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committed to the cuftody of the town of Edinburgh; a ftandard pint jug for regulating liquid measures was depofited in Stirling; a ftandard forlot for dry measure was committed to the care of the magiftrates of Linlithgow; and a standard stone weight to Lanerk: exact duplicates of all which meafures were carefully depofited in the king's exchequer at Edinburgh, and it was ordained that all merchandise fhould be bought and fold according to thefe ftandards, under very fevere penalties.

Thus ftood the law before the Union in 1707. It had good effe&s, in fo far as it clearly cftablished what were the ftandard weights and measures: but as care was not taken to ascertain and publish the proportions which the customary weights and meatures bore to the standards, the former were not laid aide; and it could not be otherwife. Even the ufe of the Trone weight, though exprefsly discharged by the act of 16.8, was continued as before.

The diverfity of the whole at this day, not only in the different counties, but in different parts of the fame county, is well known, and appears in a striking light in the annexed tables.

By the 17th article of the Union, in 1707, it was enacted, "That the fame weights and meafures thall be ufd throughout the united kingdom as are now eftablished in England; and that ftandards of weights and measures thall be kept by thofe boroughs in Scotland to whom the keeping the landards of weights and measures does of fpecial right belong: all which tandards thall be fent down to fuch boroughs from the standards kept in the exchequer at Weftminster, &c."

They were fent down accordingly; and they added to the number of our different weights and measures, but did not fuperfede any of them; probably for the reason above given, that no pains was taken to make the people in general acquainted with their proportion to the Scotch weights and measures.'

He then mentions fome glaring inftances of misconduct in the legiflature, by enacting laws directly fubverfive of that uniformity aimed at in the 17th article of the Union, for which we think no apology can be offered.-Shame! that our lawgivers fhould be fo ignorant, or careless, as to pay no attention to a circumftance of fuch capital importance to the nation!

He concludes the introductory part of the work with fome obfervations on the most proper means of enforcing the prefent laws fo as to obtain an uniformity of weights and measures in Scotland, which he thinks might, in a great measure, be effected without the aid of any new law. We fufpect that a new law will be neceffary, were it only to give a fresh spur to thofe who ought to fee the laws put into execution. It is certainly a defect in the British conftitution, that more effectual means are not adopted for executing the laws that are enacted; for it is from this circumftance that laws are unneceffarily multiplied, and trefpaffes more common. It is not, fays the em grefs of Ruffia, the feverity of the punishment, but the cer

† Another Scotticifm. The Writer means prohibited.

tainty

tainty of it, which prevents crimes.-With equal juftice may it be faid, that it is not the multiplicity of ftatutes, but the due enforcing of them. that establishes order in a ftate.

The greatest part of the volume before us confifts of tables for reducing the different weights and meafures employed in Scotland to one common ftandard; and this is naturally divided into two parts. The first confifts of general tables of the standard weights and measures in England and Scotland, and the proportions they reciprocally bear to one another; the fecond, of tables fhewing the contents of the feveral provincial weights and measures, and the proportion they bear to the legal ftandards.

That our readers may have a clear idea of the great utility of this work, we fhall collect, for their fatisfaction, an alftract of the account here given of the feveral measures of capacity, which go under the fame denomination in different parts of the Country: these are indeed much more diverfified than we could eafily have imagined.

The boll is the common term employed as an unit for meafures of capacity in Scotland. But we have already fhewed that there are two fizes of the ftandard boll,-one for barley, oats, and malt; the other for wheat, pease, &c.-It appears that this distinction is univerfally adhered to through all Scotland. We shall only exhibit the variations of the first of thefe bolls.

