significance of the dodecatemories is this: not only is a planet’s influence affected by the sign in which it stands, but it is further modified by the sign of the particular dodecatemory which it occupies.
No more than this need the poet have said. But operating with multiples of 2 ½ in Latin calls for mental dexterity, and our teacher cannot resist helping with our arithmetical calculations. We should therefore note the degree of a sign that the Moon (given as the most obvious example of a planet) occupies at the moment of a nativity (let us suppose it to be the 9th degree of Aries): it is desired to ascertain in what sign’s dodecatemory that degree falls. Multiply the number by twelve (9 x 12 = 108); dole out thirty apiece to the signs in order beginning with itself (30 to Aries, 30 to Taurus, 30 to Gemini), and note the sign in which the multiples of thirty give out (here Cancer, for 108 - 90 = 18): that will be the sign of the Moon’s dodecatemory. This is merely a variation, of course, on what the poet has previously told us, and the whole point of multiplying by twelve is that we may operate with the easier number 30 instead of 2 ½.
[2. 732–734: The dodecatemory of the Moon]
So much is easy. But the explanation of the lines 2. 732–734 is complicated: “When the number fails, then let the remainder be divided into portions of two and a half, so that these may be distributed in order among the remaining signs”
The term “dodecatemory,” which is simply the Greek for “a twelfth,” is frequently used as a synonym for “a sign of the zodiac,” but occasionally we encounter it in a special conception, the dodecatemory of the Moon. This significant place in the zodiac (somewhat like the Lot of Fortune, to which we shall come at 3. 160–202) one found by a procedure described by Porphyry, Isag. 194 Wolf (= CCAG V. 4. 211) and repeated in essentially the same form at CCAG VIII. 2. 50: “Count the number of degrees from the Sun to the Moon, and from these take away all multiples of thirty; as for the remainder, divide it into portions of two and a half, and distribute them in order from the zodiacal sign in which the Moon is situated.” Let the Sun be situated in the 15th degree of Gemini, the Moon in the 23rd of Scorpio: the distance is 158 degrees. Take away 5 x 30: that leaves 8. Divide this into portions of 2 ½: one will go to Scorpio, one to Sagittarius, one to Capricorn, and the remainder comes to an end in Aquarius. The dodecatemory of the Moon is thus Aquarius.
Now this has nothing to do with Manilius, whose rule when the Moon stood in the 23rd degree of Scorpio would lead to the following computation: (726 - 728) 23 x 12 = 276; (729 f.) of this 30 go to Scorpio, leaving 246; (731) 8 x 30 go to Sagittarius, Capricorn, Aquarius, Pisces, Aries, Taurus, Gemini, and Cancer, with 6 left over; (735 f.) so the thirties give out in Leo, and therefore when the Moon (or any other planet) occupies the 23rd degree of Scorpio it stands in the dodecatemory of Leo.
We can now see what has happened. At the point in Manilius’s procedure where the casting out of thirties left a remainder, some astrological interpolator, believing this casting out of thirties to be part of the Porphyrian procedure, has fabricated three verses to express the rest of the operation (italicized above). His composition, which shrewdly included several echoes of Manilian language, was good enough to deceive Housman, though it is exposed as a fake