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The whole leaf with its tendril, as well as the young upper internodes, revolves vigorously and quickly, though irregularly, and thus sweeps a wide space. The figure traced on a bell-glass was either an irregular spire or a zigzag line. The nearest approach to an ellipse was an elongated figure of 8, with one end a little open, and this was completed in 1 hr. 53 m.
They are the two foci of the ellipse in which moves history; the two shores between which oscillates the tossing tide of humanity. Lord Morley calls them "the two incendiary forces of history, ever shooting jets of flame from undying embers." This explains why the soil of history is so volcanic, so filled with burning lava which time itself has not cooled.
The motion of the earth around the sun is mainly effected in an ellipse, the form of which is liable to vary from the effects of planetary perturbation. These alterations of form are periodic; sometimes the curve, without ceasing to be elliptic, approaches the form of a circle, while at other times it deviates more and more from that form.
If a celestial body, the moon, for example, gravitated solely towards the centre of the earth, it would describe a mathematical ellipse; it would strictly obey the laws of Kepler, or, which is the same thing, the principles of mechanics expounded by Newton in the first sections of his immortal work. Let us now consider the action of a second force.
When I say that the planets go round the sun in circles I am only speaking generally; as a matter of fact, the orbits of the planets are not perfect circles, though some are more circular than others. Instead of this they are as a circle might look if it were pressed in from two sides, and this is called an ellipse.
He had to content himself with the knowledge that it was diminishing at a uniform rate of which indeed a little reflection on a well known law of Dynamics readily convinced him. He had not much difficulty even in explaining the matter to his friends. "Once admitting," said he, "the Projectile to describe an orbit round the Moon, that orbit must of necessity be an ellipse.
But if there were any alteration in the shape or size of the earth's orbit, then that might involve such changes in the distance between the earth and the sun as would possibly afford the desired agent for producing the observed lunar effect. It is known that the earth revolves in an orbit which, though nearly circular, is strictly an ellipse.
Her extremities, which are strongly depressed in the upperworks, and the excessive inclination of her sides, give the boat as a whole a certain resemblance to the rams of our navy, such as the Taureau and Tigre. A transverse section of the Poti approaches an ellipse in shape. Her water lines are exceedingly fine, and, in point of elegance, in no wise cede to those of the most renowned yachts.
To avoid misapprehension, we must remark that Kepler, in one respect, performed a real act of induction; namely, in concluding that because the observed places of Mars were correctly represented by points in an imaginary ellipse, therefore Mars would continue to revolve in that same ellipse; and even in concluding that the position of the planet during the time which intervened between two observations, must have coincided with the intermediate points of the curve.
From it results an apparent displacement of the stars, each of them describing a little ellipse about its true or "mean" position, in a period of nearly nineteen years.
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