Glossary: Home Tables A B C D E F G H I J K L M N O P Q R S T Th U V W X Y Z
888888888888888 | g/dm³ 888888888888888 | Description |
---|---|---|
187.012 987 | 739.500 237 | 1 wine gallon = 8 tower lb wheat. |
189.243 746 | 748.321 265 | 1 imperial bushel = 60 lb avoirdepoise |
192.857 142 | 759.220 243 | 224 cu in = 8 tower pounds. |
194.726 070 | 770.000 000 | 1 hectolitre = 77 kilograms (finland) |
195.087 342 | 771.428 571 | 27/35; = tower / avoirdepoise. |
195.310 684 | 772.311 589 | 1 us bushel = 60 lb avoirdepoise |
200.000 000 | 790.854 420 | 216 cu in = 8 tower pounds |
201.860 000 | 798.209 366 | 1 imperial gallon = 8 lb avoirdepoise. |
888888888888888 | g/dm³ 888888888888888 | Description |
---|---|---|
235.688 043 651 | 931.974 655 657 | 112 lb = 12 coal gallons = 3326.32 cu in |
Tables: Home - m2in - kg2oz - gm2gr - Water - Gallon - Gal2in
- Inches - Technic - Pi
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 thingie |
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 |
Tables: Home - m2in - kg2oz - gm2gr - Water - Gallon - Gal2in - Inches - Technic - Pi
This is a list of the various gallons, and their expressions in terms of the cubic inch.
These were defined geometrically, either by their ratings in cubical inches, or in terms of a cylinder of defined height and diameter. A cylinder inch, is the measure, one inch in diameter and one inch high, and is used as a unit. The volume of cylinder gallons is thus D²H, in cylinder inches.
Year | Gallon |
1490 | The 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 these, the corn bushel becomes the US dry bushel, and the wine gallon becomes the liquid gallon.
There is a heaped bushel, formed by adding a cone to the top of this,
The Winchester Wine gallon is derived from a definition switch. The conversions of wine gallons to the imperial gallon G1 is 231/277.274 or 0.83311093 imperial gallons, rounded to 0.8331. When the gallon was recalibrated in 1897, this definition was not updated, and the WWG is 0.8331 of 4.54609 Litre or 231.186020 cu in, or 3.78734759 litres. This is somewhat larger than the US gallon of 231 cu in or 3.7854117 litres.
The imperial gallon is defined as the space occupied by that measure of water that would balance 10 pounds, when measured against brass weights at 62°F, and 30 inches Hg. Later, these conditions were defined in terms of their metric equalivants. The values shown here are those adopted for the 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 | 4.546 091 878 49 cu dm; 277.420 994 598 uk cu in 277.420 275 561 ub cu in |
The principle of bouyancy applies. Here, the balance is against apparant weights, which is the true weight reduced by the mass of the displaced air. This effectively reduces the density of the brass and water by that of air. The calculation goes like this. The mass m of brass occupies m/b units of volume. This volume has an apparent mass, as reduced by air of m÷b×(b-a). Likewise, the mass of water M has an apparant value of M÷w×(w/a). Now the apparent masses are equal, and because water is less dense than brass, displaces more air and so has a higher mass. Thus M = m÷b×(b-a)÷(w-a)×w. Now the volume is the space occupied by this mass at the density D, ie the gallon is M/D, or m×(b-a)×w÷b÷(w-a)÷D.
Putting the numbers into the above equations, we find: (here, 1 L = 1.000 028 cu dm)
The old gallon of 277.273 915 097 cu UV inches equates to 4.543 460 532 cu dm. The value 4.546 091 878 49 cu cm convers to cubic inches thus: 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 the time the value is set (1898), the current legal equalivants were the UC and as an auxhilary, UC, the value 277.420 can only arise from the UB.
The modern rating of the gallon, as defined in the act of 1985, is 4.546 09 litres. This rounds the equalivents of the gallon in terms of litre to five decimals, but in doing so, invalidates the 277.420 rating, since the gallon becomes 277.419 432 792 cu inches (UI). In terms of the other 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 this gallon as an alternate definition of the previous.
