Aug. 22, 1884.] 



♦ KNO\VLEDGE ♦ 



151 



noticed is, that every star in the heavens obeys the law of 

 uniform rotation round the axis F G, precisely as the sun 

 and moon had been observed to do. 



This is indeed a most imiiortant discovery ; and will be 

 found, when we come to examine it, to be full of sig- 

 nificance. 



In the first place it is to be noted that if the stars were 

 bright points on the inner surface of a vast sjihere rotating 

 uniformly around the earth, their motions would be pre- 

 cisely such as we have thus seen them to be. So that the 

 notion entertained of old by Anaxagoras and his followers 

 — that the stars are the heads of nails driven into the con- 

 cave of a vast dome — however bizarre it may seem in the 

 light of modern science, was founded at any rate on an 

 observed relation. 



Another notion, somewhat less fanciful, was equally 

 consistent with observed appearances. If a vast spherical 

 crystal shell surrounded the earth, and the stars were 

 bright points fixed within the substance of this crystalline 

 dome, but not necessarily at the same distance from the 

 observer, then the observed diurnal motion of the stars 

 would be accurately reproduced by the rotation of the 

 crystalline shell about a fixed axis through its centre. 



Let us carefully consider the points thus suggested. 

 Let us take the case of one of those stars which never set. 



Fig 



Suppose E (Fig. 1) to be a part of the earth's surface 

 (we are supposed to know nothing as yet of the shape of 

 the earth), and let A C B repre.-ient the imaginary dome of 

 the heavens on which the stars seem to move. Let P 

 be the point to which the axis of our instrument (F G, 

 in Fig. 5 to Chapter I.) was directed throughout our 

 observations. Further, let C D be the apparent path of a 

 star. 



Now our observations showed us the star going round 

 and round in the circle D, at a perfectly uniform rate. 

 When we saw the star in direction O C, the star must 

 have been somewhere along that line (produced if 

 necessary). Suppose the star was at S. Now where was 

 the star when it seemed to be at other parts of the circle 

 C D ■? The line of sight went round and round P, 

 uniformly and keeping always inclined at the same angle 

 to O P. It therefore described a conical surface of which 

 O P was the axis. Now if our star travelled in S S', a 

 circular section of this cone, then the star motion really was 

 as equable ai it seemed, and the fixed axis O P (produced) 

 passed through the centre of the star's motion at F. But 

 if our star travelled in any other section (necessarily non- 

 circular) as S s, then its motion was not equable, but 

 obviously was slowest at S and swiftest at s. Also the 

 fixed axis O P did not in this second case pass through the 

 centre of the star's path, but through an eccentric point Q. 



We fee that the path S S' explains observed appearances 

 simply, while the path S s requires altogether artificial 

 assumptions of varying motion around an eccentric axis. 



But this is only a small part of the difficulties in which 

 we become involved if we give to a star a diurnal motion 



(relatively to the earth) in any other but a circular path 

 around the axis O P. The path S a- lies wholly above the 

 plane of the earth's surface at E where the observer is sup- 

 posed to stand, and, in fact, I have made the oval S s 

 parallel to A B, because that is the sort of path by which 

 one of the paradoxists explains the diurnal celestial motions. 

 When, however, we take the case of a star which rises and 

 sets, we get a cone corresponding to S E S', but having part 

 of its surface below the plane A B ; so that we have to con- 

 ceive an oval path quite diflferent to S s, not only as regards 

 shape and centring, but in position also. 



Even this, however, is not all. When we take the case 

 of a star which rises due east and sets due west, the coue 

 corresponding to S E S' becomes a plane. We have, in 

 fact, the case illustrated in Fig. 2, where eOtv represents 



Fig. 2. 



the apparent path of such a star on the heavens. Now, in 

 this case, if the true path of the star (relatively to the 

 observer at E) is not a circle (as that of which S A S' is the 

 half), uniformly described, it must either be some other 

 curve s A s' in the same plane, not uniformly described, or 

 if it belong to some other plane as vxll as the plane e C w, 

 it must be a straight line as ^i A S'. For it cannot by any 

 possibility lie out of the plane e C w, since the line of sight 

 from E to the star is observed always to lie in that plane ; 

 therefore, if it belongs to another plane also, it must be on 

 the intersection of two planes ; and we know that two 

 planes can only intersect on a straight line.* 



When we see that so many artificial and incongruous 

 assumptions have to be made if the a]i[iarent motions of 

 the stars are to be explained in any other way, we can no 

 longer feel any doubt that the simple explanation sug- 

 gested by our observations is the correct one. We con- 

 clude, therefore, that the motions of all stars relatively to 

 the earth, take place uniformly in circles having one line 

 (EP of Fig. 1) as common axis. 



As yet, however, we do not know whether the celestial 

 sphere, carrying all its stars with it, rotates around the 

 earth on this axis, or whether the earth rotates within the 

 celestial sphere, on an axial line in the same direction. We 

 must make excursions over the earth's surface to determine 

 what the figure of the earth may be, before we can form a 

 probable opinion on this point. And before we can feel 

 abselutely certain we shall need yet other observations. 



But first it will be necessary to somewhat extend our 



* It may be noticed in passing that the snn's course when he 

 rises dne east is so very nearly coincident with the conrse of a star 

 so rising, that the account just given is true appreciably for the sun 

 also ; so that if the sun really were travelling parallel to the earth's 

 surface as conceived by one of the paradoxists, he would on Marcli 

 22 or Sept. 23 (when he rises due east) be travelling in a straight 

 line as 2 A S' with a variable velocity saving its least value when 

 he was at A. How he should ever come back again after going off 

 in the direction A S', until by the enormity of his distance he ap- 

 peared close to the horizon (though, strangely enough, looking 

 appreciably undiminished), we may leave to be settled by those 

 who have flattened the earth. 



