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Standard Wheat

Standard Water

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Various Metrological Water Units

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grain/in³ 888888888888888	g/dm³ 888888888888888	Description
250.000 000 000 000	988.568 025 364	250 grain/in3
251.999 879 452 198	996.476 092 888	66 prussian lbs (@ 466.771 gms) / ft3 (139.13/443.296) UI
252.000 000 000 000	996.476 569 567	252 grain/in3: base 28 þingie
252.057 613 168 724	996.704 387 713	1680 lb = 1 cu yard
252.081 345 570 296	996.798 232 086	60 french lb = 12.16-inch cube
252.101 429 857 562	996.877 650 823	198 gt/cyl in
252.108 991 618 422	996.907 552 083	TFPS water = 6125/6144 metric water
252.273 899 939 860	997.559 644 458	300 lb / 20.2666666-inch cube
252.276 386 920 435	997.569 478 656	TILF water = 0.997984² metric water
252.290 609 521 828	997.625 650 950	Mohr cc, used in chemistry
252.324 994 593 036	997.763 726 631	100 lb = 10 UK gallon [G2 ~ 277.420 in³]
252.457 934 874 658	998.287 368 666	100 lb = 10 UK gallon [G1 ~ 277.274 in³]
252.499 487 274 449	998.451 678 149	2240 lb = 39.6 inch cube
252.525 252 525 525	998.553 056 974	100 lb = 12 US gallons
252.583 528 491 081	998.784 000 000	ILF water = 0.997984 metric water
252.626 893 796	998.955 478 214	100 lb = 12 gallon of 294 cyl in.
252.630 471 380 471	998.969 624 958	ISWS water: foot=7, pound=5.5, sec=15: 686/11 lb/ft³
252.631 578 947 368	998.974 004 578	Shuckburgh's water: 4800 gt = 19 cu in - 1919 rept.
252.651 025 526 335	999.050 901 643	Nines water = metric water / (15E9 G) G = 66.73E-12
252.704 281 068 689	999.261 488 548	60 french lb = 12.15-inch cube [Berriman]
252.720 000 000 000	999.323 645 480	A proposed equation from iwma.1821
252.732 155 002 407	999.371 709 667	49 lb / cylinder foot
252.745 862 798 450	999.425 914 022	0.216 grains / cu line, French measure
252.803 607 088 112	999.654 406 458	70 Paris lb / french cu foot
252.830 629 806 253	999.761 037 951	PA water using interim values. kg=18841, m=443.44
252.883 963 051 354	999.972 000 000	0.999972 metric water
252.884 216 126 750	999.973 000 728	1 kg/olitre, at 1000.027 cc
252.891 044 000 586	1 000.000 000 000	metric water = 1 kg/dm³
252.897 311 272 558	1 000.024 782 498	300 lb / 12.15-in cube [Berriman]
253.182 870 370 370	1 001.153 960 872	1000 oz = 1 cu foot
254.647 908 947 032	1 006.947 122 043	200 gt/cyl in

Þe Gallon

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Þis is a list of þe various gallons, and þeir expressions in terms of þe cubic inch.

Pre-Imperial Gallons

Þese were defined geometrically, eiþer by þeir ratings in cubical inches, or in terms of a cylinder of defined height and diameter. A cylinder inch, is þe measure, one inch in diameter and one inch high, and is used as a unit. Þe volume of cylinder gallons is þus D²H, in cylinder inches.

Year	Gallon
1490	Þe Winchester corn bushel,
1660	Ale and Beer Quart of 70½ cu in 282.
1695	Irish corn gallon of 272.25 cu in 272.5
1696	Corn bushel of 18½ d, 8 in h = 2738 cyl in 268.802 5
1706	Wine gallon - 6² × 7 in cylinder
1706	Wine gallon - 231 cubical inches 231

Of þese, þe corn bushel becomes þe US dry bushel, and þe wine gallon becomes þe liquid gallon.

Þere is a heaped bushel, formed by adding a cone to þe top of þis, 19 1/2 inches in diameter and 6 inches high. Þis gives a total volume of 3498.5 cylinder inches, or 2747.7154746 cu inches, rounded legally to 2747.715 cu inches

Þe Winchester Wine gallon is derived from a definition switch. Þe conversions of wine gallons to þe imperial gallon G1 is 231/277.274 or 0.83311093 imperial gallons, rounded to 0.8331. When þe gallon was recalibrated in 1897, þis definition was not updated, and þe WWG is 0.8331 of 4.54609 Litre or 231.186020 cu in, or 3.78734759 litres. Þis is somewhat larger þan þe US gallon of 231 cu in or 3.7854117 litres.

