Note, A Firkin of Soap, and of Herrings, are the same with that of Ale.

33. This diftinction or difference betwixt Ale and Beer Measure, is now only used in London. But in all other places of England, the following Table of Beer or Ale, whether it be ftrong or small, is to be observed, according to a Statute of Excife made in the year 1689.

34. Dry measure is different both from Wine and Ale meafure, being as it were a mean betwixt both, tho' not exactly fo; which, upon examination, will be found to be in proportion to the aforefaid old standard Wine-gallon, as Avoirdupoifeweight is to Troy-weight; that is, as one pound Troy is to one pound Avoirdupoife, fo is the cubic inches contained in the old Wine-gallon, to the cubic inches contained in the dry or Corngallon, viz. 12: 14 13 :: 224 : 272, the common received content of a Corn-gallon nearly. Altho' now it is otherwise fettled by an act of parliament, made in 1697, the words of that act are thefe: Every round Bufhel with a plain and even bottom, being made eighteen Inches and a half wide throughout, and eight Inches deep, fhould be efteemed a legal Winchester Bufhel, according to the ftandard in his Majefty's Exchequer. Now a veffel thus made, will contain 2150,42 cubic inches, confequently the Corn-gallon doth contain but 268 cubic Inches.

Note, When Salt and Sea-coal are measured by the Cornbufhel, they are heaped; 36 Bufhels is a Chalder of Coals, and 21 Chalders a Score.

35. As the leaft part of Weight was originally a Wheat-corn, fo the least part of Long-measure was a Barley-corn, taken out of the middle of the ear, and being well dried, three of them in length were to make one inch; and thence the reft, as in the following Table.

Note, That a Yard is usually subdivided into four Quarters, and each Quarter into four Nails.

And each Ell into four Quarters; but each Quarter of an Ell contains five Nails.

36. Superficial, or fquare Measures of Land, are fuch as are exprefs'd in the following Table:

For 40 Poles or Perches in length, and 4 in breadth do make

a Statute Acre of Land; that is 220 yards multiplied by 22

4

yards,

Chap. II. yards, which is equal to 4840 Square Yards are a Statute Acre.

Note, Land is best measured by a Chain of 4 Poles long, divided into 100 parts, called Links.

And if you would exprefs, by Figures, these quantities of Land, viz. thirty-fix Acres three Roods twenty Perches; also seven Acres no Roods thirty-two Perches, the ordinary way to fet them down, is thus:

37. A TABLE of TIME is this that follows:

But in ordinary computations of time, the whole year, confifting of three hundred fixty-five days, is divided either into twelve equal parts or months; every month then containing thirty days and ten hours; or elfe into twelve unequal Kalendar-months, according to the ancient Verse :

Thirty Days hath September, April, June, and November ; February hath twenty-eight alone, and each of the reft, thirty-one.

Note, That every Leap-year (which happens once in four years) contains three hundred fixty-fix days; and, in such year, February contains twenty-nine days,

38. Of Things accounted by the dozen, a Grofs is the Integer, confifting of twelve dozens, each dozen containing twelve particulars. So that if you would exprefs, in Figures, feven grofs four dozens and five particulars; alfo four dozens and eight particulars, they may be written thus:

39.

СНАР.

III.

ADDITION of Whole Numbers.

Oncerning Notation of Numbers, and how thereby the quantities of things are ufually expreffed, a full declaration has been made in the preceding Chapters: Numeration follows, which comprehends all manner of operations by Numbers.

40. In Numeration, the four primary or fundamental operations are these, Addition, Subtraction, Multiplication, and Divifion.

41. Addition is that, by which divers numbers are collected together, to the end that their fum, aggregate or total, may be discovered.

42. In Addition, place the numbers given one above another, in fuch fort, that like places or degrees in every number, may stand in the same rank; that is, Units above Units, Tens above Tens, Hundreds above Hundreds, &c. So thefe numbers 1213 and 462, being given to be added together, you are to order them as appears in the margin.

1213

462

43. Having thus placed the numbers, and drawn a line under them, add them together, beginning with the units firft, and faying thus, 2 and 3 make 5, which write under the rank of units; then proceed to the fecond rank, and fay, 6 and I make 7, which write under the fecond rank (being the place of tens); again 4 and 2 make 6, which write under the 1213 third rank, Laftly, write down 1, being all that ftands in the fourth rank; fo the fum of the faid given numbers is found to be 1675, and the operation will appear 1675 as in the margin.

141,

In like manner, the numbers 2315, 7423, and being given to be added together, their fum will be found to be 9879, and the operation will ftand as in the example.

462

2315

7423

141

9879

44. When the fum of the figures of any of the ranks amounts to ten, or any number of tens without any excess, write down a cypher under that rank; but when the fum of any rank exceeds ten, or any number of tens, fet down the excess under fuch rank; and for every ten contained in the fum of any rank, referve an unit or 1 in your mind, and add

fuch

4937 9878 394

15209

fuch unit or units to the figures of the next rank towards the left-hand; fo the numbers 4937, 9878, and 394, being given to be added together, the operation will be thus, viz. Beginning with the rank of units, 4, 8 and 7 make 19, wherefore write down 9, the excefs above ten, and carry 1 in mind instead of the ten contained in the faid 19: Then I and 9 (9 being the lowermoft figure of the fecond rank) make 10, which added to 7 and 3, the other figures of the fame rank, the whole fum of them is 20; therefore fet down a cypher under the line in that rank, because the excefs above the two tens is nothing; next, carry 2 to the third rank: 2 and 3 (3 being the lowermoft figure of the third rank) make 5, which being added to 8 and 9 (the other figures of the fame rank) the sum of them is 22; therefore writing down 2 (being the excess above the two tens) under the line in the third rank, carry 2 in mind (because there were two tens in 22) to the fourth rank: Lastly, 2 and 9 make II, which added to 4 make 15, this 159 because it is the fum of the last rank, write totally down under the line, on the left-hand of the figures before subscribed; so the sum of the three numbers given, is found to be 15209, as in the example.

45. The reason of the above operations will be very evident from this undeniable maxim, viz. that the whole is equal to all its parts; and the method of fetting down the total, may easi ly be accounted for, from the nature of numeration, which explains the different value of places as they proceed from the right, to the left-hand: For, as 9 is the greateft fimple character or figure, fo every number exceeding 9, being compound, must require more places than one to exprefs it. Thus, the number Io can no otherwise be expreffed in figures, but by removing. the figure into the place of tens, which is done by fupplying the unit's place with a cypher: And as it is the fame with every other column (ten being still the proportion of increase) consequently, when the fum of any column amounts, to 10 or more, the units exceeding, if there be any, or a cypher, if none, must be fet under fuch column, and the ten or tens of the amount carried on, as fo many units, to the next column on the left.

What is here obferved, as to carrying the tens (the proportion of increase) from one column to another in integers, may be as juftly applied to the proper numbers in adding fums of different denominations.

This demonftration may be applied to the example work'd in Art. 44, as follows:

The