The standard boll being 100, the other county bolls will be as under:

Aberdeenshire boll

109.677 Bamfshire Inverary 107.258 Argylefhire, Campbeltown

128.709 [Byle and Carrick

Ayrshire +,<

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Berwickshire t
Bute and Arran
Caithnessfhire
Dumbartonshire S
Dumfriesshire ||
Edinburghshire
for bear

Elgin for oats

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112.985 Another for Tiends 125.784

Cunningham

127.015

Another 124.169 Fifeshire

in some cases

195.103 104.838

134.677

106.280

106.597

2.8.339

101.613

105.256

131.570

210.512

103.225

The certainty of punishment,' please to note that, ye who fo frequently (through mistaken lenity) interpofe between the judgment of the law and its due execution; and fo often, to the irreparable detriment of the Public, turn afide the band of jußice!

† N. B. In fome parts of this county the wheat boll is 15.808 per cent. better than standard; in others it is 2.135 per cent. less than fandard.

↑ N. B. The wheat boll in this county is 52.941 ¡er cent, above fandard.

The wheat boll in this county is 16.63 per cent. above fandard.
The wheat boll in this county is 202.184 per cent. above standard.
Forfarshire

Forfar hire

103.629 Perthshire

103.024 Renfrewshire

Kincardinfhire
Kinross thire
Kirkcudbright flewartry 184.483
Lanerkshire

Haddingtonshire
Invernessfhire [ barley 109.786 Rofshire*
oats 137.232 Roxburghshire
106.451 Tiviotdale +
103.024 Selkirkshire
Stirlingshire

Nairnshire

104.176 Sutherland hire
139.354 Wigtonshire ‡

Peeblesshire

104.459

While fuch different measures go under the fame name (and the fame diverfity is obfervable in all other weights and measures), it muft occafion great confufion in the ideas that different perfons form of the price of different kinds of grain, and the amount of the produce of different fields, when these fubjects are mentioned in converfation, or in books; an attempt therefore to reduce thefe meafures, &c. to one ftandard, must be confidered as very laudable. And as the prefent performance puts it in the power of every perfon, who may fo incline, eafily to compare thefe different meafures with one another, it highly merits our approbation; and we wish to fee other performances of the fame kind with regard to England, France, and all the other countries in which a fpirit for improvement prevails. For want of fuch tables as thefe, many of the experiments recorded by Du Hamel, and others, are altogether ufelefs, as it is impoffible to form any adequate idea of the extent of ground, or real amount of the produce mentioned in their experiments.

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104.164 106.250

103.225

133.064

365.128

126.008

107.258 110.644

201.254

In forming an estimate of the value of money at different periods, it is a common practice, and feemingly a very natural one, to compare the price of a measure of any kind of grain which we find incidentally mentioned in any tranfaction, with the common price of the fame nominal measure of grain in modern times: but here we are liable to err in two ways; first, by not knowing exactly what proportion the particular meafure fpoken of bore to the legal ftandard at that time ;--and secondly, from our forming an improper eftimate of the fize of the legal ftandard at the period mentioned: fot there is no doubt that the legal measures have varied at different periods both in England and Scotland, and probably in every other country, fo that we ought to be extremely cautious about drawing important con

The wheat boll in this county is 12.941 per cent. better than fandard.

In the north of England the boll is a measure for grain, as well as in Scotland. About Sunderland and Newcattle two Wincheller buthels, we are informed, are called a boll. The boll in Tiviotdale, therefore, is more than ten times the size of the Newcastle boil.

In the north of England,

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clufions from data that are fo fufpicious. Our ingenious Author, although he profeffes not to be an antiquary, has, in an appendix, thrown fome light on the contents of the standard weights and meafures of Scotland at different periods. We with we had an equally authentic account of thofe of England, and the nations with which we are, or were formerly, much connected.

It appears from our Author's account, that from the reign of David I., about the year 1130, to that of James I., anno 1426, the boll contained 4044 cubic inches; fo that it was fomewhat lefs than half of the prefent ftandard wheat boll, and alfo less than one-third of the prefent ftandard boll of oats or barley, being to the wheat boll as 1 to 2.1735, and to the barley boll as I to 3.1953.