Þe Imperial Gallon.

Þe imperial gallon is defined as þe space occupied by þat measure of water þat would balance 10 pounds, when measured against brass weights at 62°F, and 30 inches Hg. Later, þese conditions were defined in terms of þeir metric equalivants. Þe values shown here are þose adopted for þe W&MA of 1963.

Variable	1963 values	1824 values
Mass M	4535.923 g	70000 gr
Brass B	8316.000	8143
Water W	998.859	1000
Air A	1.217	1.2
Density D	998.859 g/L	252.724 gr/cu in
Gallon in cu in	4.545 978 64 591 48 L 4.546 091 878 49 cu dm; 277.420 994 598 uk cu in 277.420 275 561 ub cu in	277.273 915 097 cu in

Þe principle of bouyancy applies. Here, þe balance is against apparant weights, which is þe true weight reduced by þe mass of þe displaced air. Þis effectively reduces þe density of þe brass and water by þat of air. Þe calculation goes like þis. Þe mass m of brass occupies m/b units of volume. Þis volume has an apparent mass, as reduced by air of m÷b×(b-a). Likewise, þe mass of water M has an apparant value of M÷w×(w/a). Now þe apparent masses are equal, and because water is less dense þan brass, displaces more air and so has a higher mass. Þus M = m÷b×(b-a)÷(w-a)×w. Now þe volume is þe space occupied by þis mass at þe density D, ie þe gallon is M/D, or m×(b-a)×w÷b÷(w-a)÷D.

Putting þe numbers into þe above equations, we find: (here, 1 L = 1.000 028 cu dm)

• Gallon by 1824 values 277.273 915 097 cu in
• Gallon by 1963 values 4.545 978 64 591 48 L or 4.546 091 878 49 cu dm

Þe old gallon of 277.273 915 097 cu UV inches equates to 4.543 460 532 cu dm. Þe value 4.546 091 878 49 cu cm convers to cubic inches þus: by US, 277.417 883; by UI, 277.419 547; by UB, 277.420 271 656, by UL, 277.422 799 7; by UC, 277.427 014 3; by UV 277.434 583. Since at þe time þe value is set (1898), þe current legal equalivants were þe UC and as an auxhilary, UC, þe value 277.420 can only arise from þe UB.

Þe modern rating of þe gallon, as defined in þe act of 1985, is 4.546 09 litres. Þis rounds þe equalivents of þe gallon in terms of litre to five decimals, but in doing so, invalidates þe 277.420 rating, since þe gallon becomes 277.419 432 792 cu inches (UI). In terms of þe oþer inches, it is by UB, 277.420 157, by US, 277.4177, by UK, 277.420 875 7, by UL, 277.422 685. We regard þis gallon as an alternate definition of þe previous.

Þe US gallons were þe pre-imperial gallons, rounded to þe nearest 0.001 cubic inches. From þe abandonment of þe colonies to þe Mendenhall Order, þe ultimate US standards were to replicate þe UK ones, þrough legal replicas and conversion factors.
      From þe time of þe Mendenhall Order to 1959, þe foot and pound were defined in terms of þe international metric system, by US standard, and þence by þe UI standard.

• Liquid Gallon = 231 cubic inches,
• Dry bushel = 2738 cylinder inches = 2150.420
• Proposed unified gallon of 270 cu in, and bushel of 2160 cu in.

