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 light and the direction of the motion of the æther at the point considered is taken for the plane $$x z$$. Now, in consequence of the motion of the æther, the direction of the light in space will deviate from the normal to the wave through the angle $$\tfrac{u_{2}}{V}$$ in the contrary direction, as may be very easily shown (see Phil. Mag. for February 1846, p. 78). Hence the direction of the light coming from a star is the same as that of a right line drawn from the star, not merely at such a distance from the earth that the motion of the æther is there insensible, and again close to the surface of the earth, where the æther may be supposed to move with the earth, but throughout the whole course of the light; so that a ray of light will proceed in a straight line even when the æther is in motion, provided the motion be such as to render (a.) an exact differential. The orthogonal trajectory represented in fig. 2 of my paper of July, must not be confounded with the path of a ray of light. In that paper I supposed that the æther close to the surface of the earth was at rest relatively to the earth; in fact, the very object of the paper was to get rid of the apparent necessity of supposing the æther to pass through the whole atmosphere and through the earth itself. It should be observed, however, that the phænomenon of aberration allows us to suppose that the æther passes through the atmosphere and through the earth with any velocity, either constant, or varying from point to point, provided only (a.) be an exact differential.

P.S. I take this opportunity of adding a few words on the subject of Prof. Challis's last communication. There is nothing so far as I can make out in which we differ, except the sense in which we use the expression explaining a phænomenon from certain causes. According to my use of the term, a person would be said to explain a phænomenon when he has shown that certain causes being assumed, the phænomenon would necessarily follow. In this sense we explain the formation of images in common optics, assuming the properties of rays. We are able to show what must be the form, &c. of the image. In this sense Prof. Challis has not explained aberration by assuming merely the motion of the earth and the velocity of light, since, for aught that appears from his reasoning, a star might be displaced through double the angle through which it is observed to be displaced. It was for this reason, that in order to allow that Prof. Challis had explained aberration, I attached, in a former communication, a peculiar meaning to the word aberration.