bushel, or 1/32 of 2150.4 cubic inches, which is about 67-1/5 cubic inches, while a quart liquid measure is 1/4 of 231 cubic inches, or 57-3/4 cubic inches.

Cu. In. Cu. In. Cu. In. Cu. In. in 1 Gal. in 1 Qt. in 1 Pt. in 1 Gi. Liquid measure 231 57-3/4 28-7/8 7-7/32 Dry measure 268-4/5 67-1/5 33-3/5 8-2/5

In determining the capacity of cisterns, reservoirs, etc., 31-1/2 gallons are considered a barrel (bbl.), and 2 barrels, or 63 gallons, a hogshead (hhd.). In commerce, however, the barrel and hogshead are not fixed measures.

Casks of large size, called tierces, pipes, butts, tuns, etc., do not hold any fixed quantity. Their capacity is usually marked upon them.

The standard gallon of the United States contains 231 cubic inches, and will hold a little over 8-1/3 pounds of distilled water. The imperial gallon, now adopted by Great Britain, contains 277.274 cubic inches, or 10 pounds of distilled water, temperature 62 degrees Fahrenheit, the barometer standing at 30 inches.

TABLE OF APOTHECARIES’ LIQUID MEASURE

These measures are used in mixing medicines.

60 minims (m) = 1 fluid dram (_f_ʒ) 8 fluid drams = 1 fluid ounce (_f_℥) 16 fluid ounces = 1 pint (_O._) 8 pints = 1 gallon (_Cong._)

A minim is about 1 drop.

TABLE OF DRY MEASURE

2 pints (pt.) = 1 quart (qt.) 8 quarts = 1 peck (pk.) 4 pecks = 1 bushel (bu.)

Bushel Pecks Quarts Pints 1 = 4 = 32 = 64

A common Winchester bushel (the standard of the United States) contains 2150.42 cubic inches.

A dry quart contains 67.2 cubic inches.

A liquid quart contains 57.75 cubic inches.

EXAMPLE 1: Reduce 5 bushels 2 pecks 4 quarts 1 pint to pints.

OPERATION:

4 8 2 bu. pk. qt. pts. 5 2 4 1 4 --- 22 pk. 8 --- 180 qt. 2 --- 361 pt.

EXPLANATION: As there are 4 pecks in 1 bushel, any number of bushels is equal to 4 times that number of pecks. Then, 5 bushels = 20 pecks, and 2 pecks added make 22 pecks. As there are 8 quarts in 1 peck, any number of pecks is equal to 8 times that number of quarts. Then 22 pecks = 176 quarts, and 4 quarts added make 180 quarts. As there are 2 pints in 1 quart, any number of quarts is equal to 2 times that number of pints. Then, 180 quarts = 360 pints, and 1 pint added make 361 pints. Hence, 5 bushels 2 pecks 4 quarts 1 pint = 361 pints.

EXAMPLE 2: Reduce 361 pints to bushels.

OPERATION: 2 |361 pt. +--- 8 |180 qt. + 1 pt. +--- 4 | 22 pk. + 4 qt. +--- | 5 bu. + 2 pk.

EXPLANATION: As there are 2 pints in 1 quart, 361 pints are equal to one-half that number of quarts = 180 quarts, with a remainder of 1 pint. Also, 180 quarts are equal to one-eighth of that number of pecks = 22 pecks, with a remainder of 4 quarts. Finally, 22 pecks are equal to one-fourth of that number of bushels = 5 bushels, with a remainder of 2 pecks. Hence, 361 pints are equal to 5 bushels 2 pecks 4 quarts 1 pint.

MEASURES OF WEIGHT

AVOIRDUPOIS WEIGHT

Avoirdupois Weight is used for weighing heavy articles as grain, groceries, coarse metals, etc.

16 ounces (oz.) = 1 pound (lb.) 100 pounds = 1 hundredweight (cwt.) 20 hundredweight = 1 ton (T.)

