- Scottish acre
- Scottish acre based on Jardine's ell
- Scottish acre based on Gregory's ell

In Scotland, a unit of land area, ? – 20^{th} century, = 4 (Scottish) roods = 160 square falls = 5760 square Scottish ells. Taking the ell at 37 inches, which is the original value, the Scottish acre is 6084 2/5 square yards.

1

The Mesuring of Landis.

In Þe first tyme Þat the law wes maid and ordainit / thai began at Þe fredome of halikirk and syne at Þe mesuring of landis Þe plew land Þai ordani to contene .viij. oxingang / Þe oxgang sall contene .xiij. akeris The aker sall contene four rude / Þhe rude .xl. fallis The fall sall hald .vj. ellis.

When law was first made and ordained they began, with the liberality of holy church and synod, at the measuring of land. The ploughland they ordained to contain 8 oxgangs. The oxgang shall contain 13 acres. The acre shall contain 4 roods; the rood 40 falls. The fall shall hold 6 ells.

*The Acts of the Parliaments of Scotland.
Volume 1. A.D. MCXXIV–MCCCCXXII.*

London: Great Britain Record Commission Publications, 1814.

Page 751. As with the furlongs in the English acre, each of the 4 rudes
(roods) was 40 falls long and 1 fall wide. Thus the aker was 160 square falls.

2

In some counties in Scotland, the chain consists of 74 feet and a fractional part, but as the Court of Session has determined, that the standard chain is 74 feet net, this Table is made upon that principle, by which the number of English yards in a Scotch acre is ascertained to be 6084 and 444/1000 parts of a yard.

James Cleland.

*Statistical Tables relative to the City of
Glasgow, with other matters therewith connected.* 3rd edition, with Additions.

Glasgow: James Lumsden and Son, 1823.

Cleland was
the Superintendent of Public Works for the city of Glasgow.

3

There having been some uncertainty regarding the length of the Scottish ell, a jury was appointed by the Sheriff-Depute of the County of Edinburgh, which met 4th February, 1826, and determined, in conformity by a report by competent persons, that the standard ell-bed, in the custody of the city of Edinburgh, measured 37.0598 Imp. inches, and the Scotch chain of 24 ells 74.1196 Imp. feet, divided into 100 links, each 8.894352 inches.

Some land measurers, reckoning the Scotch ell at 37 inches, used a chain of 74 Imp. feet, divided into 100 links, each 8.88 inches; others, reckoning the Scotch ell at 37 2/10, used a chain of 74 4/10 feet, divided into 100 links, each 8.928 inches.

Anonymous.

*The Hay and Cattle Measurer*.

London: Blackie and Son, 1876.

Page 122.

The second-oldest surviving standard for the Scottish ell is the Edinburgh ell bed,
a wrought iron bar probably made in the mid-16^{th} century.
Near either end are substantial, integral jaws with flat parallel faces. The
faces are an ell apart, so a merchant’s ell-wand can be checked by trying to fit it within the jaws. In other words, an ell bed resembles a modern go/no go gauge. The law of 1618 confirmed this ell bed and its ell as the national standard for the ell.¹ (The law speaks of an ell matching the bed, but even if it existed in 1618 it was lost by the 19^{th} century.)

In October 1811 the bed was
measured by a civil engineer, James Jardine, who found the distance between the
jaws to be (after corrections for temperature) 37.0598 inches, which is comparable to
20^{th} century
measurements of the same object. That value also closely resembles the lengths found
by measuring other old ell beds.

When imperial measure was adopted in 1824, official inquiries were held county by county to determine the sizes of the old Scottish weights and measures in terms of the new Imperial units. Jardine’s value was formally adopted by the county of Edinburgh, and then by reference by other counties. It was incorporated in the tables of conversion factors that resulted from the counties' work,² and subsequently has often been reprinted as the official length of the Scottish ell. But does this value really represent the length of an ell?

By the standards of 19^{th}-century metrology, the faces of the Edinburgh ell bed are neither flat nor parallel. Moreover they are pitted from rust. The idea that the distance between the faces can be measured to the nearest ten-thousandth of an inch is absurd. And, of course, the blacksmiths who made the ell bed (around 1550?) did not work to ten-thousandths of an inch. It is more sensible to round off the measured distance to hundredths, 37.06 inches, and most people have.

The Edinburgh ell bed's humble construction raises the question of whether it was originally made as a primary, national, prototype.³ Such a prototype may have existed and been destroyed during the warfare in Edinburgh. The existing ell bed seems to have been made as a gauge for a burgh, for the month-to-month checking of merchants' ell wands. Regular use would have subjected the faces to a great deal of wear, enlarging the distance between them. Thus, one would expect the distance between the faces to be greater than 1 ell. (The ell wands would also be worn, shortening them, which is why for at least the last century metrologists have frowned on using end measures as standards for linear measures.)

