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The magnitudes are five, six, seven and a half, and twelve; distances 2.4", p. 121°; 208", p. 56°; and 35", p. 264°. The color of the largest star is white and that of its nearest companion blue; the star of magnitude seven and a half is also blue. The star cluster 4681 is a fine sight with our largest glass. In the map we find the place marked where the new star of 1876 made its appearance.
The little star nu is double, magnitudes five and nine, distance 50", p. 31°, colors contrasted but uncertain. In delta we find a closer double, magnitudes three and four, distance 3.5", p. 190°. It is a beautiful object for the three-inch.
By this transformation of all questions of quality into questions only of quantity, geometry is reduced to the single problem of the measurement of magnitudes, that is, the ascertainment of the equalities which exist between them.
As we have seen, the discovery of the incommensurable rendered inadequate the Pythagorean theory of proportion, which applied to commensurable magnitudes only. It would no doubt be possible, in most cases, to replace proofs depending on proportions by others; but this involved great inconvenience, and a slur was cast on geometry generally.
When the problem is extended to these huge dimensions, the prospect of an ultimate cessation of cosmical work is indefinitely postponed, but at the same time it becomes impossible for us to deal very securely with the questions we have raised. The magnitudes and periods we have introduced are so nearly infinite as to baffle speculation itself: One point, however, we seem dimly to discern.
The magnitudes are five and eight, distance 26", p. 73°. Where the two arms of the cross meet is gamma, whose remarkable cortége of small stars running in curved streams should not be missed. Use the lowest magnifying power.
We represent also all multiplications of light, which we carry to great distance, and make so sharp, as to discern small points and lines. Also all colourations of light: all delusions and deceits of the sight, in figures, magnitudes, motions, colours; all demonstrations of shadows. We find also divers means, yet unknown to you, of producing of light, originally from divers bodies.
On the walls of the temple and on the dome, which is let down when the priest gives an address, lest the sounds of his voice, being scattered, should fly away from his audience, there are pictures of stars in their different magnitudes, with the powers and motions of each, expressed separately in three little verses.
O foolish man! so timid of all future possibilities of bliss that he must grasp and burn himself with such delights as he finds here! And equally mistaken and small-minded man who thinks that all our Mighty God will have to offer us hereafter are crowns, damp clouds and mists, and endless hymns! Such little hearts are far away indeed from knowing the magnitudes of Life.
With the slightest magnifying this object splits up into two stars, of magnitudes four and seven, situated rather more than 40" apart. Next we shall need a rather low-power eyepiece and our largest aperture in order to examine a star cluster, No. 4173, which was especially admired by Sir William Herschel, who discovered that it was not, as Messier had supposed, a circular nebula.
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