The US gallons were the pre-imperial gallons, rounded to the nearest 0.001
cubic inches. From the abandonment of the colonies to the Mendenhall Order,
the ultimate US standards were to replicate the UK ones, through legal replicas
and conversion factors.
From the time of the Mendenhall Order to 1959, the foot and pound were
defined in terms of the international metric system, by US standard, and thence
by the UI standard.
Tables: Home - m2in - kg2oz - gm2gr - Water - Gallon - Gal2in - Inches - Technic - Pi
in cu inches 888888888888888 | Description |
---|---|
224.000 000 000 | The gallon at the Guildhall, as reported in Berriman [p161]. This is rated as 8 lb at 250 grains / cu in. This is an early rating of the Wine Gallon. |
230.400 000 000 | The Berriman version of the Wine Gallon, being 8 lb troy at 250 gr / cu in. |
230.907 060 039 | The wine gallon is described as a cylinder, 6 inches high and 7 inches diameter. This makes 294 cylinder inches. |
230.996 969 400 | This is 0.8331 G1, the original rating of the Winchester Wing Gallon. This is the 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. The US uses this one. |
231.118 155 15 | This is the Winchester Wine Gallon, as 0.8331 G2, a version met in some conversion tables. This gallon appears in Horvath, for example. Note that 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 | The US dry gallon is defined as an eighth of a bushel. The bushel rounds 2738 cylinder inches to 3 places of decimal. |
268.802 521 423 | A dry gallon, rated as 342.25 cylinder inches. The proportional bushel is described as a cylinder, 18½ in in diameter and 8 in high. This is the Winchester bushel of 1696-7. |
269.391 570 045 | A seven-inch cylinder. It should be remembered that the Japanese unit of capacity is defined as a cube, the side of which is 7/10 of their foot or 7/33 metre. |
270.000 000 000 | Proposed US gallon |
272.000 000 000 | In 1688 three gallon prototypes each yielded 272 cu in - Berriman pp158 |
272.160 000 000 | Berriman rated this as the prototype corn gallon. This 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, the Irish parlement defined a corn gallon of this measure. |
276.480 000 000 | G0 The original intent of the imperial gallon was for water to be 1000 oz per cubic foot. |
276.799 095 262 | This is 10 lb of metric water, rated as 252.891 grains per cu in. |
277.083 333 333 | 10 lb of Shuckburgh's water; that 1 troy oz = 1.9 cu in |
277.202 568 400 | A coal gallon, as in [MS], this is 33/32 × 268.8025. |
277.228 285 714 | [39.6 inch] cube = 224 gallons. |
277.273 843 570 | This gallon is 10 lb, where 1 cu in weighs 252.458 grains. This is the value used in [MS] and Gwilt. |
277.273 915 097 | The unrounded value of G1, expressed in UV inches. This is calculated from the 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. This is 70000 ÷ 8.143 × 8.1418 ÷ 0.9988 × 1 ÷ 252.724. |
277.274 000 000 | G1: This gallon is the version as described in the act of 1820. |
277.419 432 792 | This is the UI gallon, rated as 4 546.09 cu cm, where the inch is 2.54 cms. The value of 4.546 09 is derived from 277.420 cu UB inches. |
277.419 547 424 | The gallon, as defined in 1963, here, the densities in g/L of brass = 8136, water = 998.859, air = 1.217, the litre = 1.000 028 cu dm, the conversions follow UI. The gallon becomes 4.545 964 591 48 litres, or 4.546 091 878 49 cu in. |
277.419 994 055 | This is 10 lb, where 1 cu in corresponds to 252.325 grains. |
277.420 000 000 | G2: This is the normal form the new gallon is quoted in. |
277.420 184 147 | The 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. This is converted using the UB factors. |
278.400 000 000 | four Quarts, measured from the 1758 measuring of a qt dated 1601. This appears to be the origion of the imperial gallon [a quart that gave nearly 20 oz of water]. |
280.000 000 000 | Berriman's proposed rating of this gallon (276-282). This is 10 lb at 250 gr / cu in. |
282.000 000 000 | This gallon is defined in terms of a Quart, rated as 70½ cubic inches. This is based on the 1688 measuring of the 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 |
Tables: Home - m2in - kg2oz - gm2gr - Water - Gallon - Gal2in - Inches - Technic - Pi
This section arranges in increasing order, the various appoximations to the ratio of the circumfenence to the diameter of the circle, expressed normally by the greek letter pi π.