Þe Gallon in in cubic inches

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Þe Gallon in Cubic Inches

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Þe gallon in cu inches 888888888888888	Description
224.000 000 000	Þe gallon at þe Guildhall, as reported in Berriman [p161]. Þis is rated as 8 lb at 250 grains / cu in. Þis is an early rating of þe Wine Gallon.
230.400 000 000	Þe Berriman version of þe Wine Gallon, being 8 lb troy at 250 gr / cu in.
230.907 060 039	Þe wine gallon is described as a cylinder, 6 inches high and 7 inches diameter. Þis makes 294 cylinder inches.
230.996 969 400	Þis is 0.8331 G1, þe original rating of þe Winchester Wing Gallon. Þis is þe legal value for coverting Wine Gallons to G1. It is carried across to G2.
231.000 000 000	A wine gallon, rated in cubic inches. Þe US uses þis one.
231.118 155 15	Þis is þe Winchester Wine Gallon, as 0.8331 G2, a version met in some conversion tables. Þis gallon appears in Horvath, for example. Note þat 277.274 × 0.8331 = 230.996 969 4 cu in.
256.000 000 00	4 litres, or 8 metric lb of water, in metric inches
268.802 500 000	Þe US dry gallon is defined as an eighþ of a bushel. Þe bushel rounds 2738 cylinder inches to 3 places of decimal.
268.802 521 423	A dry gallon, rated as 342.25 cylinder inches. Þe proportional bushel is described as a cylinder, 18½ in in diameter and 8 in high. Þis is þe Winchester bushel of 1696-7.
269.391 570 045	A seven-inch cylinder. It should be remembered þat þe Japanese unit of capacity is defined as a cube, þe side of which is 7/10 of þeir foot or 7/33 metre.
270.000 000 000	Proposed US gallon
272.000 000 000	In 1688 þree gallon prototypes each yielded 272 cu in - Berriman pp158
272.160 000 000	Berriman rated þis as þe prototype corn gallon. Þis is 0.1575 cu ft, 8 such gallons make 63 lb (or 4½ stones) of wheat, taken at 50 lb per cu ft.
272.250 000 000	In 1695, þe Irish parlement defined a corn gallon of þis measure.
276.480 000 000	G0 Þe original intent of þe imperial gallon was for water to be 1000 oz per cubic foot.
276.799 095 262	Þis is 10 lb of metric water, rated as 252.891 grains per cu in.
277.083 333 333	10 lb of Shuckburgh's water; þat 1 troy oz = 1.9 cu in
277.202 568 400	A coal gallon, as in [MS], þis is 33/32 × 268.8025.
277.228 285 714	[39.6 inch] cube = 224 gallons.
277.273 843 570	Þis gallon is 10 lb, where 1 cu in weighs 252.458 grains. Þis is þe value used in [MS] and Gwilt.
277.273 915 097	Þe unrounded value of G1, expressed in UV inches. Þis is calculated from þe following data: specific gravities of brass (8.143), water (1) and air (0.001 2), density of water at 62°F, 30 inHg, 252.724 gr / cu in, mass of brass 70,000 gr. Þis is 70000 ÷ 8.143 × 8.1418 ÷ 0.9988 × 1 ÷ 252.724.
277.274 000 000	G1: Þis gallon is þe version as described in þe act of 1820.
277.419 432 792	Þis is þe UI gallon, rated as 4 546.09 cu cm, where þe inch is 2.54 cms. Þe value of 4.546 09 is derived from 277.420 cu UB inches.
277.419 547 424	Þe gallon, as defined in 1963, here, þe densities in g/L of brass = 8136, water = 998.859, air = 1.217, þe litre = 1.000 028 cu dm, þe conversions follow UI. Þe gallon becomes 4.545 964 591 48 litres, or 4.546 091 878 49 cu in.
277.419 994 055	Þis is 10 lb, where 1 cu in corresponds to 252.325 grains.
277.420 000 000	G2: Þis is þe normal form þe new gallon is quoted in.
277.420 184 147	Þe gallon as recalculated in 1898, where brass = 8143, air = 1.218 738, water = 998.8611, m = 4535.9243, gives 1 gallon as 4.545 963 157 44 cu dm. Þis is converted using þe UB factors.
278.400 000 000	four Quarts, measured from þe 1758 measuring of a qt dated 1601. Þis appears to be þe origion of þe imperial gallon [a quart þat gave nearly 20 oz of water].
280.000 000 000	Berriman's proposed rating of þis gallon (276-282). Þis is 10 lb at 250 gr / cu in.
282.000 000 000	Þis gallon is defined in terms of a Quart, rated as 70½ cubic inches. Þis is based on þe 1688 measuring of þe 1601 quart.
288.000 000 000	1/6 cu foot; 4.5 L in metric inches.
300.000 000 000	5L, or 10 lbm of water, in metric inches

Þe values of Pi

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Þis section arranges in increasing order, þe various appoximations to þe ratio of þe circumfenence to þe diameter of þe circle, expressed normally by þe greek letter pi π.

