The 30 Ayres and their correspondences (an individual interpretation):

   The 30 Ayres of the Enochian system are clearly the first three decads of this new mathematical model.  Following Dee’s diaries, we know that the Ayres ascend from Earth in the innermost Ayre (30^th) up to Fire; and that each Ayre is divided into three (3 Governors, 3 Principles), except the 30^th, which has 4 Governors and is composed of 4 elements.  We can also surmise, through the fact that the Black Cross of Union in the Great Table is composed of the names of the Governors of the 10^th Ayre (LEXARPH-COMANAN-TABITOM; but minus the initial L, making 20 letters), that the inner 20 Ayres (11–30 inc.; matching the number of letters in EXARP-HCOMA-NANTA-BITOM) are in some sense governed through these names, which represent the 4 elements multiplied through the 5 elements.14It is worthy of note that the 40 letters on the circumference of the Sigillum Dei are the same in number as the (duplicated) letters of the Black Cross, which therefore provides the union of the cross and the circle.  These letters on the Sigillum Dei each have a corresponding number, which summate to 440; to which 1 is added for the unity of the Seal itself, thus making 441, which is AMTh, “Truth” – hence the Hebrew name of the Seal.  Now the Tree of Life is composed of 4 worlds, each composed of a single Tree, making 40 Sephiroth; and in each Sephiroth there is a further tree, making 440 Sephiroth in total.  It is therefore possible to suggest that the Enochian system is in some sense a reconstitution of the Hebrew Qabalah.  The leftover L then fits with the 4^th element of the 30^th Ayre.15Interestingly, since the names EXARP-HCOMA-NANTA-BITOM are written twice in the Black Cross, and if we add the two missing “L”s, we find there are 666 letters in the Great Table.

   It is also possible to gauge from Crowley’s attribution of the first three Sephiroth that there is a way to attribute the planets (and the 21 Enochian letters)16Which are divided into three groups of seven in the relevant Spirit Action. to the Ayres 10–30 inc.  This is likened to the attribution of the Sephiroth in the hexagram, where Saturn represents the Supernals, and Luna contains Malkuth.  In this arrangement (but not shown in the table) the planets are equivalent to the Sephiroth Chesed–Yesod, in the final Yesod of which is contained Malkuth (=L, Earth).

   More importantly, by “exalting Malkuth to Binah” in the hexagram,17i.e., equilibrating Earth (Malkuth) and Saturn (the Supernals). we have a 27-fold schema, which may then correspond with Liber Trigrammaton.

   The English alphabet corresponds with the Trigrams in the above table, and numerical values may be attributed by reference to Liber Trigrammaton and The Book of the Law.  Liber Trigrammaton begins: “Here is Nothing under its three forms.  It is not, yet informeth all things.”  This corresponds with the attribution of A to the numbers 1, 2 and 3; and it suggests that its value should be zero.  Yet it is also possible to suggest that A (as “nothing”) informs “all things” in the trinity of triads (1–9 inc.), as a triform expression of zero; thus giving values of B = 0 and C = 0.  This is both supported and denied in the descriptions of their respective Trigrams:

Now cometh the glory of the Single One, as an imperfection and stain.

   Consider this with reference to my description of the number 2 as “Not-One”.  And then:

But by the Weak One the Mother was it equilibrated.

   The equilibration of the Not-One in the number three.

   Therefore the first triad may be seen to subsume the first three triads into itself, as the threefold expansion of the Not-Trinity (zero).  However, these triads are of course distinct, composing respectively Kether-Chokmah-Binah, Chesed-Geburah-Tiphareth and Netzach-Hod-Yesod.  Therefore there are also positive values for these three letters.  These have been gleaned from the text of The Book of the Law:

For I am perfect, being Not; and my number is nine by the fools; but with the just I am eight, and one in eight: Which is vital, for I am none indeed. (Liber AL, II:15)

   This has a solution both in Hebrew188 the letter Cheth, which is spelt ChITh, adding to 418; and moreover nine is Teth, spelt TITh, which is 419.  Thus, 419 – 418 = 1 is the “one in eight”.  Note also 2³ = 8 and 3² = 9, and cf. AL II:7. and in English.  “Nine” is the first 9 Ayres, and “eight” is then the value of A (which is also Aleph = 1, therefore “one in eight”, being the union of the triform nothing).  This is supported by the following:

Nothing is a secret key of this law.  Sixty-one the Jews call it; I call it eight, eighty, four hundred & eighteen.  But they have the half: unite by thine art so that all disappear. (Liber AL, I:46 & 47)

