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Footnote: Average Mobility

In one 19th-century book, however, I saw a better attempt made; in that book, the author repeated the process for every square on the board, and then calculated the average mobility.

I wish I knew what book it was; I think it was German, from the 1840s. Do you know?

The Knight can move to two squares from a1, to three squares from b1, and so on; this next table shows the Knight's mobility on 16 different squares: 

            KNIGHT'S MOBILITY

    .................................
4   |   4   |   6   |   8   |   8   .
    |-------|-------|-------|-------.
3   |   4   |   6   |   8   |   8   .
    |-------|-------|-------|-------.
2   |   3   |   4   |   6   |   6   .
    |-------|-------|-------|-------.
1   |   2   |   3   |   4   |   4   .
    |-------|-------|-------|-------.
        a       b       c       d
Thus, ( 8+8+8+8+6+6+6+6+4+4+4+4+4+3+3+2 ) divided by 16 gives us a result of 5.25, the average mobility of a Knight.

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