Note 110 — Chapter IV · Sequel to the Inductive Epoch of Hipparchus.

I will insert here the explanation which my German translator, the late distinguished astronomer Littrow, has given of this point. The Rule of this Inequality, the Evection, may be most simply expressed thus. If a denote the excess of the Moon’s Longitude over the Sun’s, and b the Anomaly of the Moon reckoned from her Perigee, the Evection is equal to 1°. 3.sin (2a − b). At New and Full Moon, a is 0 or 180°, and thus the Evection is − 1°.3.sin b. At both quarters, or dichotomies, a is 90° or 270°, and consequently the Evection is + 1°.3.sin b. The Moon’s Elliptical Equation of the centre is at all points of her orbit equal to 6°.3.sin b. The Greek Astronomers before Ptolemy observed the moon only at the time of eclipses; and hence they necessarily found for the sum of these two greatest inequalities of the moon’s motion the quantity 6°.3.sin b − 1°.3.sin b, or 5°.sin b: and as they took this for the moon’s equation of the centre, which depends upon the eccentricity of the moon’s orbit, we obtain from this too small equation of the centre, an eccentricity also smaller than the truth. Ptolemy, who first observed the moon in her quarters, found for the sum of those Inequalities at those points the quantity 6°.3.sin b + 1°.3.sin b, or 7°.6.sin b; and thus made the eccentricity of the moon as much too great at the quarters as the observers of eclipses had made it too small. He hence concluded that the eccentricity of the Moon’s orbit is variable, which is not the case.