   Sixty-one is AIN, “the Not”, which is the letter A (Trigram 1) in its three forms.  The “art” referred to is the method of I:25, “Divide, add, multiply, and understand”:

   (A)
   (AI)
   (AIN)

A
A × Yod
A + Yod + (A × Nun)

= 8
= 80
= 418

   Eight is the central sphere of the third trinity of 7-8-9, which suggests that the letters B and C might be similarly representative of the second and third trinity respectively, as it were a process of redintegration.19Notwithstanding the earlier correspondences.  Thus we have B = 5 and C = 2.  It may be noted that the three “manifest nothings” A, B and C show forth respectively the Berashith Equation20This is:  [see footnote below].

See Berashith in Crowley, Collected Works; which is online at: [see footnote below].
   Please note that 0⁰ is the “Absolute [Qabalistic] Zero”, not merely “non-extension”.  The number 8 may be considered logically as as a 3-dimensional cube (having 8 vertices, and being 2³), which is equivalent to the portion .  The argument that the “rules” of algebra are designed not to produce such awkward results is a petitio principii, since the universe evidently “is”!, the Pentagram-Circle of I:60 and the 0 = 2 equation (which may be discussed at length elsewhere).  It will be noted that these are the bases of Life, Light and Love.

   Continuing with the rest of the letters, we find that D, E, F, and G (the 4 elements governed by the 10^th Ayre) must be 3, 4, 6 and 7, and the other letters are then H=9, I=10, J=20, etc., down to Z=900.  The letter A fills up the last place both in the same way that in Hebrew, Aleph “writ large” is 1000; but here, it completes the system of the Ayres in the letters AL, the key of The Book of the Law, which is 31 in the Hebrew, suggesting the 30 Ayres “and the unity thereof”.  It is also LA, “Not”.

   These values may be tried in the fire of gematria.  There are a few obvious words to start with, assuming first that A = 0, B = 0, C = 0:

boleskine = 418
   See AL II:78.

stélé babalon = 718
   This corresponds with Crowley’s στηλη 66621Using the stau or compound στ, which equals 6. = 718.  666 is clearly the Beast,22ThRIVN and το μεγα θηριον both equal 666. and so there is an identification of Babalon and the Beast.

aleister = 666
   For this, one must use the value A = 8.  If A = 0, it adds to 658, which is “half” and “understanding” in Greek; thus giving some initial justification for the use of two different values for A.

   These alphabetic values form the basis for the following brief analysis of The Book of the Law.

14 It is worthy of note that the 40 letters on the circumference of the Sigillum Dei are the same in number as the (duplicated) letters of the Black Cross, which therefore provides the union of the cross and the circle.  These letters on the Sigillum Dei each have a corresponding number, which summate to 440; to which 1 is added for the unity of the Seal itself, thus making 441, which is AMTh, “Truth” – hence the Hebrew name of the Seal.  Now the Tree of Life is composed of 4 worlds, each composed of a single Tree, making 40 Sephiroth; and in each Sephiroth there is a further tree, making 440 Sephiroth in total.  It is therefore possible to suggest that the Enochian system is in some sense a reconstitution of the Hebrew Qabalah.

15 Interestingly, since the names EXARP-HCOMA-NANTA-BITOM are written twice in the Black Cross, and if we add the two missing “L”s, we find there are 666 letters in the Great Table.

16 Which are divided into three groups of seven in the relevant Spirit Action.

17 i.e., equilibrating Earth (Malkuth) and Saturn (the Supernals).

18 8 the letter Cheth, which is spelt ChITh, adding to 418; and moreover nine is Teth, spelt TITh, which is 419.  Thus, 419 – 418 = 1 is the “one in eight”.  Note also 2³ = 8 and 3² = 9, and cf. AL II:7.

19 Notwithstanding the earlier correspondences.

20 This is: 

See Berashith in Crowley, Collected Works; which is online at: http://lilytears.com/spirituality/thelema/qabalah/berashith.htm.
   Please note that 0⁰ is the “Absolute [Qabalistic] Zero”, not merely “non-extension”.  The number 8 may be considered logically as as a 3-dimensional cube (having 8 vertices, and being 2³), which is equivalent to the portion .  The argument that the “rules” of algebra are designed not to produce such awkward results is a petitio principii, since the universe evidently “is”!

21 Using the stau or compound στ, which equals 6.

22 ThRIVN and το μεγα θηριον both equal 666.