246

NOTES TO BOOK III.

(G.) p. 230. 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 6 the Anomaly of the moon reckoned from her Perigee, the Evection is equal to 1o.3.sin (2a − b). At New and Full Moon, a is 0 or 180°, and thus the Evection is 1o. 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 center is at all points of her orbit equal to 6o. 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 6 - 1o.3.sin b, or 5o. sin b and as they took this for the moon's equation of the center, which depends upon the excentricity of the moon's orbit, we obtain from this too small equation of the center, an excentricity 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 excentricity 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 excentricity of the Moon's orbit is variable, which is not the case.

(H.) p. 232. The Equation of the Center is the difference between the place of the Planet in its elliptical orbit, and that place which a Planet would have, which revolved uniformly round the Sun as a center in a circular orbit in the same time. An imaginary Planet moving in the manner last described, is called the mean Planet, while the actual Planet which moves in the ellipse is called the true Planet. The Longitude of the mean Planet at a given time is easily found, because its motion is uniform. By adding to it the Equation of the Center, we find the Longitude of the true Planet, and thus, its place in its orbit.-Littrow's Note.

I may add that the word Equation, used in such cases, denotes in general a quantity which must be added to or subtracted from a mean quantity, to make it equal to the true quantity or rather, a quantity which must be added to or subtracted from a variably increasing quantity, to make it increase equably.

(1.) p. 233. The alteration of the apparent diameter of the moon is so great that it cannot escape us, even with very moderate instruments. This apparent diameter contains, when the moon is nearest the earth, 2010 seconds, when she is farthest off, 1762 seconds; that is, 248 seconds; or 4 minutes 8 seconds, less than in the former case. [The two quantities are in the proportion of 8 to 7, nearly]-Littrow's Note.

(J.) p. 235. Ptolemy determined the Radius and the Periodic Time of his two circles for each Planet in the following manner : For the inferior Planets, that is, Mercury and Venus, he took the Radius of the Deferent equal to the Radius of the Earth's orbit, and the Radius of the Epicycle equal to that of the Planet's orbit. For

these Planets, according to his assumption, the Periodic Time of the Planet in its Epicycle was to the Periodic Time of the Epicyclical Center on the Deferent, as the synodical Revolution of the Planet to the tropical Revolution of the Earth above the Sun. For the three superior Planets, Mars, Jupiter, and Saturn, the Radius of the Deferent was equal to the Radius of the Planet's orbit, and the Radius of the Epicycle was equal to the Radius of the Earth's orbit; the Periodic Time of the Planet in its Epicycle was to the Periodic Time of the Epicyclical Center on the Deferent, as the synodical Revolution of the Planet to the tropical Revolution of the same Planet.

Ptolemy might obviously have made the geometrical motions of all the Planets correspond with the observations by one of these two modes of construction; but he appears to have adopted this double form of the theory, in order that in the inferior, as well as in the superior Planets, he might give the smaller of the two Radii to the Epicycle: that is, in order that he might make the smaller circle move round the larger, not vice versâ.— Littrow's Note.

BOOK IV.

HISTORY

OF

PHYSICAL SCIENCE IN THE MIDDLE AGES;

OR,

VIEW OF THE STATIONARY PERIOD OF

INDUCTIVE SCIENCE.

As one by one, at dread Medea's strain,
The sickening stars fade off th' ethereal plain;
As Argus' eyes, by Hermes' wand opprest,
Closed one by one to everlasting rest;
Thus at her felt approach and secret might,
Art after art goes out, and all is night.
See skulking Truth to her old cavern fled,
Mountains of casuistry heaped on her head;
Philosophy, that reached the heavens before,
Shrinks to her hidden cause, and is no more.
Physic of Metaphysic begs defence,
And Metaphysic calls for aid to Sense:
See Mystery to Mathematics fly!

In vain! they gaze, turn giddy, rave, and die.

Dunciad, B. iv.