Hundred- Ton weight Pounds Ounces 1 = 20 = 2000 = 32000

Scale.--20, 100, 16.

In weighing coal at the mines and in levying duties at the United States Custom House, the long ton of 2240 pounds is sometimes used.

The ounce is considered as 16 drams.

The unit is the pound. It contains 7000 grains.

The following denominations are also used:

14 pounds = 1 stone 100 pounds butter = 1 firkin 100 pound grain or flour = 1 cental 100 pounds dried fish = 1 quintal 100 pounds nails = 1 keg 196 pounds flour = 1 barrel 200 pounds pork or beef = 1 barrel 280 pounds salt at N. Y. works = 1 barrel

TROY WEIGHT

Troy Weight is used in weighing gold, silver, and jewels.

TABLE

24 grains (gr.) = 1 pennyweight (pwt.) 20 pennyweights = 1 ounce (oz.) 12 ounces = 1 pound (lb.)

Penny- Pounds Ounces weights Grains 1 = 12 = 240 = 5760

In weighing diamonds, pearls, and other jewels, the unit commonly employed is the _carat_, which is equal to 4 carat grains, or 3.168 Troy grains.

The term _carat_ is also used to express the fineness of gold, and means 1/24 part. Thus, gold that is 18 carats fine is 18/24 gold, and 6/24 alloy.

The _standard unit_ of weight is the _Troy pound_. It is equal to the weight of 22.7944 cubic inches of distilled water at its maximum density, the barometer being at 30 inches. It is identical with the Troy pound of Great Britain.

The following are approximate avoirdupois weights of certain articles of produce according to the laws of the United States, and in the majority of States:

