10 18 1 14 22
23 6 19 2 15


It will be noticed that every number from 1 up to the highest possible
occurs once, and that no number occurs twice. It will also be seen
that the sum of each row and of each column is always 65. Similar
squares can be constructed containing any square number of figures,
and it is, indeed, by no means surprising that the remarkable
properties of such "magic squares," before these were explained
mathematically, gave rise to the belief that they had some occult
significance and virtue. From the magic squares can be obtained
certain numbers which are said to be the numbers of the planets;
their orderliness, we are told, reflects the order of the heavens,
and from a consideration of them the magical properties of the
planets which they represent can be arrived at. For example, in the
above table the number of rows of numbers is 5. The total number of
numbers in the table is the square of this number, namely, 25, which is
also the greatest number in the table. The sum of any row or column is
65. And, finally, the sum of all the numbers is the product of the
number of rows (namely, 5) and the sum of any row (namely, 65), _i.e_.
325. These numbers, namely, 5, 25, 65, and 325, are the numbers of Mars.
Sets of numbers for the other planets are obtained in exactly the same
manner.[1]


[1] Readers acquainted with mathematics will notice that if _n_ is
the number of rows in such a "magic square," the other numbers derived
as above will be n<2S>, 1/2_n_(_n_<2S> + 1), and 1/2_n_<2S>(_n_<2S> + 1).
This can readily be proved by the laws of arithmetical progressions.