place must be in the third compartment of the second wall. If the number in question be higher than the number of the compartments in one room, its place will be readily found by dividing it by that number. Thus, suppose 48 to be the number whose place is required:
| 36 | ) 48 ( | 1.2 |
| 9 | ) 12 ( | 1.2 |
| 3 |
As 48 exceeds 36, we know that it cannot be in the first room, the 1 is therefore changed into 2; and the fraction remaining, shows it to be in the twelfth compartment. There being nine compartments on every wall, this remainder, or number of the compartment, is divided by 9, for the purpose of ascertaining the wall. Now, as the divisor is contained more than once, but not twice, in the dividend, it follows that the compartment sought must be on the second wall; the remainder gives the specific compartment. This operation, then, shows that 48 is in the third compartment, on the second wall, in the second room. This was the plan adopted by the antients when they divided their rooms into parts; but being both complicated and difficult, it has been rejected in the present system, and another scheme has been introduced in its place, which is more simple in its construction—less difficult in its application—and much more extensive in its powers.
