said before about the curvature of the orbit, and examine the subject for yourselves, you will see that it must be so. The moon I will suppose is travelling from M"" to M'. All this time the sun is attracting her more than the earth, and therefore increasing her velocity till she reaches M'. When she is passing from M' to M" the sun is pulling her back, and her velocity is diminished till she reaches M". From this point her velocity increases again till she reaches M'", and then diminishes again till she reaches M"". Therefore, when the moon is nearest to the sun, and furthest from the sun, she is moving with the greatest velocity; when she is at those parts of her orbit at which her distance from the sun is equal to the earth's distance from the sun, she is moving with the least velocity. I mentioned in a former lecture (see page 106) that the curvature of the orbit depends on two considerations: one is the velocity; and the greater the velocity is, the less the orbit will be curved: the other is the force; and the less the force is, the less the orbit will be curved. The consequence is this: that as the velocity is greatest at M' and M'", and the force directed to the earth is least (because the sun's disturbing force there diminishes the earth's attraction,) the orbit must be the least curved there. At M" and M"" the velocity has been considerably diminished; the force which draws the moon towards the earth is greatest there (because the sun's disturbing force there increases the earth's attraction), and therefore the orbit must be most curved there. The only way of reconciling these conclusions is by saying that the orbit is lengthened in the direction M" M""; a conclusion opposite to what we should have supposed if we had not investigated closely this remarkable phenomenon. It will easily be understood that
