24 



♦ KNOWLEDGE ♦ 



[Jan. 9, U 



THE EARTH'S SHAPE AND MOTIONS. 



By Eichard A. Proctor. 



{Contimied from p. 502, Vol. 17.) 



IN nearly all works on astronomy, the Ptolemaic system 

 of the universe is describe d and illustrated. Ju<!ged 

 by the ordinary illustrations, it seems sufficiently simple. 

 We find the earth in the centre, and a number of concen- 

 tric circles, representing the paths of the sun, moon, and 

 planets ; so that the sjs'em appears even simpler than the 

 Copernican, in which the sun is the centre of the planetary 

 motions, while the earth is the centre of the moon'.s motion. 

 But in reality there is no such simplicity in the Ptolemaic 

 system. It need hardly be said that, if the planets really 

 circled around the earth, they would appear to describe 

 circular paths round the heavens, and not the looped or 

 eoDvoluled paths which they are actually seen to traverse. 



What Ptolemy really a'-serted about the planets was 

 difTerent, however. He by no means argued, in the face of 

 the most obvious evidence, that the concentric circular 

 paths seen in his system are the actual paths of the planets. 

 These circles are the paths traversed by imat;inary points 

 round which the planet itself travels in a smaller circle. It 

 is clear that by this conception the looped path of a planet 

 is, to a ceitaiu extent, explained. 



Suppose, far instance, that A B represents part of the 

 path of a moving point, round which a planet is travelling 

 in a circle such as 1, 2, 3, 4, the centre of the point's path 

 being the earth at E. Then it is perfectly 

 obvious that, if the jjlanet travel more quickly 

 in its circle 1, 2, 3, 4, than the point travels 

 along A B, it will appear, when at 1, to travel 

 backwards. When at 2, it will be travelling 

 on its own path directly away from E ; but, as 

 the centre of its motion is continually ad- 

 vancing, it will itself appear to advance at 

 the same rate. At some point between 1 

 and 2 the backward motion must have 

 changed into forward motion, and this point therefore was 

 one of the |)lauet's statknmrij po'uds. At 3, the planet is 

 not only advancing with the moving centre, but with its 

 own more rapid motion round C. Here, then, it seems to 

 advance most rapidly. At 4 it is still advancing, thoiigh 

 its own motion is now in such a direction as not to add 

 to its apparent motion. Then between 4 and 3 comes a 

 stationary point, as between 3 and 2, after which the planet 

 aeema to travel, for a short time, backwards. Next it 

 reaches another stationary point, then advances, and so on 

 continually. 



And, without entering into the special relations presented 

 by the different jdanets, we can .see at onoe that, according 

 to the principles of the Ptolemaic system, the advance.", 

 stations, and retrogressions of the planets can, in a (jenenil 

 way, be fairly accounted for. Further, by giving a suitable 

 inclination to the plane of the smaller ciixle 12 3 4, the 

 looped Ggures of the planets' apparent paths and the various 

 shapes of the loops can be explained : still, however, only 

 in a general way. 



It is clear, however, to begin with, that this system, 

 which requires an imaginary as well as a real centre cf 

 motion for each planet, is far from commending itself by 

 the simpRcity of its character. If we consider it a little 

 farther, and try to conceive the actual path travelled by a 

 single planet, we recognise yet more distinctly the difficul- 

 ties it presents. But to these considerations we mu.st add 

 the fact, that even in Ptolemy's time it did not account for 

 more than the general features of the i)lanetary motions, 

 while, since his day, a number of irregularities have been 



Fig. 1. 



detected, of which each would enforce a new form of com- 

 plication, either in the addition of third, fourth, or fifth 

 smaller circles, or in the displacement of the centres of 

 motion, or in oscillatory motions of the planes in which the 

 planets are supposed to move. It is at once seen, then, that 

 the Ptolemaic system, accepted at (ir»t on account of its 

 apparent simplicity, is one of the most complicated and 

 unnatural explanations of observed peculiarities that could 

 by any possibility have been devised. 



Passing over the Egyptian system, as simply the Ptole- 

 maic deprived of its es.sential unity of character, we come 

 to the Copernican, in which the sun is the centre of the 

 planetary motions, the earth being only a member of the 

 planetary scheme. 



The Copernican, like the Ptolemaic system, is illustrated 

 in every respectable treatise on astronomy, although, in 

 every instance which has yet come under my notice, such 

 illustrations are very badly executed, insomuch that they 

 pain the souls of those who know anything of the real 

 proportions of the planetary scheme. I therefore refer the 

 reader here to the [jictures of the planetary paths which 

 appeared on pp. 310 and 311 of Vol. V. of Knowledge. 

 I have to show how it accounts for the loops in the 

 planetary paths. 



Suppose E c' E' e (Fig. 2) the earth's path round the sun 



at S ; P' P P" the 

 path of a planet 

 outside the earth ; 

 and, further, th.at 

 the earth travels 

 faster than the 

 planet. Then we 

 I'ig- 2. might determine 



all the circumstances of the planet's apparent motion by 

 taking the earth and planet round S, according to their 

 respective rates of motion. But it will be convenient to 

 consider, instead, the varying effects according to the 

 relative situations of the earth and planet. The reader 

 will see at once that the following proof, while much 

 simpler, is not a whit less complete than that obtained by 

 following the motions of both bodies. As I have always 

 found the corresponding explanation given in books on 

 astronomy very little satisfactory to beginners, I have 

 thought it necessary to adopt this simpler one : — 



Consider first the case where the earth i-i as at E, the 

 planet as at P, S E P being a straight line. Since the 

 earth is moving faster away from this line than the planet 

 i.ii, it is clear the planet, as seen from the earth, must 

 appear to lag behind, as though moving towards P' ; sup[)Ose 

 the earth as at E', the planet as at P'; then, as the eaith and 

 planet are moving in opposite dii'ections from the line 

 E' S P, it is obvious that the planet will seem carried 

 forward, or as though moving towards P", with the sum of 

 the effects due to its own and to the earth's motion re- 

 spectively. Hence, at some intermediate positions (placed, 

 it is clear, somewhat as e and e') the planet situated as at 

 P would seem to be at rest. 



Now, both bodies moving at the rates supposed, it is 

 obvious that their relative situations will change through 

 all the arrangements just considered, as the earth, by her 

 more rapid motion, comes again and again into conjunction 

 with the advancing planet (*.«., to a position such as that 

 first considered in the preceding paragraph). Hence, ob- 

 viously, we have, starting from conjunction, the following 

 successive characteristics of the planet's motion : — 



A relatively slow retrogression, gradually diminishing till 

 the planet seems momentarily at rest, then advance, gra- 

 dually increasing, till it attains its maximum, when it is 

 much more rapid than the former retrogradation ; thence 



