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Indeed, it is often the case that the illustration is made clearer by exaggerating some of these and reducing others; thus, for example, the causes of the variation in the lengths of the days and nights, and of the changes in the seasons, can be exhibited to much better advantage by an apparatus in which the diameter of the sun and its distance from the earth are enormously reduced than they possibly could be were they of their proper proportionate magnitudes; nor is the presence of any other planet, or the attendance of a satellite, at all necessary or even desirable for the purpose named.

"The compound minerals or aggregate substances composing the earth, the relations which constituent masses hold to each other, the magnitudes, distances, and revolution of the celestial bodies, are of no real importance.... Material substances, astronomical calculations, and all the paraphernalia of speculative theories ... will ultimately vanish, swallowed up in the infinite calculus of spirit."

Now, the choice of the variable magnitudes, the distribution of nature into objects and into facts, has already something of the contingent and the conventional.

The magnitudes of the components of gamma are four and four and a half, or, according to Hall, both four; distance 8.5", p. 180°. A few degrees above gamma, passing by beta, is a wide double lambda, magnitudes five and eight, distance 37", p. 45°, colors white and lilac or violet.

Having got closer to immensity than their fellow-creatures, they saw at once its beauty and its frightfulness. They more and more felt the contrast between their own tiny magnitudes and those among which they had recklessly plunged, till they were oppressed with the presence of a vastness they could not cope with even as an idea, and which hung about them like a nightmare.

In epsilon we have a beautiful combination of a yellow with a blue star, magnitudes four and eight, distance 3.4", p. 198°. Finally, let us look at theta for a light test with the five-inch. The two stars composing it are of the fourth and twelfth magnitudes, distance 50", p. 170°.

Sigma 2306 is a triple, magnitudes seven, eight, and nine, distances 12", p. 220°, and 0.8", p. 68°. The third star is, however, beyond our reach. The colors of the two larger are respectively yellow and violet. The star cluster 4400 is about one quarter as broad as the moon, and easily seen with our smallest aperture.

It must, therefore, be exceedingly erratic in its changes, resembling rather the temporary stars than the true variables. In that part of Scutum Sobieskii contained in map No. 12 we find an interesting double, Sigma 2325, whose magnitudes are six and nine, distance 12.3", p. 260°, colors white and orange.

In reality the observations and the facts of astronomy do not depend either upon the magnitudes or the distances of the heavenly bodies. They proceed in the first place upon what may lie seen with the naked eye. They require an accurate and persevering attention. They may be assisted by telescopes. But they relate only to the sun and the planets.

They had ascertained the dimensions of the earth; they had registered or catalogued all the stars visible in their heavens, giving to those of the larger magnitudes the names they still bear on our maps and globes; they determined the true length of the year, discovered astronomical refraction, invented the pendulum-clock, improved the photometry of the stars, ascertained the curvilinear path of a ray of light through the air, explained the phenomena of the horizontal sun and moon, and why we see those bodies before they have risen and after they have set; measured the height of the atmosphere, determining it to be fifty-eight miles; given the true theory of the twilight, and of the twinkling of the stars.