From the year 1426 to 1457, the boll contained 5283.26 cubic inches, and was to the prefent ftandard wheat boll as 1 to 1.663, and to the prefent ftandard boll of barley as I to 2.426.

From the year 1457 to 1587, the boll contained 5594.04 cubic inches, and was to the prefent ftandard wheat boll as i to 1.57, and to the boll of barley as 1 to 2.222.

From the year 1587 to 1618 (at which time the present ftandards were fixed), the boll contained 7910.4 cubic inches, and was to the prefent ftandard boll of wheat as 1 to 1.11, and to the boll of bear as 1 to 1.62. Thus have the measures been gradually increafed to more than double their fize in wheat and pease, and to more than three times their original dimensions as to oats, barley, malt, &c.; other measures and weights were liable to fimilar variations, fome greater and others less than the original ftandards. But we have chofen to follow out the meafures of capacity for things dry, that the reader may have a connected view of one branch of the fubject.

We fhall take leave of this very respectable Author, after making one remark that naturally arifes from the foregoing facts; viz. that we ought not to entertain fuch an extravagant idea as is ufually formed of the poverty of Scotland, or the exceeding high value of money in that part of the kingdom, from the notices that fometimes occur, of the prices of grain in old times being reckoned immoderately high, when, at firft fight, it appears to have coft but very little money. The fize of the boll we fee has gradually increased, as above, to more than double or three times its original dimenfions, while the weight of a pound in money has decreafed to about the thirty-feventh part of its original weight; fò that without making allowance for these variations, we may naturally enough form an idea that filver, at a certain period, was about eighty or a hundred times of higher value than it really was at the time,

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To conclude, we confider this as a moft ufeful performance, and hope the author will be rewarded for the pains he has taken to promote the benefit of his native country.

Com

ART. V. ISAACI NEWTONI Opera Que Exfant Omnia. mentariis illuftrabat Samuel Horfley, LL. D. R. S. S. &c. 4to. 5 1.5 s. Subfcription for the whole Set. Nichols, Conant, &c.

1779.

S this publication is only the first volume of an intended

A work,

volumes, illuftrated with a commentary by the Editor; we think it fufficient for the present to enumerate the contents of it, and to specify the order in which the Editor has thought proper to arrange the different pieces; which, notwithstanding their value and importance, had never yet been collected together. The work is, with propriety, dedicated to the King.

The prefent volume is divided into two parts. According to the learned Editor's propofals, all the tracts of Newton which relate to pure Mathematics, were intended to be first given. In conformity to this plan, the Arithmetica Univerfalis forms the first part of this volume. This tract is accompanied with very few notes; for which circumstance the Editor accounts, by informing us that he had digefted his principal explanatory comments (comprehended in nineteen chapters, the titles of which are here given) into a feparate article, which he originally intended to have added as an appendix to this tract: but the great bulk of the prefent volume not allowing of its infertion, it is omitted. The Editor hints, however, that it may appear hereafter, either in one of the fubfequent volumes, or in a separate publication.

The fecond part comprehends thofe valuable tracts that relate to the higher geometry; particularly to the doctrines of feries, and fluxions. The firft of thefe pieces is the fection on Prime and Ultimate Ratios, which the Editor has thought fit to detach from the beginning of the Principia, as being a proper introduction to the doctrine of fluxions contained in the fucceeding pieces. This is followed by the tract intitled, De Analyf per Equationes numero terminorum infinitas; which is fucceeded by the Excerpta ex Epiftolis Newtoni, formerly publifhed by Jones at the end of the last mentioned tract; but which are here placed in a fomewhat different order. The piece De Quadratura Curvarum, and the Geometria Analytica, next fucceed; and are followed by the Methodus Differentialis, and the Enumeratio linearum tertii Ordinis, which is the laft of Newton's tracts contained in this volume.

The manner in which our Editor and Commentator has fulfilled his task in thefe two capacities, with respect to these opufcula, will be moft concisely exhibited by giving his own

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general

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