greatest facilities to the calculator in the addition of numbers, enabling him to add a whole day with. out any mental fatigue; whereas, by the ordinary way, it is very laborious and fatiguing.

Our system of calculation also embraces a concise, rapid, and at the same time practical method of Multiplication, by which one is enabled to arrive at the product of any number of figures, multiplied by any number, immediately, without the use of partial products.

This small work also embraces the shortest and most concise method for the computation of Interest ever introduced to the public. Our system for computing interest is entirely different from any rule ever introduced, for the computation of either Simple or Compound Interest. A student having gone no further than Long Division in Arithmetic, can, by our rule, calculate Simple or Compound Interest at any given rate per cent., for any given time, in one-tenth of the time that the best calculators will compute it by the rules laid down in other books. By using our rules, you can entirely avoid the use of fractions, and save the calculation of 75 to 100 figures, where years, months and days are given on a note.

UNIV. OF CALIFORNIA

ADDITION

TO BE able to add two, three or four columns of figures at once, is deemed by many to be a Her culean task, and only to be accomplished by the gifted few, or, in other words, by mathematical prodigies. If we can succeed in dispelling this illusion, it will more than repay us; and we feel very confident that we can, if the student will lay aside all prejudice, bearing steadily in mind that to become proficient in any new branch or principle a little wholesome application is necessary. On the contrary, we can not teach a student who takes no interest in the matter, one who will always be a drone in society. Such men have no need of this principle.

If two, three, or more, columns can be carried up at a time, there must be some law or rule by which it is done. We have two principles of Addition; one for adding short columns, and one for adding very long columns. They are much alike, differing only in detail. When one is thoroughly learned, it is very easy to learn the second. By a little attention to the following example, much time in future will be saved.

ADDITION OF SHORT COLUMNS OF FIGURES.

ADDITION is the basis of all numerical operatians, 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

727

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 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 igure 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.

6

36

9

4

Commence at 9 to add, and add as near 20 as posBible, thus: 9+2+4+3=18, place the 8 to the right of the 3, as in example; commence at 6 to 7' add 6+4+8=18; place the 8 to the right of 4 the 8, as in example; commence at 6 to add 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, as in example; commence at 6 to add 6+4 77 +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 88 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 the original 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 an 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 ás near 20 as possible, because you will save the forming of extra figures in your new column.

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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+ 45 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 2 figure 2, under the original column; thismakes 52, which is the sum of the column. 52

5

6

75

6