brightness to be nearer than the other. It is, for example, evident that if, in the figure, e, e' represent two positions of the earth in its path round the sun, and a, b two stars at different distances, but nearly in the same direction, then to the observer at e the star a appears to the left of b, whereas six months afterwards, when the observer is at e', a appears to the right of b. Such a motion of one star with respect to another close to it would be much more easily observed than an alteration of the same amount in the distance of the star from some standard point such as the pole. Salviati points out that accurate observations of
this kind had not been made, and that the telescope might be of assistance for the purpose. This method, known as the double-star or differential method of parallax, was in fact the first to—lead two centuries later—to a successful detection of the motion in question (chapter xiii., § 278).
130. Entirely new ground is broken in the Dialogue when Galilei's discoveries of the laws of motion of bodies are applied to the problem of the earth's motion. His great discovery, which threw an entirely new light on the mechanics of the solar system, was substantially the law afterwards given by Newton as the first of his three laws of motion, in the form: Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force applied to it to change that state. Putting aside for the present any discussion of force, a conception first made really definite by Newton, and only imperfectly grasped by Galilei, we may interpret this law as meaning that a body has no more inherent tendency to diminish its motion or to stop than it has to increase its motion or to start, and that any alteration in either the speed or the direction of a body's motion is to be explained by the action on it of some other body, or at any rate by