The dimensions of any two closely mating parts, like an ell and its ell bed, must be made with some tolerance. In the case of the bed, to permit insertion of an ell wand which was fully 37.00 inches long, the tolerance for the distance between the faces would have to be minus zero, plus something. It would not matter much if an ell wand that was slightly too long passed, but it would matter a great deal if a merchant was condemned whose ell wand really was fully 37 inches long. Again, one would then expect the distance between the jaws to be greater than 1 ell.

People of their times, Jardine and his associates mistakenly approached the
16^{th}-century ell bed as if it were made to
be used in the same way as the prototypes produced for the 18^{th}-century, revolutionary, French metric system. What they took as an ell was actually 1 ell plus an allowance. Instead of verifying the 37-inch ell
described in the law, and which the ell bed was supposed to represent, they created a new (imaginary) unit, the Scottish inch, which differed from the English inch by only a few thousandths. They do not seem to have taken to heart William of Occam's
principle, that one should not needlessly multiply entities.

Taking the ell at 37.06 inches, the Scottish acre is 6104.194 square yards.
The original 19^{th} century sources give 6104.12789 square yards. But these are bogus results.

1. “Sicklyke have found and declared that the elne and stand thereof committed to the keiping of the burgh of Edinburgh conteineth thrittie seven inches”—The act anent the setling of measures and weights, concluded at Edinburgh the 19 day of Februar 1618 yeeres by the commissioners having power to doe the same by act of parliament made the tuentie eight day of June 1617.

Available on the web as record [A1617/5/1] at www.rps.ac.uk

2. For example:

*An Abstract of the act 5. George IV. cap 74 … for
ascertaining and establishing uniformity of weights and measures; also of the
Act 1618, establishing the late Scottish standards … To which is subjoined
an appendix,* etc.

Edinburgh: Waugh and Innes, 1827.

George Buchanan.

*Tables for converting the weights and
measures hitherto in use in Great Britain into those of the imperial standards
established by the recent act of Parliament.*

Edinburgh: Fraser and Crawford, 1838.

Second Report. Page 5.

3. Compare the elegant engraving on the Inverkeithing ell bed, made for William Carmichael, Treasurer of Edinburgh, in 1500.

1

It appears by the very accurate measurement of the Scottish standard ell, made by Mr Jardine, Civil Engineer, and which has been ratified by the Jury lately appointed by the Sheriff of the county of Edinburgh,* to settle the proportions between the Scottish standard and the Imperial measures, that the length of the ell, reduced to the temperature of 62° Fahrenheit, is exactly 37.0598 Imperial inches; it is equal, therefore, to 1.02943888, &c. yards; and to convert ells into yards, multiply by this fraction. …

THE CHAIN

The Scottish chain contains 24 ells, which is equal, by the above rule, to 24.70653333, &c. yards, or very nearly 74.1196 feet. …

superficial measures — chain, acre.

The square chain will contain, by the above fraction, 6104.12789, &c. square yards; and as the acre is just 10 square chains, it will contain 6104.12789 yards. …

*See Report and Verdict, among the County Reports. [*These
follow.-ed.*]

Edinburgh.

*Report to *Adam Duff, *Esq. his Majesty’s
Sheriff-Depute of the County of Edinburgh, regarding the Weights and Measures
heretofore in use in said County. By* James Jardine,
Civil-Engineer, Alexander Adie, *Optician,
and* David Murray, *Accountant, all in Edinburgh*.

…

1. Length of the Scotch Ell, &c.

The late Mr John Playfair, Professor of Natural Philosophy in the University of Edinburgh, was anxious to ascertain the true length of the Standard Scotch Ell, continued in the custody of the city of Edinburgh by the Act of 1618, and for that purpose he, in the year 1811, borrowed from the Magistrates the standard iron ell-bed, then fastened by a chain to the top of the wall of the Council Chamber.

In October 1811, Mr Jardine, one of the present reporters, carried the said ell-bed to Aberdeen, where, in conjunction with the late Mr Patrick Copland, Professor of Mathematics in Marischal College, he with great care ascertained its length, by means of an accurate standard brass scale of comparison, made by Mr Edward Troughton of London, in 1801, for the Magistrates of Aberdeen. After allowing the ell-bed and scale to remain over-night close together in the observatory of Marischal College, to acquire the same temperature, it was found by repeated trials, scarcely differing from each other, that the length of the ell-bed, on an average of these trials, after making allowance for the difference between the temperature at which the experiments were made and the temperature of 62deg; Fahrenheit, was thirty-seven Inches, and five hundred and ninety-eight ten thousandths parts of an Inch, or 37.0598, of Bird's Standard Yard of 1760, now the Imperial Standard Yard.

