The Physics
Opus in profectus

British-American System of Units

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In like manner there were natural measures of quantity, such as fathoms, cubits, inches, taken from the proportion of the human body, were once in use with every nation. But by a little observation, they found that one man's arm was longer or shorter than another's, and that one was not to be compared with the other, and therefore wise men who attended to these things would endeavour to fix upon some more accurate measure, that equal quantities might be of equal values. Their method became absolutely necessary when people came to deal in many commodities, and in great quantities of them.

Adam Smith, 1763

This intro should talk about the cultural origin of these traditional units, but I haven't decided what to write yet. Let's just say they evolved in ways that were more organic and less logical than the SI units. The rest of the discussion follows this sequence: traditional units (length, mass, area, volume), non-metric scientific units (the foot-pound-second systems), and then let's try to end it.


The English system is composed of a lot of very sensible length units. Hands, feet, rods, paces — these are things most of us can relate to. Furlongs, fathoms, miles, yards — these make sense if you know a little bit of etymology (the study of the origin and evolution of words). Unfortunately, the conversion factors are a mess. Feet don't fit into furlongs in an easy to grasp way. There are a lot of "nice" numbers in this system — numbers like 3, 4, 5, 6, 8, 12 and 16 — but after a while the "nice" numbers put you through combinatoric gyrations that bring computational pain and suffering.

One thousandth of an inch. Called a mil in the United States. The plural of thou is thou. One thousand thou equal one inch. The plural of mil is mils. One thousand mils equal one inch.
An inch was originally the width of a man's thumb, but was later defined as the length of three barleycorns placed end to end. The word inch comes from the Latin word for one-twelfth (uncia). The Romans brought the concept of the 12 inch foot to England when they invaded in the year 43 and left it behind when they were expelled in the year 409. The inch is commonly subdivided into halves, quarters, eighths, sixteenths, and other powers of two; but can also be divided into hundredths (as in the caliber of firearms) or thousandths (called thou in the UK and mils in the US). One inch is now defined as 0.0254 m (or 2.54 cm if you prefer).
A hand is the width of a man's hand measured across the palm and including the thumb. It was traditionally used to measure the height of horses and not much else as far as I can tell. A standard hand is 4 inches.
A foot is the length of a man's foot — a convenient measuring tool for men with feet. A standard foot is 12 inches.
A cubit is the distance from the elbow to the tip of the middle finger on a man's arm. The name is derived from the Latin word for elbow (cubitum). The cubit is an ancient unit that has varied somewhat over time and place. The Roman cubit was 17.47 inches long, the Greek 18.20 inches, the Sumerian 20.42 inches, and the Egyptian 20.6 to 20.8 inches. The English cubit is 18 inches.
A yard is the length from the King's nose to his outstretched hand. Presumably, after the king held out his hand someone placed a stick in the gap and marked it. This stick would then be the standard stick of the kingdom. Yard is an Old English word for staff, rod, or stick. That makes the word yardstick a candidate for the Department of Redundancy Department since a yardstick is literally a stickstick. A standard yard is 3 feet long.
The pace has its origins in Rome. The passus was measured from the heel of one foot to the heel of the same foot when it next touched the ground. This is a convenient unit for measuring walking distances (again, for men with feet). A standard pace is 5 feet long.
The fathom is a measure of length that was commonly used by navigators. It was the length to which a man could extend his arms while measuring ropes used to determine the depth of navigable waters. The word fathom has its roots in the Old English word for embracing arms (fæðm). A standard fathom is 6 feet long.
A rod is a measure of length equal to 16½ feet or 5½ yards. It is also called a pole or a perch. (I'd hate to meet the budgie that needed a sixteen and a half foot perch.)
Surveyors commonly used chains for measuring distances. The most famous of these was developed by the English mathematician Edmund Gunter (1581–1626). The links of Gunter's chain were each 792100 inches long. One hundred links gave it a total length of 792 inches, 66 feet, or 22 yards. Not a sensible number if you ask me, but then I don't play cricket. The distance between wickets on a cricket pitch is 22 yards.
Literally, the length of a furrow (the trench made in the ground by a plow). A sensible length for farmers that later evolved into the acre, which is discussed later in this section. A standard furrow is 220 yards long or ⅛ mile
Like the inch, this word is a remnant of the Roman conquest of Britain (and since it appears in so many other languages, the Roman conquest of many other places). One mile was the distance of a thousand paces — in Latin, mille passus. A pace being 5 feet gives a mile of roughly 5000 feet. The mile acquired its current value of 5,280 feet (1,760 yards) by the decree of the English parliament during the reign of Elizabeth I. Since this was a legal definition it became known as the statute mile — statute being another word for law.

