ellipses. Another important thing made out was this: that the planets describing these ellipses move with very different velocities at different times. Each planet, when in that part of its orbit which is nearest to the sun, travels quickly, and when in that part which is furthest from the sun, travels slowly. The way in which he expressed the law of motion is this: if in one part of the orbit I draw two lines SK, SL, from the sun, inclosing a certain space, (when I say "inclosing a certain space," I mean inclosing a superficial area, containing a certain number of acres, or of squares miles,) and if in another part of the orbit I draw two lines Sk, Sl, and if the two lines Sk, Sl, inclose the same number of acres as are inclosed by SK, SL, then the planet will be just as long moving over the long arc KL, as in moving over the short arc kl. From that law of equal areas in equal times, you will see that the planet is moving much more rapidly between K and L, than between k and l.
Having spoken so much of the motion in an ellipse, I will now proceed to speak of the cause of that motion; the force of the sun's attraction, which acts upon every planet. We are now coming to a thing totally different from what we have had before. We have spoken of the form of the orbits of planets, and the proportion of their speed in the different parts of their orbits, as determined from the observation of the planets; and I will now proceed to the consideration of the causes of these motions, in reference to the mechanical theory first propounded by Sir Isaac Newton, and received by every person who possesses a competent acquaintance with the subject. The theory is this: that if we suppose the planets to be once set in motion, (by some cause which we do not pretend to know,) then the attraction of the sun