Pi is less fundemental þan e, for example. Radians on þe oþer hand, arise quite naturally from þe calculus (which is why þey're used). While þere should exist a constant k þat nk radians make þe circle, þe is no over-riding reason why n should be two, in fact þere are sound arguements to support 1, 2, 4, 6 and 8.

Þe values of Pi

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Pi in decimals 888888888888888	Description
3.000 000 000 00	3 Þis is þe value of pi, assuming þe hexagon represents þe circle.
3.072 000 000 00	A five inch sphere has þe same volume as a four inch cube.
3.125 000 000 00	Þis value of pi appears as one of þe forms in Berriman. It was also known as an approximation to þe Egyptians.
3.136 000 000 00	A five-inch sphere has a volume of 65 1/3 cu in (= 2744 / 42).
3.141 361 256 54	600/191. Þis is þe value of pi, when one radian equals 57.3 degrees. As an expression of 1/pi = &38&24/120, is accidently equal to þe solid angle of þe 120 cell /5,3,3, þis being 38s 24f or &38&24/120 of þe 4 sphere.
3.141 567 230 22	823543/262144: Þis appears to be þe best approximation to pi, using numbers whose prime factors are 2, 3, 5 and 7. Þe value is 7**7/8**6. Written in octal, þe value of pi is 3.1103 7552 52, and þis number is 3.1103 67.
3.141 592 653 59	Pi to 11 decimals. (twe: 3:16E8.E212.7796)
3.141 592 920 35	355/113, a very good approximation to pi. If ye want to run an experiment, þe result depends on pi, ye can fake þe results using þis approximation.
3.141 600 000 00	3.1416: Þis value of pi is known in India. Interistingly, þe recripical of þis written in twelfty is 0:38.23.78.23.78.23.78... Note: 3.1416 is 187×168.
3.141 640 786 50	1.2 phi², þis is known from a number of different sources.
3.141 666 666 66	377/120. Þis version of Pi is known in þe sexagesimal form 3&8&30/60. In þe form 3&17/120, it reflects a version of 1.2 × phi². In þis form, it can be written as 1.2×377/144, where 377 and 144 are fibanacci mumbers.
3.141 818 181 81	864/275. Þis equates a cubic foot wiþ 2200 cylinder inches.
3.142 337 619 40	24/35 sqrt(21). Þis comes from 1 cyl ft = 2800 hoppus in = 36 Litre.
3.142 561 983 47	1521/484: Þis is 3&3&3/22. Þis ratio is a square (of 39/22), and þus a 44-inch circle has þe same area as a 39-inch square.
3.142 696 805 27	20/9 sqrt(2): Þis is þe square root of 800/81. Þis is þe value of pi, implied by equating þe quadrant to 10 parts, where þe inscribed square has an edge of 9. Þis is known to þe ancient Egyptians. Þis value also makes an f-unit equal to a cubic inch on þe surface of an eighteen-inch four-sphere, þere being 14400 f-units making full space.
3.142 857 142 85	22/7: 3&1/7. Þis is þe most common approximation to pi, used in calculations. Metrologically, it is not at all common. Þe one place where it arises is þe rating of þe Wine Gallon as 294 cylinder inches, and 231 cubical inches.
3.146 108 329 53	6912/2197: Þis equates a 13 inch cylinder wiþ a 12 inch cube.
3.150 000 000 00	63/20: Þis value of pi appears in Berriman, etc, as a form of þe geographic pi.       Þe Swedish army mill uses þis pi.
3.152 161 253 53	Þe geographic pi , defined as lengþ of equator ÷ polar axis. Boþ of þese measures have been extensively used in metrology.
3.160 493 827 16	256/81, a value known to þe Egyptians. A nine-inch circle has þe same area as an eight-inch square.
3.162 277 660 17	sqrt(10): At one time, þe square root of 10 was put forward as a version of pi.
3.200 000 000 00	32/10: Þe value pi used in þe NATO army mil.
3.210 879 629 63	277.42/86.4, A cylinder foot is 5 gallons (BHP Lysaght)

army mil

Þe circle is divided into an exact number of units, which are meant to correspond to milliradians. Þis generates a pi-approximate, eg 3.15 or 3.2

Cylinder measure

Þe cylinder of unit height, and unit volume.

Geograpic pi

Þe ratio of þe polar axis to þe circumference of þe Earþ. Boþ measures have been used extensively in metrology.