Dec. 19, 1884.] 



♦ KNOWLEDGE ♦ 



501 



Te-enter. The circle is continually shifting in position, 

 though always inclined at about the same angle to the circle 

 E E' (Fig. 1). The mode of shifting is very complex. It 

 fnay be thus generally described : — 



N 



Fig. 2. 



Suppose S N S' N' (Fig. 2) the sun's path on the celestial 

 sphere, M N M' N' the moon's path at any moment — by 

 which I mean the path she would follow if she performed 

 a complete circuit without any shifting of her plane of 

 motion. Now the two paths intersect in a line N E N', and 

 this line it is which is continually shifting. Sometimes the 

 end N travels towards S, sometimes towards S' ; but on the 

 whole a motion in the former (or retrograde) direction pre- 

 vails ; and in the course of about nineteen years the line 

 N E N' has shifted completely round in the plane S N S' 

 until it has the same position as at first. 



Here, then, we have another set of facts to explain. 

 Either the moon travels round the eaith, or the earth 

 travels round the moon. 



In considering which view is the more probable, we may 

 fairly take into account the estimates which have been 

 formed respecting the moon's distance and magnitude ; 

 because at a very early epoch astronomers obtained reliable 

 information on this point. It has been proved that the 

 moon is somewhat less than a quarter of a million miles 

 from the earth, and that consequently her apf)arent mag- 

 nitude indicates a real magnitude falling far short of the 

 earth's. Her diameter is, in fact, little more than a quarter 

 of the earth's, and her volume rather more than one- 

 fourteenth. 



So far as the evidence goes, therefore, we are led to 

 recognise a real motion of the moon round the earth as a 

 more satisfactory interpretation of her apparent motion, 

 than a real motion of the eaith around the moon. And as 

 we have as yet decided nothing about the sun's motion, we 

 are led to infer that probably the sun also goes round the 

 earth ; because it seems more reasonable to assume that 

 where two out of three bodies are certainly in motion, the 

 body at rest is the centre of bdli motions. I think it not 

 unlikely that it was from being able to show that the earth 

 is ])robab!y the centre of the moon's motion, that the 

 ancients were led to believe that she is in all probability 

 the centre of the sun's motion also. At any rate, until we 

 get fuither evidence, this is the view suggested by the 

 observed facts. 



It remains to be seen how far the motions of the planets 

 confirm this view. If we had only the sun and moon to 

 deal with, the astronomy of Ptolemy would have no un- 

 satisfactory basis to rest upon, setting aside, of course, the 

 more delicate modes of modern observation, and the facts 

 revealed by them. 



The planets also go round and round the celestial sphere, 

 each in its proper period. If they only travelled round in 

 circles, they would confirm the impression that the earth is 

 the centre of their motion. But from the very commence- 

 ment of astronomical observation, it was observed that the 

 planets follow very peculiar paths. 



Every planet moves, speaking generally, in this wise : — 

 It travels along as if it were about to describe such a circle 

 as the sun or moon describes. But gradually it moves 

 more and more slowly, until at length it stops altogether. 

 Then it retraces its path, first with continually increasing, 

 and then with continually diminishing velocity, until it again 



stops. Then it advances again ; ai d so on continually. 

 The backward motion covering a smaller range than the for- 

 ward motion, the planet advances on the whole — that is, 

 travels in the same direction as the sun. And again, the 

 backward motion not being exactly on the same track as the 

 advancing motion, the path of the planet forms a succession 

 of loops or convolutions. And not only has each planet its 

 own general way of forming loops, but each loop of a planet's 

 path has its own peculiar character. 



Saturn, for instance, forms nearly 30 loops in going 

 once round the celestial sphere, the space between the loops 

 being about equal to the loop itself. Jnpiter makes about 

 11 loops in going once round, the loops being larger than 

 Saturn's, and the space between them larger yet. Mars 

 makes a loop, and one much larger than Jupiter's, then 

 sweeps more than once round the heavens and makes 

 another loop, and so on continually. Venus gnes more 

 than once and a half round the heavens between successive 

 loops. Mercury, however, travels along a looped path 

 more resembling that of the outer planets, making about 

 three loops in going round his circuit. Fig". .3 to 7 show- 

 how these loops vary in shape and size. 



But the successive loops made by the same planet, 

 though exhibiting about the same range, yet vary sin- 

 gularly in figure. The seven figures (Fig. 8, next 

 page), for example, exhibit a set of loops traversed by 

 Jupiter in about half a complete revolution. 



it will easily be seen how, in the other half revolution, 

 the loops change back into the first figure. 



We have in these peculiar motions a problem which must 

 be solved by any theory pretending to exhibit the true 

 character of the scheme formed by the earth, the moon, the 

 sun, and the planets. The ancient astronomers, in forming 

 their theories, recognised this fact in full ; and we must by 

 no means compare the thoughtful and careful way in which 

 they tried to master the problem, imperfect as their results 

 were, with the egregious folly of the modern charlatan, who 

 puts forward theories not in themselves much more imper- 

 fect, but differing altogether in this, that they are not con- 

 structed with even the vaguest reference to the observed 

 celestial motions. 



Let us inquire whether all the complicated loops and 

 convolutions above described admit of being disentangled. 