The distance called a mile varies greatly in different countries. Its length in yards is…

  • Austria, 8,297 yards
  • Brunswick, 11,816 yards
  • England and US, 1,760 yards
  • Hungary, 9,139 yards
  • Italy, 2,025 yards
  • Netherlands, 1,094 yards
  • Norway, 12,182 yards
  • Poland, 8,100 yards
  • Prussia, 8,238 yards
  • Spain, 1,552 yards
  • Sweden, 11,660 yards
  • Switzerland, 8,548 yards

Webster's Revised Unabridged Dictionary, 1913

You can't walk on the ocean so sailors developed a variation on the thousand paces concept. A nautical mile was originally defined as the distance spanned by one minute of arc measured on a meridian of the Earth — basically 1/60 of 1/360 of the Earth's circumference from one pole to another and back. A trip around the world in this fashion is then 21,600 nautical miles.

Since the Earth is a slightly flattened sphere (an oblate spheroid) a trip around the equator is 0.2% longer than a trip around the poles. (Using the equator as the standard gives a variation on the nautical mile called the geographic mile.) This small difference is important to ships, planes, and spacecraft traveling long distances. A 0.2% error over the width of the pacific ocean is about 20 miles (20 statute miles).

For simplicity's sake, the nautical mile is currently defined as 1,852 m exactly, which works out to approximately…

1 nautical mile

1,852 m    1 inch   1 foot
1 0.0254 m 12 inches


This definition comes from Le Bureau international des poids et mesures (a.k.a. the BIPM, a.k.a. the International Bureau of Weights and Measures) in France — the folks responsible for maintaining Le Système international d’unités (a.k.a. the SI, a.k.a. the International System of Units). The nautical mile is the only English unit allowed in the SI. The BIPM calls it an "acceptable non SI unit subject to review". It is still used for marine and aerial navigation — and for some reason NASA likes it. There appears to be no standard symbol to represent this unit. The symbols M, NM, Nm, and nmi are all used for the nautical mile.
A league is usually thought of as the distance a person could walk in an hour — 3 miles. On land, that would be 3 statute miles. At sea, 3 nautical miles is called a marine league. In other countries, well… again I refer to Webster's 1913 Dictionary.

A measure of length or distance, varying in different countries from about 2.4 to 4.6 English statute miles of 5,280 feet each, and used (as a land measure) chiefly on the continent of Europe, and in the Spanish parts of America. The marine league of England and the United States is equal to three marine, or geographical, miles of 6080 feet each. Note: The English land league is equal to three English statute miles. The Spanish and French leagues vary in each country according to usage and the kind of measurement to which they are applied. The Dutch and German leagues contain about four geographical miles, or about 4.6 English statute miles.

Webster's Revised Unabridged Dictionary, 1913

The league was never adopted as a practical unit in England, which is evidenced by Webster's generally vague definition. It survived mainly as a poetical or rhetorical device.

Half a league, half a league,
Half a league onward,
All in the valley of Death
Rode the six hundred.
"Forward, the Light Brigade!
"Charge for the guns!" he said:
Into the valley of Death
Rode the six hundred.

Alfred, Lord Tennyson, 1854

Length units of the English system
  units     conversions
1 thou     = 0.001in
  inch [in] = 0.0254 m (exactly)
1 hand     = 4 in
1 foot [ft]   = 12 in
1 cubit     = 18 in
1 yard [yd]         = 3 ft = 36 in
1 pace   = 5 ft = 60 in
1 fathom       = 2 yd = 6 ft = 72 in
1 rod       = 5½ yd = 16½ ft = 198 in
1 chain   = 4 rods = 22 yd = 66 ft = 792 in
1 furlong   = 10 chains = 220 yd = 660 ft = 7920 in
1 statute mile [mi] = 8 furlongs = 1,760 yd = 5,280 ft = 63,360 in
  nautical mile   = 1,852 m (exactly) = 6076.12 ft (approximately)
1 league   = 3 miles = 5280 yd = 15,840 ft = 190,080 in

Let's move on to…

mass (or is it weight?)

Actually, it's both. The English units for mass are also the units of weight for that mass in a standard gravitational field (9.80665 m/s2 exactly). This part of the English system should probably be called the French system since so many of the units have their origins in France. There were two paths: avoirdupois and troy.

These units do not seem to come in the same kind of easily relatable sizes like those for length. There are a lot of units that just seem to mean "small". This list is also shorter than the previous one.

