18 



THE POPULAR ELUCATOB. 



The zodiacal signs are sometimes supposed to have been 

 connected with the rural occupation of the ancients. The cluster 

 of stars among which the sun was passing in spring was called 

 the Earn, because at that time the flocks were sent out into the 

 fields. The Lion, too, has been considered symbolical of the 

 intensity and power of the rays of the summer sun. The 

 Balance tells of the period of equal day and night ; the Scorpion 

 of the unhealthiness of autumn ; while the Waterbearer and the 

 Fishes betoken the rains and floods of winter. 



The names given to these twelve constellations are as fol- 

 lows : Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, 

 Sagittarius, Capricornus, Aquarius, Pisces. Their order may, 

 however, be more easily remembered by the following lines : 

 The Earn, the Bull, the heavenly Twins, 

 And next the Crab the Lion shines, 



The Virgin, and the Scales ; 

 The Scorpion, Archer, and He-Goat, 

 The .Man that bears the Watering Pot, 

 And -Fish with glittering scales. 



Among the most important of the phenomena of the heavens 

 are solar and lunar eclipses, and these of course attracted the 

 attention of early astronomers, and at length the true cause of 

 them was discovered. A careful record also appears to have 

 been kept of them, so that the Saros, or Chaldsean Period, was 

 discovered. This is a period of eighteen years and eleven days, 

 or 223 lunar months, at the expiration of which the moon enters 

 again upon its former track in the heavens, and thus the same 

 eclipses are, as it were, repeated. 



The wonder and anxiety with which these remarkable events 

 were witnessed can easily be imagined, and when the first 

 astronomer ventured to predict an eclipse, and his prediction 

 was found true, he must have been looked upon as little short of 

 divine. The first instance we have on record in which this was 

 actually done is in the year 610 B.C., when Thales, the father of 

 astronomy among the Greeks, foretold an eclipse of the sun. 

 It seems probable, however, that a similar thing had been pre- 

 viously done by the Chaldaeans. 



With Thales begins the true history of astronomy. The 

 Greeks were not, however, distinguished by any great proficiency 

 in the natural sciences. We find here and there shrewd guesses 

 and faint gleams of truth ; but it is always mixed up with 

 fanciful speculations, instead of being supported by careful 

 observation and reasoning. They seem, for the most part, to 

 have started with certain principles (which had no existence 

 except in their imaginations), as, for instance, that the earth 

 must be in the centre of the universe, and that, since the circle 

 was the perfection of shape, all the motions of the heavenly 

 bodies must be in circles. They then observed the phenomena 

 of the sky, and the apparent motions of the sun and stars, and 

 formed cumbrous and complicated systems to try and reconcile 

 these appearances with their theories. 



Hence we find all the involved mysteries of transparent wheels 

 revolving one within the other, and carrying with them the 

 planets and stars, of cycles and epicycles, and of crystal spheres 

 in ceaseless rotation, which the followers of Ptolemy were ever 

 planning and altering. The true law of discovery which is to 

 make accurate observations first, and afterwards start a theory 

 to explain the appearances seems to have been quite lost sight 

 of, and hence confusion prevailed. 



We must, however, just glance at a few of the names which 

 stand prominently forward in the history of the science. 

 Anaxagoras and Pythagoras were two of the Greek philosophers 

 who succeeded Thales, and they appear to have had much more 

 accurate views than most in their day. The truth of the earth's 

 motion round the sun seems to have been realised by them, 

 though it does not appear to have been received by others, and 

 was opposed by those in power as being impious. The former 

 of the two was indeed sentenced to death on account of his 

 philosophical views ; but his sentence was afterwards, through 

 the influence of a friend, commuted into banishment for life. 



The next we notice was the greatest of all the ancient astro- 

 nomers, Hipparchus, who lived in the second century before 

 the Christian era. He gave up all attempts to frame a system 

 for the universe, and occupied himself by carefully watching and 

 recording the motions of the sun and planets. The movements 

 of the sun in particular occupied his persevering attention, and 

 in this way he made a very near approximation to the true 

 length of the year ; and the accuracy of Ma observations is very 



remarkable when we consider the imperfect nature of the instru- 

 ments he had to employ. He also observed the irregularities in 

 the rate of the sun's motion, and determined in what part of its 

 conrse its speed was greatest, and thus ascertained that, if the 

 motion of the sun was uniform, the earth was not situated in 

 the centre of its orbit. 



Another thing for which the name of Hipparchus is memor- 

 able is a catalogue of fixed stars, 

 which he formed in order that future 

 astronomers might be able to detect 

 any alteration in their position or 

 number. He appears to have been 

 led to undertake this task by the ap- 

 pearance of a new star, and though 

 the work of carefully ascertaining and 

 noting the position of each star was, 

 especially with the imperfect instru- 

 ments possessed in his time, a work 

 requiring great labour and patience, 

 he persevered, and completed a list which contained 1081 stars. 

 In the progress of this work he made one very important dis- 

 covery. On comparing the place assigned by him to a star in 

 the constellation Virgo with that determined by some distin- 

 guished astronomers nearly two hundred years previously, he 

 found a difference of two degrees in its longitude. 



He then made similar comparisons, where it was possible, 

 with respect to other stars, and found the same change in their 

 position. It was thus evident that all the stars must have 

 moved forward, or else that the point from which the measure- 

 ments were taken had moved backwards. This phenomenon ia 

 known as the Precession of the Equinoxes, and will be fully 

 explained in its place. The reason of it was discovered by the 

 great Newton. 



Another idea for which we are indebted to Hipparchus was 

 that of representing the positions of the stars on an artificial 

 globe, and of marking the position of places on the terrestrial 

 globe by means of lines of latitude and longitude. 



Nicias, one of the followers of Hipparchus, is said to have 

 gone even further than his master, and started an hypothesis 

 that the apparent changes in the sky were caused by a daily 

 revolution of the earth. The idea, however, was not supported 

 by any arguments, and was lost sight of for ages. 



The only other one of the ancient astronomers we shall refer 

 to in this sketch is Ptolemy, who was a very learned scholar, 

 not only in astronomy, but in mathematics and geography. 

 Having carefully examined the observations of Hipparchus and 

 others, he at length promulgated a system known as the 

 Ptolemaic, which, though since proved to be quite erroneous, 

 accounted so well for all known phenomena that its errors could 

 not, with the instruments then in use, be discovered; and 

 accordingly, it was universally received until the age of 

 Copernicus, and even then it was long before it was entirely 

 given up. 



According to this system, the earth was the centre, with the 

 planets revolving round it in the following order : The Moon, 

 Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and, beyond all, 

 the fixed stars. To account for the apparent irregularities in 

 their motions, he introduced what he termed epicycles, which 

 will be understood by reference to Fig. 1. E represents the 

 earth, and ABC the orbit in which the planet should move ; 

 but, instead of this, he supposed that there was a point c 

 moving in this orbit, and that the planet p moved round this 

 point in a small circular orbit or epicycle. The combination of 

 these two motions explained the irregularities. This system 

 was afterwards rendered much more complicated by the altera- 

 tions introduced by his successors. 



LESSONS IN ALGEBRA. XIV. 



SIMPLE EQUATIONS. 



151. MOST of the investigations in algebra are carried on 'by 

 means of equations. In the solution of problems, for example, 

 we represent the uriknoivn quantity, or numbers sought, by a 

 certain letter ; and then, in order to ascertain the value of this 

 unknown quantity or letter, we form an algebraic expression from 

 the conditions of the question, which is equal to some given 

 quantity or number. 



