31. The same process is to be followed in all cases, but not at the same length. In order to be able to go through it, you must know how to add together the simple numbers. This can only be done by memory; and to help the memory you should make the following table three or four times for yourself: +----+----+----+----+----+----+----+----+----+----+ | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | +----+----+----+----+----+----+----+----+----+----+ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | +----+----+----+----+----+----+----+----+----+----+ | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | +----+----+----+----+----+----+----+----+----+----+ | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | +----+----+----+----+----+----+----+----+----+----+ | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | +----+----+----+----+----+----+----+----+----+----+ | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | +----+----+----+----+----+----+----+----+----+----+ | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | +----+----+----+----+----+----+----+----+----+----+ | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | +----+----+----+----+----+----+----+----+----+----+ | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | +----+----+----+----+----+----+----+----+----+----+ | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | +----+----+----+----+----+----+----+----+----+----+ The use of this table is as follows: Suppose you want to find the sum of 8 and 7. Look in the left-hand column for either of them, 8, for example; and look in the top column for 7. On the same line as 8, and underneath 7, you find 15, their sum. 32. When this table has been thoroughly committed to memory, so that you can tell at once the sum of any two numbers, neither of which exceeds 9, you should exercise yourself in adding and subtracting two numbers, one of which is greater than 9 and the other less. You should write down a great number of such sentences as the following, which will exercise you at the same time in addition, and in the use of the signs mentioned in (23). 12 + 6 = 18 22 + 6 = 28 19 + 8 = 27 54 + 9 = 63 56 + 7 = 63 22 + 8 = 30 100 - 9 = 91 27 - 8 = 19 44 - 6 = 38, &c. 33. When the last two articles have been thoroughly studied, you will be able to find the sum of any numbers by the following process,[6] which is the same as that in (29). [6] In this and all other processes, the student is strongly recommended to look at and follow the first Appendix. RULE I. Place the numbers under one another, units under units, tens under tens, and so on. II. Add together the units of all, and part the _whole_ number thus obtained into units and tens. Thus, if 85 be the number, part it into 8 tens and 5 units; if 136 be the number, part it into 13 tens and 6 units (20).