416 LECTURE XLIV. 



The proper motions of the fixed stars, as they are subjected to our 

 observation, undergo two modifications ; the one from the relative direc- 

 tion of the motion, by which it may be more or less concealed from our 

 view ; the other from the proper motion of the sun, and the planets attend- 

 ing him. This motion has indeed only been inferred from the apparent 

 motions of a great number of stars, which are either partly or totally 

 referrible to it, and which could scarcely have agreed so correctly as they 

 do, if they had arisen from the real and separate motion of each star. 



Among the motions of the primary planets, that of the earth itself 

 requires a principal share of our attention. The apparent places or the 

 fixed stars are not sensibly affected by the earth's annual revolution : if 

 any of them had been considerably less remote than they are, it is probable 

 that this motion would have occasioned a sensible annual parallax, or a 

 change of their relative situation, according to the earth's place in its orbit 

 round the sun ; for if this orbit, viewed from any of the stars, subtended an 

 angle even of a single second, the place of that star might be observed to 

 vary a second at different times of the year. Dr. Hooke supposed at one 

 time that he had discovered such a parallax, but later observations have 

 not confirmed those of Dr. Hooke. The stars have, however, a small aberra- 

 tion, in consequence of the progressive motion of the earth in its orbit, 

 combined with the limited velocity of light ; and the standard of com- 

 parison being the earth's axis, its nutation must also in some degree affect 

 the apparent places of the stars. It was in endeavouring to ascertain the 

 annual parallax, that Dr. Bradley discovered both the aberration of light 

 and the nutation of the earth's axis. 



The revolution of the earth, in its orbit round the sun, produces the 

 apparent motion of the sun among the stars, by which he describes his 

 annual path in the ecliptic, with an apparent angular velocity equal to the 

 angular velocity of the earth, which varies considerably at various times. 

 It required some investigation of the magnitudes and distances of the hea- 

 venly bodies, to be convinced that the sun and stars had not in reality the 

 motion which a superficial inspection of the heavens would naturally lead 

 a spectator to attribute to them ; but it is at present perfectly unnecessary 

 to enter into arguments to prove that the true cause of these apparent 

 motions is the real motion of the earth. The effect of the earth's annual 

 revolution is the change of place of the sun among the fixed stars : it is 

 obvious that the sun will always appear, when viewed from the earth, in 

 a place diametrically opposite to that in which the earth would appear, if 

 seen from the sun : consequently, since the earth and sun remain in the 

 same plane, the apparent path of the sun will mark the same circle among 

 the stars as the earth would appear to describe, if viewed from the sun, 

 that is, the ecliptic. If the light of the stars were much stronger, or that 

 of the sun much weaker, we might see him pass by the stars in each part 

 of the ecliptic, as we do the moon ; but we are now obliged to observe 

 what stars are in turn diametrically opposite to the sun, or at certain dis- 

 tances from him, and thus we obtain a correct knowledge of his path. 



The sun's apparent diameter is larger by one thirtieth in January than 

 in June ; of course the earth is so much nearer to the sun in winter than 