A grain was said equal to the mass of an average grain of wheat taken from the middle of an ear. There 7,000 grains in the the avoirdupois pound and 5,760 grains in the troy the pound.
From the Latin word scrupus, a small rough pebble or a chip of stone — basically, something small. A scruple is 20 grains.
At one time English pennies weighed 24 grains.
A fraction of an ounce — an eigth or a sixteenth depending on the system. The word is derived from the ancient Greek coin the drachma (δραχμή). One drachma weighed about one dram. Dram also refers informally to a serving of whiskey, especially Scotch. In this context, one might translate dram as "a wee bit". An actual dram of whiskey would not be considered an adequate serving, however. When someone says this, they are being witty.
The word ounce has the same origin as the word inch — the Old English word for one twelfth: uncia. An inch is one-twelfth of a foot and an ounce is one twelfth of a pound. Well, sometimes. It could also be one sixteenth, but that's not the origin of the word. I think what's really going on is that in the olden days the world for twelfth was used indiscriminately for all sorts of small fractions with very little regard for mathematical consistency. I think they had other things to worry about.
Pound comes from Latin pondus for weight. The abbreviation lb for pound comes from the Roman unit libra (about three-quarters of an English pound), which comes from the Latin libro, to weigh. A variant symbol had a bar drawn through the ascenders like this ℔. In cursive form, the symbol was reduced to two vertical and two horizontal strokes like this #. This symbol for pound lives on today as the pound key on the telephone (also known as the number sign, hash, or octothorpe).
A unit usually used for bulk agricultural commodities and legally defined as equal to 14 pounds. In practice, however, the weight of a stone varied with the article weighed.
  • glass: 5 lbs
  • meat, fish: 8 lbs
  • sugar, spices: 8 lbs
  • wax: 12 lbs
  • cheese: 16 lbs
  • hemp: 32 lbs
The word stone is both the singular and plural form of the unit (one stone, two stone, three stone, more stone).
Logically, a hundredweight should be a hundred of something — a hundred pounds would be my educated guess. This was the choice made in England way, way back and adopted by the United States at its founding. But what if you prefer the stone over the pound as your basic unit of weight? This was the case in England soon after the Americans left the Empire. The nearest multiple of a stone greater than a hundredweight is 8 stone or 112 pounds. This became the new hundredweight in England. To distinguish between the two, the original 100 pound hundredweight is called a short hundredweight or a cental while the newer 112 pound hundredweight is called a long hundredweight.
The origin of this word is the Old English tunne — a big container. Brewers are the last people who still use this word (mash tun, lauter tun, fermentation tun). Later the word also came to mean the capacity of such a container and was used as a unit of both volume and weight. The volume unit was not as popular as the weight unit except in the railroad and shipping industries. Eventually it was decided that a ton would be a good name for two thousand pounds, since that's about the weight of water that a tun could hold. When the hundredweight changed in England, so too did the ton. America kept the unit at 2000 pounds while the English changed the unit to 2240 pounds. (2240 pounds is 160 stone, by the way.) As with the hundredweight, the American ton is called a short ton while the English ton is called a long ton. The similarly sized SI unit of 1,000 kg is called a tonne in England or a metric ton in the United States. To misquote George Bernard Shaw, "England and America are two countries divided by a common unit system."
  units     conversions
1 grain [gr] = 1/7000 pound avoirdupois
1 dram [dr] = 1/256 pound avoirdupois
1 ounce [oz] = 16 drams    
1 pound [lb, ℔, #] = 16 ounces = 7000 grains
  pound avoirdupois [lb, ℔, #] = 0.45359237 kg (exactly)
1 stone [st] = 14 pounds    
1 short hundredweight [cwt] = 100 pounds    
1 long hundredweight [cwt] = 112 pounds    
1 short ton [tn] = 2000 pounds    
1 long ton [tn] = 2240 pounds    
Avoirdupois mass units of the English system
  units     conversions
1 grain [G] = 1/5760 pound troy
1 scruple [℈]     = 20 grain
1 pennyweight [dwt]     = 24 grains
1 dram [ʒ] = 3 scruples = 60 grains
1 ounce [℥] = 8 drams = 480 grains
1 pound [lb, ℔, #] = 12 ounces = 5760 grains
  pound troy   = 5760/7000 pound avoirdupois
Troy mass units of the English system


Generating area units should be a straightfoward affair. Take the length units and square them. This gives us very popular units like square inches, square feet, square yards, square miles and so on. We complete the list with two units from agriculture (the acre and the rood) and three quantities that relate to land surveying in the United States. These aren't really units, but I find them interesting nonetheless.

