Galileo's announcement, published in September, 1610, when only a slight flattening of the planet's disk was visible, received absolute confirmation in the ensuing months, as she completed her full half-circle of change on February 24th of the following year, and consequently exhibited herself to him in all her varying aspects. It was the first time they had been looked upon by a human eye, since its unaided powers do not enable it to discern them, although one exception to this rule is said to have existed. This was the case of the Swiss mathematician Gauss, who, when a child, on being shown the crescent star through the telescope, exclaimed to his mother that it "was turned wrong"; the inference being that he recognized the reversal of the image in the field of the glass. If it were indeed so, he deserves to rank with the Siberian savage, who described the eclipses, or Jupiter's satellites; or the shoemaker of Breslau, who could see and declare the positions of those minute orbs. The phases exhibited to us by Venus are due to her moving in an orbit within that of the earth, at one side of which she is between us and the sun, while at the other this position is exactly reversed. We may compare her to a performer in a great celestial circus, lit by a central chandelier, and ourselves to spectators in an external ring, from which we see her at one time facing us with the light full on her, at the opposite point in complete shadow, and at the intermediate ones in varying degrees of illumination according to our changing views of her. The same illustration may serve to show why Venus is brightest, not when full, since she is then beyond the sun, and at the farthest possible point from us, but when she approaches us at inferior conjunction, more nearly by over one hundred and thirty million miles, and still shows us a crescent of her illuminated surface, before passing into the last phase of total obscuration. When actually nearest to us she is absolutely invisible, being then, like the new moon, between us and the sun. Her varying degrees of brilliancy, even when in the same phase, are thus accounted for by her alternate retreat from and advance towards us as she circles round the sun. Completing, as she does, her revolution in about seven months and a half, she would of course go through the whole series of her metamorphoses in that time, were the earth, from which we observe them, a fixed point. Their protraction instead, over a term of five hundred and eighty-four days, or more than nineteen months, is due to the simultaneous motion of the earth in the same direction, over her larger orbit in a longer period, causing the same relative position of the sister planet to recur only as often as she overtakes her in her career. Thus the hour and minute hands of a watch, moving at different rates of speed after meeting on the dial plate at twelve o'clock, will not again come together until five minutes past one, when the swifter