330 POPULAR SCIENCE MONTHLY. 



It is to be noted that either of these explanations will completely ac- 

 count for all the observed phenomena. 



New moon occurs when the earth, moon and sun are in a straight line. At 

 sunset the new moon is seen in the west. After 27 days the moon has made 

 one circuit among the stars, moving from west to east. But in those 27 days 

 the sun has likewise moved eastwardly, about 27 degrees. The moon, then, has 

 to make one circuit and a little more in order to be again in the line joining the 

 earth and sun, in order to be again ' new.' The time from one new moon to the 

 next — the lunar month — is about 29^2 days (more exactly 29d 12h 55m 2s.9) 

 for this reason. Just as there is a difference between the moon's sidereal and 

 synodic period, so there is a corresponding difference between the sidereal and 

 tropical year, because the equinoctial points are in motion relatively to the stars. 



The Superior Planets. — In the system of Ptolemy, Mars, Jupiter 

 and Saturn were supposed to be further from the earth than the sun — 

 to be above it — and they were, therefore, called superior planets ; while 

 Mercury and Venus were called inferior planets. The facts of ob- 

 servations for one of the superior planets, for Mars, for example, are 

 as follows. If on any day Mars rises at the same time as Sirius, on 

 the next day it will rise a little later, and so on. The planet, there- 

 fore, moves eastwardly among the stars. It continues its motion so 

 that at the end of 687 days (1.88 years) the planet again rises at the 

 same time as Sirius. It has therefore made a complete circuit of the 

 sky (from one star back to the same star again) in a little less than 

 two years. Its orbit was supposed by Ptolemy to be a circle (the 

 deferent) about the earth like the sun's orbit. In like manner Jupiter 

 makes a revolution in 4,333 days (11.86 years), and Saturn in 10,759 

 days (29.46 years). Such are the general motions of the three su- 

 perior planets; but there are irregularities in their motions that must 

 be accounted for. 



For example, the actual motion of the planet Jupiter among the 

 stars for the year 1897 is as follows: Beginning on October 28, 1897, 

 the planet's motion is eastwards until January 22, 1898; here it turns 

 and moves westwards until May 28; here, again, it turns and moves 

 eastwards and its direct motion continues for the rest of its period of 

 nearly twelve years. Ptolemy accounted for the irregularities of mo- 

 tion just described by supposing that Jupiter revolved in a small 

 circular orbit — the epicycle — once in 365 days, while, at the same time, 

 the center of the epicycle moved along the circumference of the def- 

 erent circle, making a complete revolution in about twelve years. 



As time elapses the center of Jupiter's epicycle will move onwards 

 on the deferent while Jupiter will move onwards in its epicycle. 

 The combination of these two motions will produce a direct motion 

 of the planet. After Jupiter has moved through a quarter of a cir- 

 cumference on its epicycle the planet will appear to the observer on 

 the earth to move in a retrograde direction, because it will move 

 to the right or left on its epicycle faster than the center of the 