=Table I. UNITED STATES LEGAL WEIGHTS= (_in pounds_) =PER BUSHEL=

=Prepared by the United States Bureau of Standards=

================+============+====+=============+=====+=====+=====+====== STATE OR | APPLES | | BEANS | | | | TERRITORY +-----+------+ +-----+-------+ | | | |Apple| Dried|BAR-|Beans| Castor|BEETS|BLUE-|BRAN*|BROOM- | * |Apples| LEY| * | Beans,| |GRASS| | CORN | | | | |Shelled| | SEED| | SEED ----------------+-----+------+----+-----+-------+-----+-----+-----+------ =United States= | ...| ...| 48| 60| 50| ...| ...| ...| ... +-----+------+----+-----+-------+-----+-----+-----+------ =Alabama= | ...| 24| 47| 60| ...| ...| ...| ...| ... =Arizona= | ...| ...| 45|_a_55| ...| ...| ...| ...| ... =Arkansas= |_b_50| 24| 48|_a_60| ...| ...| 14| 20| 48 =California= | ...| ...| 50| ...| ...| ...| ...| ...| ... =Colorado= | ...| ...| 48| 60| ...| ...| 14| ...| ... =Connecticut= | 48| 25| 48| 60| ...|_c_60| ...| 20| ... =Delaware= | ...| ...| ...| ...| ...| ...| ...| ...| ... =Florida= |_b_48| 24| 48|_d_60| 48| ...| ...| 20| ... =Georgia= | ...| 24| 47|_e_60| ...| ...| 14|_f_20| ... =Hawaii= | ...| ...| 48| ...| ...| ...| ...| ...| ... =Idaho= | ...| 28| 48| ...| ...| ...| ...| ...| ... =Illinois= | ...| 24| 48|_e_60| 46| ...| 14| 20| ... =Indiana= | ...| 25| 48| 60| 46| ...| 14| ...| ... =Iowa= | 48| 24| 48| 60| 46| 56| 14| 20| 50 =Kansas= |_b_48| 24| 48| 60| 46| 56|_h_14| 20| ... =Kentucky= | ...| 24| 47|_e_60| *45| ...| 14| 20| ... =Louisiana= | ...| ...| 32| ...| ...| ...| ...| ...| ... =Maine= | 44| ...| 48| 60| ...| 60| ...| ...| ... =Maryland= | ...| 28| ...| ...| 50| ...| 14| 20| ... =Massachusetts= | 48| 25| 48|_k_60| ...| 60| ...| 20| ... =Michigan= | 48| 22| 48| 60| 46| ...| 14| ...| ... =Minnesota= |_b_50| 28| 48| 60| ...| 50| 14| ...| 57 =Mississippi= | ...| 26| 48|_e_60| _m_46| ...| 14| 20| ... =Missouri= | 48| 24| 48|_m_60| 46| ...| 14| 20| ... =Montana= | 45| ...| 48| 60| ...| 50| 14| 20| ... =Nebraska= | 48| 24| 48|_e_60| 46| ...| 14| 20| ... =Nevada= |_b_48| 24| 48| 60| 46| 56| _h_| 20| ... =New Hampshire= | 48| 25| 48| 62| ...| 60| ...| 20| ... =New Jersey= | 50| 25| 48| 60| ...| 60| ...| ...| ... =New York= | 48| 25| 48| 60| ...| ...| ...| 20| ... =North Carolina=| 48| ...| 48| ...| *46| ...| 14| ...| 46 =North Dakota= | 50| ...| 48| 60| ...| 60| ...| 20| 30 =Ohio= | 50| 24| 48| 60| ...| 56| ...| ...| ... =Oklahoma= | 48| 24| 48| 60| ...| 60| 14| 20| 30 =Oregon= | 45| 28| 46| ...| ...| ...| ...| ...| ... =Pennsylvania= | ...| ...| 47| ...| ...| ...| ...| ...| ... =Rhode Island= | 48| 25| 48| 60| 46| 50| ...| 20| ... =South Carolina=| ...| ...| ...| ...| ...| ...| ...| ...| ... =South Dakota= | ...| ...| 48| 60| ...| 60| ...| 20| 30 =Tennessee= |_b_50| 24| 48|_p_60| 46| 50| 14| 20| 42 =Texas= | 45| 28| 48|_e_60| ...| ...| ...| 20| ... =Vermont= | 46| ...| 48| 62| ...| 60| ...| ...| ... =Virginia= | 45| 28| 48|_e_60| ...| ...| 14| ...| ... =Washington= |_b_45| 28| 48| ...| ...| ...| ...| ...| ... =West Virginia= | ...| 25| 48| 60| ...| ...| ...| ...| ... =Wisconsin= | 50| 25| 48| 60| ...| 50| ...| 20| ... ----------------+-----+------+----+-----+-------+-----+-----+-----+------

