When I first came across the imperial system, I found it hilarious. I was trying to look up a "grain".

It turns out that a grain is a unit of mass, equal to approximately 65 mg. It comes from "the weight of a grain seed from the middle of an ear of barley". The weight of a wheat kernel was considered 45/64 of a grain of barley. As well as seeming to be the fundamental unit of mass, it's also a third of an inch - a unit of length.

Onwards! In the avoirdupois system, there are 7000 grains to the pound, 16 ounces to the pound, 16 drams to the ounce, which makes the dram, the next largest unit to the grain, a convenient 27 and 11/32ths of a grain. In the other direction there is also the hundredweight (100 pounds) and the short ton (20 hundredweights)

In the Apothecaries' system, things progress slightly more simply from the grain. There are 20 grains in a scruple, 3 scruples in a dram, 8 drams in an ounce and 12 ounces in a pound. Of course, they're not even similar weights as in the avoirdupois system, and there are, for example, exactly 175/384 avoirdupois pounds in each apothecaries pound.

The troy system has a pennyweight which is 24 grains, there are 20 pennyweights to the ounce and 12 ounces to the pound.

All that's left is a stick, which is a cooking weight equal to 4 ounces.

In terms of length, it all seems to start at the inch, which is 3 barleycorns long. 12 inches to the foot, 3 feet to the yard and 5280 feet to the mile, unless of course you're a surveyor in which case you also have the link which is 33/50th of a foot, a survey foot, which is defined as 1200/3937th of a meter (!), 25 links in a rod, 100 links in a chain, and 80 chains in a mile. The mile and foot work out pretty similar to their archaic counterparts. Then there is the hand, which isn't defined in terms of any other unit.

Then there's area! You've got all your standard units of length squared, plus the acre, which is ten square chains.

Volume is where it gets fun. Apart from the cubic versions of the above, volume seems to be based on the space taken up by a particular mass of liquid, and so you have a fluid ounce, which is almost, but not quite in any of the systems, the volume that one ounce of water takes up. Then you have the fluid dram, which is 1/8th of that, like in the apothecaries' system of weight. The disused minim is 1/60th of a fluid ounce. In the other direction, a gill is 4 fluid ounces, a cup 2 gills, a pint 2 cups, a quart 2 pints, a gallon 4 quarts, a beer barrel 31 gallons, an oil barrel 42 gallons and a hogshead 63 gallons. For liquids. For solids, the measure is still based on the volume a certain mass takes up, and so a pint of rice occupies more volume than a pint of water. The relationships between the units seem to be the same as in the liquid case, just that the actual volume is slightly different. There are also two additional units, the peck, which is 2 dry gallons, and the bushel, which is 4 peck.

Because it is difficult to measure the volume of things like wheat, a bushel is generally defined in terms of weight, and so a bushel of maize is the volume taken up by 56 pounds, and a bushel of wheat 60 pounds. This leaves the bushel in the strange situation of being a measure of weight as well as volume defined in terms of the volume of a weight of a liquid that's not quite water.

The real fun really is in derived units, and so you can merrily consider density in bushels per bushel (mass of bushel per volume of bushel = density).

Fahrenheit was constructed so that 0F is the temperature of a solution of ice brine, 32F is the melting point of water, and 96F is body temperature, so that there are 64 intervals between those two unrelated concepts… and the reason Daniel Fahrenheit chose a power of two is that he could construct the scales on his thermometer by bisecting the lines on his scale 6 times. This made labelling the thing easier. Later on, people came along and said that that's not useful and redefined the upper end in terms of the boiling point of water, as 212F. As a result, it's even more arbitrary. Zero is now somewhere near but not quite the temperature of that solution of ice brine, 32F is exactly the freezing point of water, 100F is pretty close to but still warmer than body temperature and 212F is exactly the boiling point of water. What.

[edit] Aside: Avoirdupois sort-of translates as "to have some peas", but it comes from something else. I still find it funny.