The measurement thus obtained, being consistent with the personal knowledge of one of the present reporters, we have adopted for our conversions, without any new experiment. The Scotch Chain of twenty-four Ells is therefore equal to seventy-four Imperial Standard Feet, and eleven hundred and ninety-six ten thousandth parts of a Foot, or 74.1196; and the Standard Scotch Acre is to the Imperial Acre as one, and twenty-six millions one hundred and eighteen thousand thee hundred and forty-five hundred millionth parts, or 1.26118345, to one; consequently, to convert Scotch Acres into Imperial Standard Acres, multiply the number of Scotch Acres by 1.26118345.

…

EDINBURGH

Extract Verdict
*of the Jury appointed by* Adam Duff, Esq.
*Sheriff-Depute of the shire of Edinburgh.*

*Edinburgh, 4th Feb.* 1826

I. With regard to Measures of Extent, find,—

*First,* With regard to Lineal Measure, that the
Standard Scotch Ell, at the temperature of 62 degrees of Fahrenheit, contains
thirty-seven Imperial Standard Inches and five hundred and ninety-eight ten
thousandth parts of an Inch (37.0598); that the Scotch Chain contains
twenty-four Ells; and that the Chain contains seventy-four Imperial Standard
Feet and eleven hundred and ninety-six ten thousandth parts of a Foot, or
74.1196.

*Secondly,* Find, with regard to Superficial Measure,
that a Scotch Acre contains ten square Chains, and that the Standard Scotch Acre
is to the Imperial Acre as one, and twenty-six million one hundred and eighteen
thousand three hundred and forty-five hundred millionth parts, or 1.26118345, to
one. Hence to convert Scotch Acres into Imperial Acres, the number of Scotch
Acres ought to be multiplied by 1.26118345.

Find, That in Scotch Land Measure, an Acre contains four Roods, that a Rood contains forty Falls, and that a Fall contains thirty-six square ells.

George Buchanan.

*Tables for converting the weights and
measures hitherto in use in Great Britain into those of the imperial standards
established by the recent act of Parliament.*

Edinburgh: Fraser and Crawford, 1838.

Pages 17-18,
198-199, and 205.

In the 18^{th} century a misconception in the
design of the reels used to measure the
length of linen yarn led to an
ell of 37.2 inches, which Connor and Simpson have dubbed the “linen ell.”¹ The
linen ell was a real unit for which standards were created;² in fact,
the linen ell was probably the first Scottish unit for which modern standards were
created. In his book, *A Treatise of Practical Geometry* (1745), the
mathematician David Gregory espoused this ell as the only Scottish ell. The
book, enlarged by Gregory’s successor, Colin Maclaurin, in its time was the most influential work treating Scottish measures. Their exposition on these units was reproduced in the first five editions of the *Encyclopedia Britannica*.

A Scotch acre based on the 37.2-inch ell was actually used in some
surveying in the 18^{th} century; it is impossible to say exactly where and when. The official endorsement of Jardine’s 37.0598 ell eventually suppressed it. Surveying based on 37-inch ell is known to have occurred in the same period.

Taking the ell at 37.2 inches, the Scottish acre is 6150.4 square yards (about 0.509 hectares). This acre is sometimes called the Inverness acre.³

1. Connor and Simpson. See especially chapters 2 and 3.

2. Other even longer textile ells existed, the plaiding ells, but that is another topic.

3. John Chalmers Morton.

*A cyclopedia of agriculture, practical and scientific: in which the theory, the art, and the business of farming are thoroughly and practically treated.* Vol. 2

Glasgow: Blackie and Son, 1855.

Page 938.

1

But the English foot is somewhat less than the Scots ; so that 185 of these, make 186 of those.

…

[*What follows are additions by Colin Maclaurin--ed.*] A chain that may have the same advantages in surveying in *Scotland*, as *Gunter's* chain has in *England*, ought to be in length seventy four feet, or twenty four *Scots* ells, if no regard is had to the difference of the *Scots* and *English* foot above mentioned. But, if regard is had to that difference, the *Scots* chain ought to consist of 74 2/5 *English* feet, or 74 feet 4 inches and 4/5 of an inch. This chain being divided into an hundred links, each of those links is 8 inches and 928/1000 of an inch.

English Inch |
Dec. | |

The English foot, is |
12 | 000 |

The Scots foot, |
12 | 065 |

… | ||

The Scots ell, |
37 | 200 |

…

They who measure land in *Scotland* by an ell of 37 *English* inches, make the acre less than the true *Scots* acre by 593 6/10 square *English* feet; or by about 1/93 of the acre.

David Gregory.

*A Treatise of Practical Geometry. In three Parts. *4th edition.

Edinburgh: Printed by Hamilton, Balfour, and Neill, 1761.

Pages 4, 5 and 66..

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