The word acre is related to the word agriculture. Traditionally, an acre was thought to be as much land as a pair of oxen could plow in one day. When you plow, you make a trench in the soil called a furrow. One pass across a field would leave a trench one "furrow long" — a furlong. How many furlongs could you cut in a days work? Well I have no idea, but the value that was adopted as the standard in England was the 22 yard surveyors chain developed by Edmund Gunter (1581–1626) in the Seventeenth Century. An English acre is then one furrow long by one chain wide.
1 acre
1 furlong  ×  1 chain
220 yards  ×  22 yards
4840 square yards
The word rood comes from the word rod. A rood is like an acre, only one forth as wide — as wide as a rod instead of a chain.
1 rood
1 furlong  ×  1 rod
220 yards  ×  5½ yards
1210 square yards
¼ acre
Each square mile section of the Public Land Survey System was divided into four divisions or quarter-sections (½ mi × ½ mi = 160 acres) and then divided again into sixteen subdivisions or quarter-quarter-sections (¼ mi × ¼ mi = 40 acres). This last unit became a popular size for tracts of farmland and lead to the Americanisms "back forty" (the parcel of land farthest from a farmhouse) and "forty acres and a mule" (compensation that was promised to slaves after the Civil War but never delivered — a metaphor for the failure of the Reconstruction).
A section is a survey tract in the United States of one square mile. It is the basic unit of the Public Land Survey System, which traces its origins back to the first decade after independence. You may recall that George Washington was a surveyor before he was a general in the Continental Army or the president of the United States. This system set up the rectangular coordinates that were used to identify property boundaries in the territories outside of the original Thirteen Colonies.
In the Public Land Survey System, groups of 36 sections in a contiguous 6 mile by 6 mile square are called townships. Many counties in the United States are a whole number of townships in size making their area easy to determine.
  units     conversions
1 square thou   = 0.000001 sq in
  square inch [sq in] = 0.00064516 m2 (exactly)
1 square foot [sq ft]         = 144 sq in
1 square yard [sq yd]     = 9 sq ft = 1,296 sq in
1 square rod   = 30.25 sq yd = 272.25 sq ft = 39,204 sq in
1 square chain       = 16 sq rods = 484 sq yd
1 rood   = 2.5 sq chains = 40 sq rods = 1,210 sq yd
1 acre   = 10 sq chains = 160 sq rods = 4840 sq yd
1 square mile [sq mi]         = 640 acres
Area units of the English system
  units     conversions
1 subdivision   = 40 acres
1 section (1 square mile) = 16 subdivisions = 640 acres
1 township   = 36 sections = 576 subdivisions = 23,040 acres
US Public Land Survey system


The unit systems preferred by scientists have volume units that are derived from length units. Take the meter [m] and cube it [m3]. There you go. That's a unit. Don't use the cubic meter much? Alright. Try this. Take a tenth of a meter [0.1 m or 10 cm] and cube it [0.001 m3 or 1,000 cm3]. That's a unit. Call it a litre (or a liter). That's how the International System of Units and its predecessor, the metric system, work.

The English system does not work this way. Some might say it doesn't work at all. Most of the volume units in the English system were derived sensibly from available measuring devices — droppers, spoons, cups, pitchers, buckets, … containers of all sorts. Very few were derived mathematically by cubing length units.

English and American volume units diverged in 1824 over the definition of the gallon. The English wanted a gallon of water to weigh 10 pounds and parliament passed a law to make it so — the British Weights and Measures Act. The Americans stuck with the old standard that made a gallon of water nearly equal to 8 pounds by accident. This makes most English volume units about 20% larger than American units. Americans are often surprised when they see how satisfyingly large English pints of beer are. The units set before 1824 are rightly called English units, those set after 1824 are called Imperial units, the English units that persisted in the United States are called US customary units.

Some volume units share names with mass units. This happened because the liquid dispensed was usually water based (milk, beer, cider, wine, vinegar, spirits, medicines). The measurer could be using the measuring device to measure volume or mass. The correspondence isn't all that strong, however. While one ounce of water has a mass that is very nearly one ounce, one dram of water has a mass that is just kinda sorta close to one dram.

1 Imperial fluid ounce of water  =  1.0022 avoirdupois ounces  ≈  0.2% error
1 Imperial fluid dram of water  =  0.9508 troy drams  ≈  5% error

The correspondence falls apart with the ton. A tun (a type of container) holding a ton (a unit of volume) of water is much heavier than a ton (a unit of mass).

1 register ton =  2.7869 long tons
1 register ton =  3.1214 short tons

The mass of one Imperial fluid ounce of water is very nearly one avoirdupois ounce by design. When the Imperial gallon was set at 10 avoirdupois pounds it was also divided up into 160 Imperial fluid ounces. (The US gallon is divided up into 128 ounces.) Since 16 avoirdupois ounces make an avoirdupois pound, 1 Imperial fluid ounce of water must have a mass of 1 avoirdupois ounce.

Well… not quite. The world pretty much runs on the International System. Both the UK Imperial and US customary gallons are now defined in terms of the liter.

