These ideas are the exact contrary of the truth. Mathematical, or perhaps as we might better call it, planetary astrology, as we have it to-day, concerns itself with the apparent movements of the planets in the sense that it uses them as its material; just as a child playing in a library might use the books as building blocks, piling, it may be, a book of sermons on a history, and a novel on a mathematical treatise. Astrology does not contribute, has not contributed a single observation, a single demonstration to astronomy. It owes to astronomy all that it knows of mathematical processes and planetary positions. In astronomical language, the calculation of a horoscope is simply the calculation of the "azimuths" of the different planets, and of certain imaginary points on the ecliptic for a given time. This is an astronomical process, carried out according to certain simple formulæ. The calculation of a horoscope is therefore a straightforward business, but, as astrologers all admit, its interpretation is where the skill is required, and no real rules can be given for that. Here is the explanation why the sun and moon are classed together with such relatively insignificant bodies as the other five planets, and are not even ranked as their chief. The ancient astrologer, like the modern, cared nothing for the actual luminary in the heavens; all he cared for was its written symbol on his tablets, and there Sun and Saturn could be looked upon as equal, or Saturn as the greater. It is a rare thing for a modern astrologer to introduce the place of an actual star into a horoscope; the calculations all refer to the positions of the _Signs_ of the Zodiac, which are purely imaginary divisions of the heavens; not to the _Constellations_ of the Zodiac, which are the actual star-groups.