Publisher's Synopsis
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1858 edition. Excerpt: ...with it and remained constant in it, and if the planet had continued to move in its old circular track, the velocity would still have been uniform, and thus its radius or line drawn from its own centre to the centre of revolution would still have described equal sectors in equal times. But according to the first principle of planetary motion, the excess of tangential over the gravitating force has necessarily given to its course an elliptical orbit of more or less eccentricity, and thus its rate of movement must be variable through all portions of its revolution. This excess of tangential force must, however, exactly balance itself against the'gravitating force in the resulting eccentricity of the orbit, and the whole periodic tune of revolution must be the same as that of its last rotation in the circumference of the sphere before its ejection. That rotation was in a complete circle, and the radii all described equal sectors in equal times. The radius which the planet now carries with it, or the line from its occupied focus to its own centre, called the radius vector, continually lengthens itself in the passage from the inferior to the superior apsis, in the exact proportion inversely as the velocity diminishes; and then again contracts itself in the passage from the superior to the inferior apsis, in its opposite semi-revolution, in the exact proportion inversely as the velocity increases. What is gained in the extent of the radius vector is exactly compensated in the retardation of the movement, and what on the other side of the orbit is lost in the contraction of the radius vector is also exactly compensated in the acceleration of the movement, and the whole periodic time of revolution is the same in the planetary ellipse as it was in...