1 Imperial gallon =  4.54609 liters (by definition)
1 US gallon =  3.7854117843 liters (by definition)
Imperial/US =  1.20094993… ≈ 20% difference

This is the origin of the small difference in the UK and US fluid ounces.

1 Imperial fluid ounce  =  28.4130625 milliliters (exactly)
1 US fluid ounce  =  29.5735296… milliliters (approximately)
Imperial/US  =  0.96075994… ≈ 4% difference

Grafting Imperial units onto the International System caused them to drift a little further away from their intended values. To compare things, we'll use the traditional density of water — 1g/cm3 or 1 g/ml.

1 g   28.4130625 ml   16 avoirdupois ounce
1 ml 1 Imperial fluid ounce 453.59237 g
1.00224129…  avoirdupois ounce
Imperial fluid ounce

Some volume units in the two systems are used only for measuring liquids (water, wine, beer, gasoline, oil, honey, extracts, tinctures), some only for loose dry commodities (flours, grains, fruits, nuts, tea, sugar, soil, gravel). Let's start with the liquid measures.

The minim, as the name implies, is the smallest liquid measure in the English system — 160 of a dram by definition, about as much liquid as will form a drop.
A dram is about as much liquid as one would take in a dose of medicine (the customary use of the word) or poison (the dramatic use of the word) or spirituous liquor (the humorous use of the word, since a dram is much too small to be considered a drink). The fluid dram is defined as ⅛ of a fluid ounce. A fluid dram of water weighs about as much as the dram of the apothecaries weight (to within 5% in Imperial units), thus the conflation of the two measures in one name. Recall, that the apothecaries weight called a dram was derived from the name of a Greek coin, the drachma (δραχμή).
The approximate volume of a small spoon used for stirring and sipping tea. Would it have been called the "coffeespoon" if it was invented in the US? 1 Imperial teaspoon is 1⅔ Imperial fluid drams. 1 US teaspoon is 1⅓ US fluid drams.
The approximate volume of a large spoon that would commonly be used at the table. It could also have been called a soup spoon, but it wasn't. A standard tablespoon is equal to three teaspoons.
A fluid ounce of water has a weight of about one ounce (to within 0.2% in Imperial units). The exact size of a fluid ounce depends on whether you use the older US gallon (128 ounces) or the newer Imperial gallon (160 ounces). More on this later. An Imperial fluid ounce equals 4⅘ Imperial teaspoons. A US fluid ounce equals 6 US teaspoons.
A gill is ¼ pint, which is why it's also known as a quartern. That's 4 US ounces or 5 Imperial ounces. The word is a corruption of gille, a kind of cup used to measure wine in France. Its ultimate origin was probably the Latin word for a small pot — gillo. The Latin word for a big pot became the English word gallon. Although it's spelled the same as the organ on a fish, it's pronounced like the woman's name Jill.
The volume of a typical cup for drinking water. A standard cup is 8 ounces — 8 customary ounces in the US and 8 Imperial ounces in the Commonwealth of Nations.
The word pint came to English from the Spanish word for a mark — pinta — probably a mark that was made on a larger measure. Exactly what that larger measure was is unknown to me, but my guess is something like a gallon. The connotation of the pint as a "small" unit carries over into the word pint-sized. In both the US and Imperial systems, a pint is ⅛ of a gallon but, as I stated before, the gallons aren't the same. 1 Imperial pint contains 20 Imperial ounces. 1 US pint contains 16 US ounces.
A fifth is the quantity of liquor equal to ⅕ of a US gallon, ⅘ of a US quart, 25⅗ US fluid ounces, or 757 ml (approximately). This is strictly an American unit. The origins of the fifth are lost to time. Some say it was a way to avoid onerous regulations that applied to sales of liquor in quart or larger amounts (the fifth was also known as a "short quart") but I can't find any references pointing to specific laws. Some say bottles with approximately this volume were the largest glassblowers could manage in one breath, but that's heresay not a quote. The fifth disappeared from US liquor stores in 1980 when federal regulations restricted the sale of distilled spirits to eight allowed metric measures. The closest in size to the fifth was 750 mL, which became an international standard of sorts.
A quart is one quarter of a gallon. A very obvious name.
The word gallon comes from the Latin galleta and refers to a standard container about the same size as a helmet. (The Latin word for helmet is galea.) A gallon is 4 quarts or 8 pints. A US gallon of 128 US ounces of water weighs about 8 pounds by accident. An Imperial gallon of 160 Imperial ounces of water weighs very nearly 10 pounds by design (8.34540449 pounds vs. 10.022417 pounds assuming the density of water is 1 g/cm3). That's the whole source of contention. The English wanted a gallon that weighed something meaningful to them. Both gallons are now defined in terms of SI units: the US gallon is 3.785411784 liters and the Imperial gallon is 4.54609 liters, exactly.
A unit barrel is about the equal to the volume of a typical wooden barrel. The size of a barrel is determined by what it contains (and also the year, but I won't get into that): 31½ US gallons of anything but petroleum, 36 Imperial gallons of beer, 26¼ Imperial gallons of wine, or 42 US gallons of petroleum.
A hogshead is a container about twice the size of a barrel: 63 US gallons of anything, 52½ Imperial gallons of wine, 54 Imperial gallons of beer. The word is derived from the word for oxhead in Danish (oksehoved), Dutch (okshoofd), German (oxhoft), or Swedish (oxhuvud). What this has to do with anything is a mystery.

