tion to that which results from the combination of the movements of the spheres belonging to the former system; and thus he conceives that the movement of each planet would be vitiated by that of the next exterior planet; in order, therefore, to counteract this effect he proposes that, on the exterior of the system of spheres belonging to each planet, except Saturn, which being the most remote is not affected by any thing beyond it, there should be another system producing, by the combination of its movements, a motion equal and contrary to that produced by the next exterior system; thus destroying the latter motion and permitting the next interior planet to be moved only by the action of its own system of spheres. The spheres, therefore, which belong to each planet are distinguished by Aristotle into deferents, which are those communicating motion to the planet as in the system of Calippus, and restituents, which are those employed to counteract the effect of the former on the spheres of the next inferior planet; and he observes that the number of the latter which are to be assigned to each planet must always be one less than the number of deferents, probably because the velocity of the sphere producing the diurnal motion in each planet was the same as that of the sphere of the fixed stars, and therefore no counteraction to that movement might be thought necessary. The number of restituents was supposed equal to twenty-two, and hence, that of the spheres of both kinds, including the sphere of the fixed stars, was fifty-five. The opinions of the ancients concerning the sphere of the fixed stars, or, as it was commonly called, the eighth sphere, so frequently alluded to in their writings, are very imperfectly known; there is no doubt that, originally, it was supposed to be material and that the stars were imagined to be attached to its interior surface; but a more philosophical sentiment is expressed by Geminus", who treats the above as a vulgar error; he observes that some stars are much further from us than others, and alleges, as the reason why we are not sensible of the fact, that the eye cannot judge of distances in directions tending from it. In the Somnium Scipionis, Cicero, with whom Geminus was probably eontemporary, supposes the spectator to be situated in the Via Lactea,

⚫ De Apparentiis Cœlestibus.

1

from whence, he says, may be seen stars which are not visible from the earth; which seems to shew either that the eighth sphere was thought to be ideal, or that, if material, its thickness was considered of immense extent.

a

In the age of Aristotle was made the first recorded observation of the sun; and, from it, we derive a proof that the Greek astronomy must then have penetrated beyond the Alps. Pytheas, an astronomer of Marseilles, is said by Strabo to have set up in that city a gnomon and, at the noon of the day of the summer-solstice, to have found that the length of the shadow it cast was to the height of the gnomon itself in the proportion of 41 to 120; and, as the extremity of the shadow of an upright pillar is formed by the rays emanating from the upper limb of the sun, it follows that the observed zenith distance of that part of the sun's disc must have been 19° 12′ 18′′; therefore, correcting this observation on account of the refraction of the atmosphere, for the apparent semi-diameter of the sun and, assuming the latitude of Marseilles to be, as is now known, equal to 43° 17′ 43′′ north, it can easily be shewn that the obliquity of the ecliptic to the equator must, in those days, have amounted to 23° 49′ 18′′; a determination of considerable importance because, by comparison with others subsequently made, the progressive diminution of the inclination of those circles to each other has been proved. Strabo, we must however observe, alleges that Hipparchus, on the authority of Pytheas, considered the length of the shadow to be the same both at Marseilles and Byzantium; but the latitude of this last place is less than that of the former by about 2 degrees, therefore the observations made at one or both of these places must have been very erroneous; and if it were not that the obliquity of the ecliptic, determined by the length of the shadow at Marseilles, coincides nearly with that deduced from the rate of diminution which results from a comparison of later observations, little stress would be laid upon this determination in support of the fact that the inclination of the circles has changed. Pytheas is said to have made a voyage to the Ultima Thule (Iceland), where he saw the sun touch the northern side of the horizon on the day of the summer-solstice when at the Geographiæ, Lib. II.

b

a

b Ibid.

lowest point of his diurnal course; a phenomenon which must have been considered as deciding the question of the earth's rotundity, if any doubt at that time existed concerning the fact.