Pi is less fundemental than e, for example. Radians on the other hand, arise quite naturally from the calculus (which is why they're used). While there should exist a constant k that nk radians make the circle, the is no over-riding reason why n should be two, in fact there are sound arguements to support 1, 2, 4, 6 and 8.
decimals 888888888888888 | Description |
---|---|
3.000 000 000 00 | 3 This is the value of pi, assuming the hexagon represents the circle. |
3.072 000 000 00 | A five inch sphere has the same volume as a four inch cube. |
3.125 000 000 00 | This value of pi appears as one of the forms in Berriman. It was also known as an approximation to the 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. This is the value of pi, when one radian equals 57.3 degrees. As an expression of 1/pi = &38&24/120, is accidently equal to the solid angle of the 120 cell /5,3,3, this being 38s 24f or &38&24/120 of the 4 sphere. |
3.141 567 230 22 | 823543/262144: This appears to be the best approximation to pi, using numbers whose prime factors are 2, 3, 5 and 7. The value is 7**7/8**6. Written in octal, the value of pi is 3.1103 7552 52, and this number is 3.1103 67. |
3.141 592 653 59 | Pi to 11 decimals. |
3.141 592 920 35 | 355/113, a very good approximation to pi. If ye want to run an experiment, the result depends on pi, ye can fake the results using this approximation. |
3.141 600 000 00 | 3.1416: This value of pi is known in India. Interistingly, the recripical of this 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, this is known from a number of different sources. |
3.141 666 666 66 | 377/120. This version of Pi is known in the sexagesimal form 3&8&30/60. In the form 3&17/120, it reflects a version of 1.2 × phi². In this form, it can be written as 1.2×377/144, where 377 and 144 are fibanacci mumbers. |
3.141 818 181 81 | 864/275. This equates a cubic foot with 2200 cylinder inches. |
3.142 337 619 40 | 24/35 sqrt(21). This comes from 1 cyl ft = 2800 hoppus in = 36 Litre. |
3.142 561 983 47 | 1521/484: This is 3&3&3/22. This ratio is a square (of 39/22), and thus a 44-inch circle has the same area as a 39-inch square. |
3.142 696 805 27 | 20/9 sqrt(2): This is the square root of 800/81. This is the value of pi, implied by equating the quadrant to 10 parts, where the inscribed square has an edge of 9. This is known to the ancient Egyptians. This value also makes an f-unit equal to a cubic inch on the surface of an eighteen-inch four-sphere, there being 14400 f-units making full space. |
3.142 857 142 85 | 22/7: 3&1/7. This is the most common approximation to pi, used in calculations. Metrologically, it is not at all common. The one place where it arises is the rating of the Wine Gallon as 294 cylinder inches, and 231 cubical inches. |
3.146 108 329 53 | 6912/2197: This equates a 13 inch cylinder with a 12 inch cube. |
3.150 000 000 00 | 63/20: This value of pi appears in Berriman, etc, as a form of the geographic pi.
The Swedish army mill uses this pi. |
3.152 161 253 53 | The geographic pi , defined as length of equator ÷ polar axis. Both of these measures have been extensively used in metrology. |
3.160 493 827 16 | 256/81, a value known to the Egyptians. A nine-inch circle has the same area as an eight-inch square. |
3.162 277 660 17 | sqrt(10): At one time, the square root of 10 was put forward as a version of pi. |
3.200 000 000 00 | 32/10: The value pi used in the NATO army mil. |
3.210 879 629 63 | 277.42/86.4, A cylinder foot is 5 gallons (BHP Lysaght) |