Now for the dry measures. Watch as we break the US volume units.

2 gallons, 8 quarts, or 16 pints of dry material are called a peck. The origin of this word is uncertain. It could be related to the word pick.

Peter Piper picked a peck of pickled peppers.
Did Peter Piper pick a peck of pickled peppers?
If Peter Piper picked a peck of pickled peppers,
Where's the peck of pickled peppers Peter Piper picked?

Traditional, ca. 1800

4 pecks, 8 gallons, 32 quarts, or 64 pints make a bushel. The word is French in origin and refers to a container about a bushel in size. (Not a very informative word origin story.) The original English standard, called the Winchester bushel, was 18½ inches in internal diameter and 8 inches deep for a total of 2150.42 cubic inches approximately. The volume of a cylinder is an irrational number since π appears in its definition.
1 Winchester bushel =  πr2h
1 Winchester bushel =  π(9¼ inch)2(8 inch)
1 Winchester bushel =  2150.42017… cubic inch
1 Winchester bushel =  35.2390730… liter
The Imperial bushel was a bit larger at 2218.192 cubic inches (approximately) and was defined to hold 80 pounds of water (or exactly 8 Imperial gallons) at 62 ℉ . This kept it in line with the rest of the Imperial system.
1 Imperial bushel =  8 Imperial gallon
1 Imperial bushel =  36.36872 liter (exactly)
For a while, the US standard bushel was similarly defined to hold 77.6274 pounds of water at 39.8 ℉ so that it would stay in line with the Winchester bushel. This was replaced with the simpler standard of 2150.42 cubic inches (exactly — just chop off all the digits after the hundredths place).
1 US bushel =  2150.42 cubic inch (exactly)
1 US bushel =  35.2390702… liter
This effectively leads to a second definition of the gallon, quart, and pint in the US customary unit system. The only way to make a direct comparison is through the International System.
1 US bushel =  35.2390702… liter
8 US dry gallon =  9.30917749… US liquid gallon
1 US dry gallon =  1.16364719… US liquid gallon
1 US dry quart =  1.16364719… US liquid quart
1 US dry pint =  1.16364719… US liquid pint
8 bushels make a quarter. This unit is only used for grain as far as I can determine. It's called a quarter probably because it's a quarter of a ton. Start from the true (but also false) assumption that "a pint's a pound the world around". The true part is that a US liquid pint of water weighs about a pound. That false part is that the US is the world. The questionable part is the assumption that dry commodities have the same density as water, which is wet.
1 pound   8 pint   8 gallon   8 bushel
1 US liquid pint 1 gallon 1 bushel 1 quarter
 =  512 pound  =  0.256 short ton
1 quarter 1 quarter
A similar calculation can be made using the Imperial equivalents. There is no cute mnemonic to remember the mass of an Imperial pint of water.
1.2 pound   8 pint   8 gallon   8 bushel
1 Imperial pint 1 gallon 1 bushel 1 quarter
 =  614.4 pound  ≈  0.274 long ton
1 quarter 1 quarter
There are several units called a quarter in the Anglo-American unit systems. The Oxford English Dictionary defines quarter as all of the following: eight bushels of grain, nine bushels of coal, one fourth of a peck, one fourth of a pound, one fourth of a hundredweight, one fourth of a dram, one fourth of an ell, one fourth of a yard, and one fourth of a fathom. You'll excuse me if I skip the rest of these.

