Standard Measures, to prevent error are generally derived from nature. For example, measures of time, from the time of the revolution of the earth about its axis of space, from the length of a barley-corn, taken from the middle of a full-grown ear; also, from the circumference of the earth: of weight, from the weight of a grain of wheat, taken as above; also, from the weight of a definite quantity of distilled water: of heat, from the temperature of boiling water, &c.

The four principal operations of Arithmetic are represented by the following signs:

When, in solving a question, only one operation is

csed, the answer has a distinctive name.

In addition, the answer is called the sum.

A sign made thus, called Equal to or Equals, is placed between two quantities to show their equality; Thus, 1 + 1 = 2 is read, one plus one, equal to two; or, more commonly and perhaps better, one plus one, eqrials two.

N. B. The above process of addition is only recommended for beginners.

Process. For adding the above example, commence at the bottom of the right-hand column. Add thus: 12, 16, 22; then carry the 2 tens to the second column, then add thus, 8, 10, 18, 22, carry the two hundreds to the third column, and add the same way, 9, 13, 16, 23. Never permit yourself for once to add up a column in this man. ner, 3 and 9 are 12 and 4 are 16, and 6 are 22; it is just as easy to name the sum at once, without naming the figures you add, and three times as rapid.

ADDITION OF SHORT COLUMNS OF FIGURES.

ADDITION is the basis of all numerical opers. tions, and is used in all departments of business, To aid the business man in acquiring facility and accuracy in adding short columns of figures, the following method is presented as the best:

274

346

PROCESS.-Commence at the bottom of the right-hand column, add thus: 16, 22, 134 32; then carry the 3 tens to the second 342 column; then add thus: 7, 14, 25; carry 727 the 2 hundreds to the third column, and 329 add the same way: 12, 16, 21. In this 2152 way you name the sum of two figures at once, which is quite as easy as it is to add one figure at a time. Never permit yourself for once to add up a column in this manner: 9 and 7 are 16, and 2 are 18 and 4 are 22, and 6 are 28, and 4 are 32. It is just as easy to name the result of two figures at once and four times as rapid.

The following method is recommended for the

ADDITION OF LONG COLUMNS OF FIGURES.

In the addition of long columns of figures which frequently occur in books of accounts, in order to add them with certainty, and, at the same time, with ease and expedition, study well the following method, which practice will render familiar, easy, rapid, and certain.

THE EASY WAY TO ADD.

EXAMPLE 2-EXPLANATION.

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9

Commence at 9 to add, and add as near 20 as possible, thus: 9+2+4+3:=18, place the 8 to the right of the 3, as in example; commence at 6 to add 6+4+8=18; place the 8 to the right of the 8, as in example; commence at 6 to add 6 6+4+7=17; place the 7 to the right of the 7, as in example; commence at 4 to add 4+ 9+3=16; place the 6 to the right of the 3, 4 as in example; commence at 6 to add 6+1 7 +7=17; place the 7 to the right of the 7, 4 as in example; now, having arrived at the 6 top of the column, we add the figures in the 8 new column, thus: 7+6+7+8+8=36; place 4 the right hand figure of 36, which is a 6, 6 under the original column, as in example, and 39 add the left hand figure, which is a 3, to the 4 number of figures in the new column; there 2 are 5 figures in the new column, therefore 9 3+5=8; prefix the 8 with the 6, under theoriginal column, as in example; this makes 86 86, which is the sum of the column.

Remark 1.-If, upon arriving at the top of the column, there should be one, two or three figures whose sum will not equal 10, add them on to the sum of the figures of the new column, never placing

an extra figure in the new column, unless it be ar excess of units over ten.

Remark 2.-By this system of addition you can stop any place in the column, where the sum of the figures will equal 10 or the excess of 10; but the addition will be more rapid by your adding as near 20 as possible, because you will save the forming of extra figures in your new column.

EXAMPLE-EXPLANATION.

2+6+7=15, drop 10, place the 5 to the right of the 7; 6+5+4=15, drop 10, place the 5 to the right of the 4, as in example; 8+3+7=18, drop 10, place the 8 to the right of the 7, 4 as in example; now we have an extra figure, 78 which is 4; add this 4 to the top figure of the 3 new column, and this sum on the balance of 8 the figures in the new column, thus: 4+8+ 4o 5+5=22; place the right hand figure of 22 under the original column, as in example, and add the left hand figure of 22 to the number of figures in the new column, which are three, thus: 2+3=5; prefix this 5 to the figure 2, under the original column; this makes 52, which is the sum of the column.

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52