manner of derivation here is simply to reverse the two diagonals. Both
squares are "associated"--a term I have explained in the introductory
article to this department.

The third square is a multiplying magic. The constant, 216, is obtained
by multiplying together the three numbers in any line. It is
"associated" by multiplication, instead of by addition. It is here
necessary to remark that in an adding square it is not essential that
the nine numbers should be consecutive. Write down any nine numbers in
this way--

1 3 5
4 6 8
7 9 11

so that the horizontal differences are all alike and the vertical
differences also alike (here 2 and 3), and these numbers will form an
adding magic square. By making the differences 1 and 3 we, of course,
get consecutive numbers--a particular case, and nothing more. Now, in
the case of the multiplying square we must take these numbers in
geometrical instead of arithmetical progression, thus--

1 3 9
2 6 18
4 12 36

Here each successive number in the rows is multiplied by 3, and in the
columns by 2. Had we multiplied by 2 and 8 we should get the regular
geometrical progression, 1, 2, 4, 8, 16, 32, 64, 128, and 256, but I
wish to avoid high numbers. The numbers are arranged in the square in