A few US/Imperial volume units are derived by multiplying length by width by height (or area times height).

register ton
The word ton comes from the archaic word tun, which was a kind of large container. Brewers are the only people who still use this word regularly. The register ton is a unit of volume (not mass) used in the railroad and shipping industries now equal to 100 cubic feet by definition. For example, a 50 foot long, 9½ foot wide, 13 foot tall boxcar has a capacity of 61¾ register tons and a 40 foot long, 8 foot wide, 8½ foot tall intermodal shipping container has a capacity of 27⅕ register tons. At one time, water with a volume of one ton had a mass of one ton, but the two units are now unrelated. A register ton of water weighs something like 3 tons (2.7869 long tons or 3.1214 short tons).
1 cord of wood is eight feet wide, four feet high, and four feet deep, or 128 cubic feet; measured with a cord, thus the name.
acre foot
A good unit for reservoirs and other large scale water resources. Multiply the surface area in acres by the average depth in feet. Simplicity at its best. An acre is a furlong (660 feet) by a chain (66 feet). Multiplied by one more foot gives 43,560 cubic feet.
  units     conversions
  cubic inch [cu in] = 0.00001470612 m3 (exactly)
1 cubic foot [cu ft]   = 1,728 cu in
1 cubic yard [cu yd]         = 27 cu ft = 46,656 cu in
1 register ton   = 100 cu ft    
1 cord   = 128 cu ft    
1 acre foot   = 1,613⅓ cu yd = 43,560 cu ft    
1 cubic mile [cu mi] = 5,451,776,000 cu yd = 147,197,952,000 cu ft
Volume units of the English system
  units     conversions
1 minim [min]      
1 dram [dr]   = 60 min
1 teaspoon [tbsp]         =   = 100 min
1 tablespoon [tbs]     = 3 tsp =   = 300 min
1 ounce [oz] = 1⅗ tbsp = 4⅘ tsp = 8 dr = 480 min
1 gill [gi]   = 5 oz
1 cup [c]   = 8 oz
1 pint [pt]         = 2½ c = 20 oz
1 quart [qt]     = 2 pt = 5 c = 40 oz
1 gallon [gal] = 4 qt = 8 pt = 20 c = 160 oz
  gallon [gal] = 4.54609 liters (exactly)
1 peck [pk]     = 2 gal = 8 qt = 16 pt
1 bushel [bu] = 4 pk = 8 gal = 32 qt = 64 pt
1 quarter [qr] = 8 bu = 64 gal = 256 qt = 512 pt
1 barrel [bbl]     = 26¼ gal (wine) = 36 gal (beer)
1 hogshead       = 52½ gal (wine) = 54 gal (beer)
Volume units of the Imperial system
  units     conversions
1 minim [min]      
1 dram [dr]   = 60 min
1 teaspoon [tbsp]         = 1⅓ dram = 80 min
1 tablespoon [tbs]     = 3 tsp = 4 dr = 240 min
1 ounce [oz] = 2 tbsp = 6 tsp = 8 dr = 480 min
1 gill [gi]   = 4 oz
1 cup [c]   = 8 oz
1 pint [pt]         = 2 c = 16 oz
1 fifth   = ⅘ qt         = 25⅗ oz
1 quart [qt]     = 2 pt = 4 c = 32 oz
1 gallon [gal] = 4 qt = 8 pt = 16 c = 128 oz
  gallon   = 231 cu in (exactly) = 3.7854117843 liters (exactly)
1 barrel [bbl] = 31½ gal  
1 barrel of oil [bbl] = 42 gal  
1 hogshead   = 63 gal = 2 bbl        
Liquid volume units of the US system
  units     conversions
1 pint [pt]      
1 quart [qt]   = 2 pt
1 gallon [gal]         = 4 qt = 8 pt
1 peck [pk] =   = 2 gal = 8 qt = 16 pt
1 bushel [bu] = 4 pk = 8 gal = 32 qt = 64 pt
  bushel   = 2150.42 cu in (exactly) = 35.2390717… liters (approximately)
Dry volume units of the US system


The foot-pound-second system is an attempt to make useful scientific units out of the mess that traditional English units evolved into. The foot is pretty good (since most people have two feet available for service). The second is very good (since it's an internationally recognized unit). But the pound, for lack of a better word, is bad. What is a pound? Is it a unit of mass or is it a unit of weight (and thus a unit of force)? To be precise, one should always indicate.

Start from the pound avoirdupois, the usual unit of mass and weight in the English system. SI dominates the world now and the English pound mass is now defined in terms of the kilogram.

pound mass = 0.45359237 kg

This value is exact by definition. It is not measured or calculated.

From here we move on to the first unit of force in the English system. Yes, you heard me right, the first. There are two — one in which the pound is a unit of weight and one in which it's a unit of mass. The pound force is defined as the weight of a pound mass in a standard gravitational field. Thus…

W  =  mg
pound force  =  (pound mass)(acceleration due to gravity)
pound force  =  (0.45359237 kg)(9.80665 m/s2)
pound force  =  4.44822162… N

The corresponding unit of mass is the horribly named slug. The slug is the unit of mass when the pound is a unit of force. A mass of one slug will accelerate at one foot per second squared when pushed by a one pound force.

