[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.  Rather similar but more complicated and less uniform “magic squares” are attributed to PARACELSUS.

Now to each planet is assigned an Intelligence or good spirit, and an Evil Spirit or demon; and the names of these spirits are related to certain of the numbers of the planets.  The other numbers are also connected with holy and magical Hebrew names.  AGRIPPA, and BARRETT copying him, gives the following table of “names answering to the numbers of Mars":—­

5.  He, the letter of the holy name.          hb 
25.                                hb ___
65.  Adonai.                             hb ____
325.  Graphiel, the Intelligence of Mars.     hb _______
325.  Barzabel, the Spirit of Mars.      hb _______

Similar tables are given for the other planets.  The numbers can be derived from the names by regarding the Hebrew letters of which they are composed as numbers, in which case hb (Aleph) to hb (Teth) represent the units 1 to 9 in order, hb (Jod) to hb (Tzade) the tens 10 to 90 in order, hb (Koph) to hb (Tau) the hundreds 100 to 400, whilst the hundreds 500 to 900 are represented by special terminal forms of certain of the Hebrew letters.[2] It is evident that no little wasted ingenuity must have been employed in working all this out.

[2] It may be noticed that this makes hb _______ equal to 326,
one unit too much.   Possibly an Alelph should be omitted.

Each planet has its own seal or signature, as well as the signature of its intelligence and the signature of its demon.  These signatures were supposed to represent the characters of the planets’ intelligences and demons respectively.  The signature of Mars is shown in fig. 26, that of its intelligence in fig. 27, and that of its demon in fig. 28.

These various details were inscribed on the talismans each of which was supposed to confer its own peculiar benefits—­as follows:  On one side must be engraved the proper magic table and the astrological sign of the planet, together with the highest planetary number, the sacred names corresponding to the planet, and the name of the intelligence of the planet, but not the name of its demon.  On the other side must be engraved the seals of the planet and of its intelligence, and also the astrological sign.  BARRETT says, regarding the demons:[1] “It is to be understood that the intelligences are the presiding good angels that are set over the planets; but that the spirits or daemons, with their names, seals, or characters, are never inscribed upon any Talisman, except to execute any evil effect, and that they are subject to the intelligences, or good spirits; and again, when the spirits and their characters are used, it will be more conducive to the effect to add some divine name appropriate to that effect which we desire.”  Evil talismans can also be prepared, we are informed, by using a metal antagonistic to the signs engraved thereon.  The complete talisman of Mars is shown in fig. 29.