================+=====+====+=====+=====+====+=============+==== STATE OR | | | | | | CORN | TERRITORY | | | | | +-----+-------+ |BUCK-|CAR-| CLO-| COAL|COKE|Corn |Shelled|CORN |WHEAT|ROTS| VER | | | in | Corn |MEAL | | | SEED| | | Ear | | * ----------------+-----+----+-----+-----+----+-----+-------+---- =United States= | 48| ...| ...| 80| ...| ...| ...| ... +-----+----+-----+-----+----+-----+-------+---- =Alabama= | ...| ...| ...| ...| ...| 70| 56| ... =Arizona= | ...| ...| ...| ...| ...| ...| ...| ... =Arkansas= | 52| ...| 60| ...| ...| 70| 56| 48 =California= | 40| ...| ...| ...| ...| ...| ...| ... =Colorado= | 52| ...| 60| 80| ...| 70| ...| 50 =Connecticut= | 48| 50| 60| 80| ...| ...| ...| 50 =Delaware= | ...| ...| ...| ...| ...| ...| ...| ... =Florida= | ...| ...| ...| ...| ...| 70| 56| 48 =Georgia= | 52| ...| 60| 80| ...| 70| 56| 48 =Hawaii= | ...| ...| ...| ...| ...| ...| ...| ... =Idaho= | 42| ...| 60| ...| ...| ...| 56| ... =Illinois= | 52| ...| 60| 80| ...| 70| 56| 48 =Indiana= | 50| ...| 60| 80| ...|_g_68| 56| 50 =Iowa= | 52| 50| 60| 80| 38| 70| 56| 50 =Kansas= | 50| 50| 60| 80| ...| 70| _i_56| ... =Kentucky= | 56| ...| 60| 76| ...|_j_70| 56| 50 =Louisiana= | ...| ...| ...| ...| ...| ...| ...| ... =Maine= | 48| 50| ...| ...| ...| ...| ...| 50 =Maryland= | ...| 50| 60| 80| ...| ...| 56| 48 =Massachusetts= | 48| 50| 60| ...| ...| ...| _l_56| 50 =Michigan= | 48| ...| 60| 80| ...| 70| 56| 50 =Minnesota= | 50| 45| 60| 80| ...| 70| 56| ... =Mississippi= | 48| ...| 60| 80| ...| 72| 56| 48 =Missouri= | 52| 50| 60| 80| ...| 70| 56| 50 =Montana= | 52| 50| 60| 76| ...| 70| 56| 50 =Nebraska= | 52| ...| 60| 80| ...| 70| 56| 50 =Nevada= | 50| 50| 60| ...| ...| 70| 56| 48 =New Hampshire= | 48| 50| 60| ...| ...|_e_50| ...| 50 =New Jersey= | 50| 50| 64| ...| ...| ...| ...| ... =New York= | 48| 50| 60| ...| ...| ...| ...| 50 =North Carolina=| 50| ...| 60| ...| ...| ...| ...| 48 =North Dakota= | 42| ...| 60| 80| ...| 70| 56| ... =Ohio= | 50| 50| 60|_n_80| 40| 68| 56| ... =Oklahoma= | 52| 50| 60| 80| ...| 70| 56| 50 =Oregon= | 42| ...| 60| ...| ...| ...| ...| ... =Pennsylvania= | 48| ...| 60|_o_76| 40| ...| ...| ... =Rhode Island= | 48| 50| 60| 80| 40| 70| 56| 50 =South Carolina=| ...| ...| ...| ...| ...| ...| ...| 48 =South Dakota= | 42| ...| 60| 80| ...| 70| 56| ... =Tennessee= | 50| 50|_q_60| 80| 40| 70| 56| ... =Texas= | 42| ...| 60| 80| ...| 70| 56| ... =Vermont= | 48| 50| 60| ...| ...| ...| ...| ... =Virginia= | 52| ...| 60| 80| ...| 70| 56| 50 =Washington= | 42| ...| 60| ...| ...| ...| ...| ... =West Virginia= | 52| ...| 60| 80| ...| ...| ...| ... =Wisconsin= | 50| 50| 60| ...| ...| ...| ...| 50 ----------------+-----+----+-----+-----+----+-----+-------+----

