Fire is the element of the east, where the sun rises. It gives light and heat and punishes. Therefore it is the element of dharma – morality, which is stewarded by the kṣatriya (ruler).
Air is the element of the west, where the sun sets and breezes blow. It is pleasurable, inspires relaxation and fun; and is fleeting. Therefore it is the element of kāma – pleasure, which is the only ambition of the masses (śūdra).
Earth is the element of the “below”, where the earth literally stands beneath our feet. It produces every resource – food, materials, jewels, etc. It is therefore the element of artha – prosperity, which is the aspiration of the commercial class (vaiṣya).
Water is the remaining element, corresponding to the heavens above us. It is deep, quiet, and most of all, reflective. Therefore it is the element of self-realization (mokṣa), which is the aspiration of the quiet, deep, introspective intellectual (brāhmaṇa).
The first sign, Aries is the sign in the celestial east (where the Sun rises above the celestial horizon), so it is fire. The trines from aries (Leo and Sagittarius) are also fire. Because the signs in any element have different rulers and modes, they are not identical. Leo is the most purely kṣatriya sign, but Aries is a more martial kṣatriya, and Sagittarius is s rājarṣi (“philosopher-king”). Similarly, the trines from the first house (the fifth and ninth) are dharma houses.
The seventh sign, Libra, is the sign in the celestial west (where the Sun sets below the celestial horizon), so it is air. Its trines (Aquarius and Gemini) are also air. Aquarius (the water-bearer) is the most purely śūdra. Gemini is blended with pleasure-based intellect and Libra with artistic intellect and ambition. The trines from the seventh house (third and eleventh) are all kāma houses.
The tenth sign, Capricorn, is the sign at the Sun’s nadir, so it is earth, as are its trines (Taurus and Virgo). Virgo is the most purely vaiṣya. Similarly the 10th, 2nd and 6th houses are artha houses.
The fourth sign, Cancer, is the sign at the Sun’s zenith, so it is water, as are its trines (Scorpio and Pisces). Pisces (due to being dual and ruled by Jupiter) is the most purely brāhmaṇa sign. The 4th, 8th, and 12th houses are the mokṣa houses.