In this age the influence of the moon upon the waters of the ocean appears to have been observed; for Plutarch expressly states that Pytheas of Marseilles imagined the increase of the moon to be accompanied by the rising of the tides, and her wane, by their falling: it is, also, probable that the Greeks were, then, or soon afterwards, aware of the differences produced in the elevation of the waters by the union or contrariety of the actions of the sun and moon; since, according to Strabo, Posidonius describes, in the following manner, the diurnal, the monthly and the annual tides. Speaking of the first, he says, the ocean continues to rise from the time the moon is one sign above the eastern side of the horizon till that of her arrival on the meridian, and to descend from this time till she is near the western side; in like manner, it again rises till the moon is on the meridian below the pole and, subsequently, falls till she has returned to the east. Of the second, he observes that the tides are said to be extraordinarily high at the time of new and full moon, that is, at her conjunction and opposition with the sun, and extraordinarily low when the luminaries are in quadrature; such are, in fact, those we call spring and neap tides. With respect to the third kind, he says, it is found that the tides are the highest when the new and full moons occur at the times of the equinoxes; and similar descriptions of the tides are given by Seneca and Pliny. In earlier times the wildest notions seem to have been entertained concerning these phenomena. Pomponius Mela says it was the opinion of some Pythagoreans that the earth was a living animal, and that the flowing and ebbing of the sea were caused by the emission and inspiration of its breath; but it is easy to perceive that this could have been nothing more than a figure of speech. Plato, in his dialogue Timæus, makes the tides depend upon the greater or smaller quantity of water which flows, from the mountains of Gaul, into the Atlantic ocean: and Seleucus ascribes them to a contrariety in the directions of the movements of the earth and moon, by which the air, being compressed bea De Placitis, Lib. III. cap. 17. Geograph. Lib. III. Geograph.

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tween them, falls on the Atlantic and agitates it with a reciprocating motion. A similar action on the waters is supposed by Aristotle who, however, refers the cause to the sun which, he observes, moves the atmosphere and carries it about the earth; thereby causing the ocean, alternately, to advance, and recede from, the shores.

CHAPTER X.

ASTRONOMICAL WORKS OF THE EARLIEST GREEK OBSERVERS.

Formation of the Alexandrian school. The geometrical and astronomical works of Euclid. The works of Autolycus-of Aratus.-Observations made by Aristyllus and Timocharis.-The obliquity of the ecliptic and the magnitude of the earth determined by Eratosthenes. His opinion concerning the motion of the earth.-Method employed by Archimedes for measuring the sun's visible diameter.--Method of finding the parallaxes of the sun and moon.—The systems of eccentric orbits, and of concentric orbits with epicycles. The various motions of a planet in a simple eccentric orbit explained. -The motion in an epicycle explained.--Nature of the planetary revolutions in the system of epicycles.

•

WE hear nothing of the Grecian schools after the time of Aristotle, and those Europeans who sought to acquire a knowledge of the sciences, particularly of astronomy, again repaired, for that purpose, to Egypt. The Academia and the Stoa were, probably, still frequented by the youth of Athens to hear the lectures of those who filled the chairs of Plato and Zeno, but the successors of these philosophers seem not to have deviated from the path they had formed, nor to have added to their discoveries any thing worthy of preservation. The decay of science in Greece was, probably, caused by the unsettled state of that country after the death of Alexander; and its revival in Egypt is to be ascribed to the patronage accorded to learned men by the sovereigns who were seated on the throne of the Pharaohs. After the conquest of Egypt, Alexander employed the abilities of Dinocrates in a work more useful than that of cutting Mount Athos into the figure of a man, which the artist had proposed to execute, for he appointed him to superintend the building, near one of the mouths of the Nile, of a city which was to be called by his name, and was, afterwards, to become so famous in the history of the sciences. Here the second Ptolemy, who ruled the African portion of his conquests, established a school which, from the talents of the persons connected with it, was honoured with the epithet Divine: and among these philosophers were some who are distinguished by being the first to