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], 1/2n(n[2S] + 1), and 1/2n[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.
(1) FRANCIS BARRETT: The Magus, or Celestial Intelligencer (1801), bk. i. p. 146.
ALPHONSE LOUIS CONSTANT,(1) a famous French occultist of the nineteenth century, who wrote under the name of "ELIPHAS LEVI," describes yet another system of talismans. He says: "The Pentagram must be always engraved on one side of the talisman, with a circle for the Sun, a crescent for the Moon, a winged caduceus for Mercury, a sword for Mars, a G for Venus, a crown for Jupiter, and a scythe for Saturn. The other side of the talisman should bear the sign of Solomon, that is, the six-pointed star formed by two interlaced triangles; in the centre there should be placed a human figure for the sun talismans, a cup for those of the Moon, a dog's head for those of Jupiter, a lion for those of Mars, a dove's for those of Venus, a bull's or goat's for those of Saturn. The names of the seven angels should be added either in Hebrew, Arabic, or magic characters similar to those of the alphabets of Trimethius. The two triangles of Solomon may be replaced by the double cross of Ezekiel's wheels, this being found on a great number of ancient pentacles. All objects of this nature, whether in metals or in precious stones, should be carefully wrapped in silk satchels of a colour analogous to the spirit of the planet, perfumed with the perfumes of the corresponding day, and preserved from all impure looks and touches."(2)