Here it must be noted, that when the amount of any column in any fum has a cypher in the place of units, fuch cypher is to be placed under the column; as in the firit of the three laft examples.

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The three laft examples are proved-which is done in this manner after the total is found according to the foregoing rules, and placed in the first of the three bottom lines, the top line of the fum is to be feparated by a line drawn under it, the remaining part of the fum caft up, and the amount of it placed under the aforefaid total; this laft amount, and the top line of the fum, are then to be added together; and if the amount of thefe two lines be equal to the total in the first bottom line, the fum is rightly caft up; otherwise not.

All other fums in addition are to be proved in a fimilar manner, whether they be of one denomination or of divers denominations.

Addition of divers denominations confifts in adding together numbers of different denominations, whether they be money, weights, or measures.

Before the learner proceeds to addition of money, it is neceffary that he have the following tables by heart; called the Pence Table, and the Shilling Table..

In addition of divers denominations, thofe numbers which are of the fame denomination are always placed in the fame column, and their name or mk generally at the top: thus, in addition of money, the pounds are placed in one column, with an at the top for libra, the Latin word for pounds'; the fhillings in another column, with an s at the top for folidi, the Latin word for hillings; the pence alfo by themfelves, in another column, with a d at the top for denarii, the Latin for pence; and fometimes the farthings are placed in a feparate column, with a gr. at the top for quadrans; but the most general rule is, to place them immediately after the pence, as a fraction of a penny: thus, for one fourth part of a penny, or one farthing; for one half, or a halfpenny : for three fourths of a penny, or three farthings: as in the following examples :

In addition of numbers of divers denominations, this is the general rule:-To begin at the right hand column, or the column of the least denomination: adding all the numbers in the faid column together, and obferving how many units there be in it of the next higher denomination, and how much overplus: the overplus is to be fet down under the line, and the units of the next denomination are be added to the next colunin. The next column being caft up, it must alfo

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also be noted how many units there are in it of the next higher denomination, and how much overplus: the overplus is to be placed under its own column, and the units of the next denomination added to the next column, as before; and fo on to every new column.

Thus, in the first of the three foregoing examples, I begin with the unit figures of the loweft denomination, which is pence, faying, 1 and 2 is 3, and 1 is 4, and 4 is 8, and 9 is 17, and 2 is 19, and 9 is 28; to which I add the tens in the fame column, faying, 28 and 10 is 38, and 10 is 48, and 10 i 58; now, by the pence table, I know that 50 pence is 4 fillings and 2 pence, therefore 58 pence is 4 fhillings and 10 pence: thus, I must fet down the 10 pence, which is the overplus, under the fame column; and the 4 fhillings, which are 4 units of the next higher denomination, I carry to be added to the next denomination, faying, 4 and 9 is 13, and 7 is 20, and 5 is 25, and 7 is 32, and 6 is 38, and 7 is 45; to which I add the tens, faying, 45 and 10 is 55, and 10 is 65, and 10 is 75: now, by the fhiliing table, I find that 75 fhillings is 3 pounds 15 fhillings; the 15 fhillings are to be fet under the column of fhillings, and the 3 pounds, being units of the next denomination, viz. pounds, are to be added thereto and the pounds, being the laft and highest denomi nation, are to be added together as fimple numbers of one denomination, and the total placed under the fame : thus the total is found to be 527, 155. 10d.

In the next example I begin with the farthings, being of the lowest denomination, faying, 2 farthings and 2 is 4, and 3 is 7, and 1 is 8, and 2 is 10; 10 farthings is 2 pence and 2 farthings; the 2 farthings is to be fet under the line as overplus, and the 2 pence is to be added to the column of pence, which, added up, amounts to 43 pence, which is 3 fillings and 7 pence; the 7 pence is to be fet under the column of pence, and the 3 fhillings is to be added to the column of fhillings; in which column, with the 3 added, there is 75 fillings, or 3 pounds 15 fhillings; the 15 fhil

lings must be placed under the fhillings, and the 3 pounds added to the column of pounds, and the pounds added together as before, and the total placed underneath: thus the amount of this fum is 7781. 155. 74d.

In the fame manner the third, and every other fum in this part of addition, is to be wrought. The fums are all ready proved, for the ease of the learner. The line under the total shews the amount of the fum without the top line: the bottom line fhews the amount of the line just over it added to the top line of the fum, and proves the work right, by being equal to the firft total.

Addition of 'Avoirdupois Weight.

By this weight are weighed all kinds of goods whatever, except bread, gold, filver, and precious ftones.

The

Avoirdupois weight is divided into two parts, called the greater and the lefs. Avoirdupois the greater confifts of hundreds, quarters, and pounds: avoirdupois the lefs is divided into pounds, ounces, and drams.

Thefe examples are wrought in the fame manner as the former; but having a regard to the avoirdupois table, instead of the pence table. And the number of units in each column, which compofe an unit in the next higher column, is placed at the head of the column: thus, in the first example, as 28 is the number of pounds which form one quarter of an hundred, it is placed over the column of pounds; and 4, which is the number of quarters contained in an hundred, is placed over the column of quarters. And in the last example, 16 being the number of drams contained in an ounce, it is placed over the column of drams; and, as 1 ounces form a pound, 16 is placed over the column of

ounces;