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NUMBER IN EACH PILE.
pendently any number of the Table of the price of butchers' meat, the following rule was observed:—
Take the number whose tabular number is required.
Multiply it by the first difference.
This product is equal to the required tabular number.
Again, at p. 53, the rule for finding any triangular number was:—
| Take the number of the group | 5 |
| Add 1 to this number, it becomes | 6 |
| —— | |
| Multiply these numbers together | 2)30 |
| —— | |
| Divide the product by 2 | 15 |
This is the number of marbles in the 5th group.
Now let us make a bold conjecture respecting the Table of cannon balls, and try this rule:—
| Take the number whose tabular number is required, say | 5 |
| Add 1 to that number | 6 |
| Add 1 more to that number | 7 |
| —— | |
| Multiply all three numbers together | 2)210 |
| —— | |
| Divide by 2 | 105 |
| —— |
The real number in the 5th pyramid is 35. But the number 105 at which we have arrived is exactly three times as great. If, therefore, instead of dividing by 2 we had divided by 2 and also by 3, we should have arrived at a true result in this instance.
The amended rule is therefore—
