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Scottish gallon

In Scotland, a unit of liquid capacity, as a survival in the 19ᵗʰ century following the introduction of the imperial gallon in 1826, about 13.552 liters (about 2.9835 imperial gallons).

David I's Assize, attributed to 12ᵗʰ c

Item the galloun suld be sax inches and ane half in deipnes and in breid of the boddom viij inchess and a half with the thicknes of the trie on baith the sides and in rowndnes abone xxvij inches and a half and in rowndnes below xxiij inches.

Item the gallon aw to conteyn xij pundis of watir that is to say iiij pundis of salt watir of the see, iiij pundis of standande watir and iiij pundis of rynnand watir.

Item. The gallon should be 6½ inches deep and the bottom 8½ inches in broadth with the thickness of the staves on both sides, and in roundness above 27½ inches and in roundness below 23 inches.

Item. The gallon ought to contain 12 pounds of water, that is to say, 4 pounds of salt water from the sea, 4 pounds of standing water, and 4 pounds of running water.

Thomas Thomson and Cosmo Innes, editors.
The Acts of the Parliaments of Scotland, vol 1.
Edinburgh: 1844.
Page 673.

The first paragraph mixes interior and exterior dimensions. A bottom 8½ inches in diameter would have a circumference of (8.5π =) 26.7 inches, hard to confuse with 23.

A liquid-tight standard like this would have been made by a master cooper. To find the interior's volume, which is a frustrum of a cone, we need its height and the radii of the top and bottom. It is easy to measure the opening in the finished article. The bottom, however, is best measured on the head before assembly, and that figure is provided by "roundness below". A circumference of 23 inches gives a diameter of 7.3 inches. That leaves (8.5 − 7.3 =) 1.2 inches for the staves "on both sides", and 0.6 inch is a reasonable thickness for a stave of a small barrel.

So, taking the inside dimensions of this frustrum to be 6.5 inches deep, bottom radius 3.7 inches, and top radius ((27.5/π)/2) 4.4 inches; gives a capacity of 333.9 cubic inches, 5.47 liters

Let us compare this result with the capacity defined by weight of water. A cubic meter of seawater has a mass of 1020 to 1029 kilograms; a cubic meter of clear river water has a mass of, say, 999 kg.30 parts per thousand. At that time a 15-ounce pound, each ounce the same as those of the mark of Cologne, so the oound woul be 437.1 grams, and 12 pounds 5245.2 grams. , 5.25 liters.

The Assize of 1426

Item the bol sal contene in breid xxix inche within the burdis and abufe xxviij inche and a half evin oure thort, ande in depnes ix inche.

Item. The furlote sal contene twa galonis ande a pynte ande ilk pynt sal contene be wecht of cleir watter of Tay xlj unce, that is for to say ij pundis and ix unce troyis.¹ Swa weyis the galone xx punde and viij unce; swa weyis the furlote xlj pundis. Ande the bol contenande four furlotis weyis viijxx and iiij pundis. The old boll frist maid be King Dauid contenit a sextarn, the saxtarn contenit xij galonis of the auld mete, ande ilk galone weyit ten pundis trois and foure unce of divers watteris.³ Swa weyit the boll vjxx iij pundis. Sua this new bol new maid weyis mar than the auld boll be xlj lib', quhilkis makis twa galounis and a half.⁴ And a chopyn of the auld mete ande of the new mete now ordanit ix pyntis and thre muchekynis.

Item, the boll shall contain in breadth twenty-nine inches within the boards, and above twenty-eight inches and a half, in a straight line from side to side, and nine inches in depth.

The firlot shall contain two gallons and a pint, and each pint shall contain by weight of clear Tay water, forty-one ounces, that is to say two pounds and nine ounces Troy.¹ So the gallon weighs 20 pounds and 8 ounces;² so the firlot weighs 41 pounds. And the boll containing four firlots weighs 164 pounds. The old boll first made by King David [I] contained a sextern, the sextern contained twelve gallons of the old measure, and each gallon weighed ten pounds Troy and four ounces of various waters.³ So the boll weighed 123 pounds. So this new boll weighs more than the old boll by forty-one pounds, which makes two and a half gallons.⁴ And a chopin of the old measure and the new measure now ordained, nine pints and three mutchkins.

1. Thus confirming that the troy pound being used has 16 ounces (41 = 2 ×16, + 9), which is also explicitly stated in an earlier section of the document, not reproduced here.

2. Thus the gallon contains (20×16, + 8 =) 328 ounces which, taking the Scottish troy ounce of 1427 at 480 grains each of 0.06479 grams, suggests a capacity of about 10.2 liters. For the argument that the Scottish and English Troy ounces were both 450 grains at this date, see Connor and Simpson, page 117 and following.

3. The old gallon (David I's) weighed “ten pundis trois and foure unce of diverse watteris”, (164 ounces of a mixture of equal parts seawater, standing, and flowing water). If that mixture had a density of , David's gallon

4. If 41 pounds makes 2½ gallons, a gallon of water weighs 16 pound 6.4 ounces, or 262.4 ounces.

After this assize the gallon ceases to appear in definitions of liquid measures in the Scottish legal record. In Scotland, the pint played the role the gallon did in England. The gallon does appear in definitions of special units like the salmon barrel.

1587