=Table I. UNITED STATES LEGAL WEIGHTS= (_in pounds_) =PER BUSHEL--Continued=

================+======+======+=============+=====+=====+======+=====+===== STATE OR | | | COTTON SEED | | | | | TERRITORY | | +------+------+ | | | | | CORN | CORN |Cotton|Sea- |CRAN-|FLAX-|GOOSE-|PLAS-|HEMP- | MEAL,| MEAL,| Seed*|Island| BER-| SEED| BER- | TER-| SEED |BOLTED| UN- | | | RIES|(LIN-| RIES | ING | | |BOLTED| | | |SEED)| | HAIR| ----------------+------+------+------+------+-----+-----+------+-----+----- =United States= | ...| ...| ...| ...| ...| 56| ...| ...| ... +------+------+------+------+-----+-----+------+-----+----- =Alabama= | ...| ...| 32| ...| ...| ...| ...| ...| ... =Arizona= | ...| ...| ...| ...| ...| ...| ...| ...| ... =Arkansas= | ...| ...|33-1/3| ...| ...| 56| ...| ...| ... =California= | ...| ...| ...| ...| ...| ...| ...| ...| ... =Colorado= | ...| ...| ...| ...| ...| ...| ...| ...| 44 =Connecticut= | ...| ...| 30| 44| ...| 55| ...| ...| ... =Delaware= | 44| 48| ...| ...| ...| ...| ...| ...| ... =Florida= | ...| ...| 32| 46| ...| ...| ...| ...| ... =Georgia= | ...| ...| 30| ...| ...| 56| ...| 8| 44 =Hawaii= | ...| ...| ...| ...| ...| ...| ...| ...| ... =Idaho= | ...| ...| ...| ...| ...| 56| ...| ...| ... =Illinois= | ...| ...| ...| ...| ...| 56| ...| 8| 44 =Indiana= | ...| ...| ...| ...| 33| ...| ...| ...| 44 =Iowa= | ...| ...| ...| ...| ...| 56| 40| ...| 44 =Kansas= | ...| ...| ...| ...| ...| 56| ...| _r_8| 44 =Kentucky= | ...| ...| ...| ...| ...| 56| ...| 8| 44 =Louisiana= | ...| ...| ...| ...| ...| ...| ...| ...| ... =Maine= | ...| ...| ...| ...| ...| ...| ...| 11| ... =Maryland= | ...| ...| ...| ...| ...| 56| ...| ...| 44 =Massachusetts= | ...| ...| 30| 44| 32| 55| ...| ...| ... =Michigan= | ...| ...| ...| ...| 40| 56| ...| ...| 44 =Minnesota= | ...| ...| ...| ...| 36| ...| 40| _r_8| 50 =Mississippi= | 44| 48| 32| ...| ...| 56| ...| ...| 44 =Missouri= | ...| ...| 33| ...| ...| 56| ...| ...| 44 =Montana= | ...| ...| ...| ...| ...| 56| ...| ...| 44 =Nebraska= | ...| ...| ...| ...| ...| 56| ...| 8| 44 =Nevada= | ...| ...| ...| ...| ...| 56| ...| ...| 48 =New Hampshire= | ...| ...| ...| ...| 32| 56| ...| ...| ... =New Jersey= | ...| ...| ...| ...| ...| 55| ...| ...| ... =New York= | ...| ...| 30| 44| ...| 55| ...| ...| ... =North Carolina=| 48| 48| 30| 44| ...| 55| ...| ...| 44 =North Dakota= | ...| ...| ...| ...| ...| 56| ...| ...| ... =Ohio= | ...| ...| ...| ...| ...| 56| ...| ...| 44 =Oklahoma= | ...| ...| 32| ...| ...| 56| ...| ...| 44 =Oregon= | ...| ...| ...| ...| ...| ...| ...| ...| ... =Pennsylvania= | ...| ...| ...| ...| ...| ...| ...| ...| ... =Rhode Island= | ...| ...| 30| 44| ...| 56| ...| ...| 44 =South Carolina=| 48| 48| 30| ...| ...| ...| ...| ...| ... =South Dakota= | ...| ...| ...| ...| ...| 56| ...| ...| ... =Tennessee= | 50| 48| 28| ...| ...| 56| 48| 8| 44 =Texas= | ...| ...| 32| ...| ...| 56| ...| ...| 44 =Vermont= | ...| ...| ...| ...| ...| ...| ...| ...| ... =Virginia= | ...| ...| 32| ...| ...| 56| ...| 8| 44 =Washington= | ...| ...| ...| ...| ...| 56| ...| ...| ... =West Virginia= | ...| ...| ...| ...| ...| 56| ...| ...| ... =Wisconsin= | ...| ...| 30| 44| ...| 56| ...| 8| 44 ----------------+------+------+------+------+-----+-----+------+-----+-----