of knowledge—inasmuch as he possesses the consciousness that he does not know—and he has the moral courage to avow it.[1]
If papa fail to inform him, let him go to mamma, who will not fail to find means to satisfy her darling's curiosity. In the meantime the author of this sketch will endeavour to lead his young friend to make use of his own common sense for the purpose of becoming better acquainted with the triangular figures he has formed with his marbles.
In the case of the Table of the price of butchers' meat, it was obvious that it could be formed by adding the same constant difference continually to the first term. Now suppose we place the numbers of our groups of marbles in a column, as we did our prices of various weights of meat. Instead of adding a certain difference, as we did in the former case, let us subtract the figures representing each group of marbles from the figures of the succeeding group in the Table. The process will stand thus:—
| Table. | 1st Difference. | 2nd Difference | |
| Number of the Group |
Number of the Marbles in each Group. |
Difference between the number of Marbles in each Group and that in the next. |
|
| 1 | 1 | 1 | 1 |
| 2 | 3 | 2 | 1 |
| 3 | 6 | 3 | 1 |
| 4 | 10 | 4 | 1 |
| 5 | 15 | 5 | 1 |
| 6 | 21 | 6 | |
| 7 | 28 | 7 |
It is usual to call the third column thus formed the column of
- ↑ The most remarkable instance I ever met with of the distinctness with which any individual perceived the exact boundary of his own knowledge, was that of the late Dr. Wollaston.
