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Updated: June 11, 2025
Some measures taken on the day when the nucleus subtended only an angle of a single second, gave as its real angle 6/100 of the diameter of the earth. Herschel saw no phase at an epoch when only 7/10 of the nucleus could be illuminated by the sun. The nucleus then must shine by its own light.
The comet was seen on the 30th. It was a little above the horizon, in the eastern part of the heavens, at one in the morning; and at about half an hour after four it passed the meridian, and its tail subtended an angle of forty-two degrees.
If the hypotheses had been exact, the results would have been correct too; but Aristarchus in fact assumed a certain angle to be 87° which is really 89° 50', and the angle subtended at the centre of the earth by the diameter of either the sun or the moon to be 2°, whereas we know from Archimedes that Aristarchus himself discovered that the latter angle is only 1/2°. The effect of Aristarchus's geometry is to find arithmetical limits to the values of what are really trigonometrical ratios of certain small angles, namely
In the meantime, Gascoigne had been measuring an equilateral triangle of twelve paces and marked it out. Mr Tallboys, on his return with the purser's steward, went over the ground, and finding that it was "equal angles subtended by equal sides," declared that it was all right.
The neighbouring hills, and those of Alegranza and Isla Clara, were scarcely above one hundred or one hundred and twenty toises. We may be surprised at the small elevation of these summits, which, viewed from the sea, wear so majestic a form; but nothing is more uncertain than our judgment on the greatness of angles, which are subtended by objects close to the horizon.
In other families each flower of such an inflorescence would be subtended by a bract, according to the general rule that in the higher plants side branches are situated in the arils of leaves. Bracts are reduced leaves, but the spikes of the cruciferous plants are generally devoid of them. The flower-stalks, with naked bases, seem to arise from the common axis at indefinite points.
During the now brief interval of darkness a meteoric stone again passed in my vicinity, and the frequency of these phenomena began to occasion me much apprehension. "April 17th. This morning proved an epoch in my voyage. It will be remembered that, on the thirteenth, the earth subtended an angular breadth of twenty-five degrees.
Tallboys had smuggled on shore; and as soon as they were on the ground, the gunner called Mr. Easthupp. In the meantime, Gascoigne had been measuring an equilaterial triangle of twelve paces, and marked it out. Mr. Tallboys, on his return with the purser's steward, went over the ground, and finding that it was "equal angles subtended by equal sides," declared that it was all right.
But this represents only the angle subtended by the star's disk. To learn its linear diameter, we must know its distance. Four determinations of the parallax, which determines the distance, have been made. Elkin, with the Yale heliometer, obtained 0.032 of a second of arc. Schlesinger, from photographs taken with the 30-inch Allegheny refractor, derived 0.016.
In viewing the spectra of bright objects, as of an area of red silk of half an inch diameter on white paper, it is easy to magnify it to tenfold its size: for if, when the spectrum is formed, you still keep your eye fixed on the silk area, and remove it a few inches further from you, a green circle is seen round the red silk: for the angle now subtended by the silk is less than it was when the spectrum was formed, but that of the spectrum continues the same, and our imagination places them at the same distance.
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