Dictionary of Physics or an Attempt at an Explanation of the Most Important Concepts and Technical Terms of Natural Philosophy

If the angle B is a right angle, and CB : BA is as 10313 : 1, then trigonometry gives the aberration angle ACB = 20 seconds.

If, however, as in Plate I. Fig. 3, CB is inclined toward AB, then ACB is smaller than in the previous case, or, as trigonometry teaches, = 20" multiplied by the sine of the angle CAB. Also, the aberration always shifts the apparent position of the star E toward that region toward which the Earth itself is moving.

Now let Plate I. Fig. 4 be CROH, the Earth's orbit around the sun S, and e a star under the northern latitude eSG; then it will appear in conjunction with the sun S when the Earth is at C, and in opposition when it is at O. In both cases, the light rays eC and eO, falling from e and everywhere parallel to eS, strike the directions of the Earth's orbit at C and O at right angles; therefore, the aberration angle is 20" both times, and is directed westward toward c during conjunction, and eastward toward o during opposition. Therefore, the distance of the two apparent positions c and o must amount to 40".

In the intermediate moments, however, when the star's longitude is different by 90° from the sun's position, i.e., when the Earth is at R and H, the light rays eR and eH falling from e make angles with the direction of the Earth's orbit at R and H which are equal to the star's latitude eSG; therefore, the size of the aberration here is = 20" multiplied by the sine of the star's latitude, directed once toward r and another time toward h, whereby in the first case the latitude is diminished, and in the other increased. The difference of both latitudes at r and h therefore amounts to 40" multiplied by the sine of the latitude. The Earth at C, R, O, H therefore sees the star traverse the ellipse c, r, o, h, whose major axis parallel to the ecliptic co = 40", and the minor axis rh = 40" multiplied by the sine of the latitude.

Thus Arcturus, whose northern latitude amounts to approximately 30 degrees, describes an annual aberration ellipse, th