F  =  ma
1 pound force  =  (1 slug)(1 ft/s2)
(1 pound mass)(acceleration due to gravity)  =  (1 slug)(1 ft/s2)
(1 pound mass)(32.1740486 ft/s2)  =  (1 slug)(1 ft/s2)


slug = 32.1740486… pound mass

In SI units, this is approximately…

slug  =  (32.1740486… lb)(0.45359237 kg/lb)
slug  =  14.5939029… kg

And now for the second unit of force in the English system. The poundal is the unit of force when the pound is the unit of mass. A one pound mass will accelerate at one foot per second squared when pushed by a one poundal force.

F  =  ma
poundal  =  (1 pound mass)(1 ft/s2)
poundal  =  (1 pound force)(1 ft/s2)
(acceleration due to gravity)
poundal  =  (1 pound force)(1 ft/s2)
(32.1740486 ft/s2)
 poundal  =  0.03108095… pound force

In SI units, this is exactly…

poundal  =  (1 pound mass) (1 ft/s2)
poundal  =  (0.45359237 kg) (0.3048 m/s2)
poundal  =  0.138254954376 N

Now that we've sort of resolved the whole mass-weight debacle let's get on with this subsystem of the English system of units.

Units of the foot-pound-second systems
quantity full name symbol
pound force pound mass
distance foot ft
time second s
speed   ft/s
acceleration   ft/s2
acceleration due to gravity   32.1740486 ft/s2
force pound force lb (also lbf)  
poundal   pdl (lb ft/s2)
mass slug slug (lb s2/ft)  
pound mass   lb (also lbm)
energy   ft lb ft pdl
power   ft lb/s ft pdl/s
moment of inertia   slug ft2 (lb ft s2) lb ft2
torque   ft lb ft pdl
area   ft2
volume   ft3
mass density   slug/ft3 lb/ft3
weight density   lb/ft3 pdl/ft3
volume flow rate   ft3/s
mass flow rate   slug/s lb/s
weight flow rate   lb/s pdl/s
pressure   lb/ft2 pdl/ft2
dynamic viscosity   lb s/ft2 (slug/ft s) pdl s/ft2 (lb/ft s)
kinematic viscosity   ft2/s

some more units

Blah, blah, blah. So many, many units.Base notes from the public domain Webster's Revised Unabridged Dictionary of 1913

A unit of power, used in stating the power required to drive machinery, and in estimating the capabilities of animals or steam engines and other prime movers for doing work. It is the power required for the performance of work at the rate of 33,000 English units of work per minute; hence, it is the power that must be exerted in lifting 33,000 pounds at the rate of one foot per minute, or 550 pounds at the rate of one foot per second, or 55 pounds at the rate of ten feet per second, etc.
{Mechanical equivalent of heat} (Physics), originally defined as the number of units of work which the unit of heat can perform, equivalent to the mechanical energy which must be expended to raise the temperature of a pound of water one degree Fahrenheit; later this value was defined as one {British thermal unit} (B.t.u). Its value was found by Joule to be 772 foot pounds; later measurements give the value as 777.65 foot-pounds, equivalent to 107.5 kg-meters. This value was originally called Joule's equivalent, but the modern Joule is defined differently, being 10^{7} ergs. The B.t.u. is now given as 1,054.35 absolute Joules, and therefore 1 calorie (the amount of heat needed to raise one gram of water one degree centigrade) is equivalent to 4.186 Joules.
100,000 Btu
quadrillion Btu
{Standard candle} (Photom.), a special form of candle employed as a standard in photometric measurements; usually, a candle of spermaceti so constructed as to burn at the rate of 120 grains, or 7.8 grams, per hour. {Candle power} (Photom.), illuminating power, as of a lamp, or gas flame, reckoned in terms of the light of a standard candle.
foot candle
The amount of illumination produced by a standard candle at a distance of one foot.
inches of mercury
{Fahrenheit thermometer} is so graduated that the freezing point of water is at 32 degrees above the zero of its scale, and the boiling point at one atmosphere of pressure is 212 degrees. It is commonly used in the United States and in England.

212 ℉ = 100 ℃ and 32 ℉ = 0 ℃

T[℉] = (T[℃]*9/5 +32)

T[℃] = (T[℉] − 32)*5/9

(a) A division of the log line, serving to measure the rate of the vessel's motion. Each knot on the line bears the same proportion to a mile that thirty seconds do to an hour. The number of knots which run off from the reel in half a minute, therefore, shows the number of miles the vessel sails in an hour. Hence: (b) A nautical mile, or 6080.27 feet; as, when a ship goes nautical eight miles an hour, her speed is said to be eight knots. [1913 Webster] a unit of length used in navigation; equivalent to the distance spanned by one minute of arc in latitude; 1,852 meters
Dynamic viscosity. 144 lb s/ft2

Anything else? Don't answer that question.