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By a process which at that time I did not accurately follow, and which I had not subsequently the means of verifying, the distance as well as the angle subtended by the height was obtained. Kevimâ, after working out his father's figures, informed me that the highest peak in view the highest in Mars was not less than 44,000 feet.
The ascertainment of these angular distances ascertained their supplements; and since the angle at the earth’s centre subtended by the distance between the two places of observation was deducible by spherical trigonometry from the latitude and longitude of those places, the angle at the moon subtended by the same line became the fourth angle of a quadrilateral of which the other three angles were known.
Not once did the strange occupant of that machine relax his stony stare at the sky, and Smith tried to forget how hungry he was by estimating the extent of his vision. He decided that the angle subtended about a hundred and sixty degrees, or almost half a circle; and he further concluded that if his agent possessed a nose, it was a pretty trifling affair, too small to be noticed.
The extremely small angle subtended by this enormous disk is explained by the great distance of the star, which is about 160 light-years. That is to say, light travelling at the rate of 186,000 miles per second spends 160 years in crossing the space that lies between us and Betelgeuse, whose tremendous proportions therefore seem so minute even in the most powerful telescopes.
The four arteries all arise in inner regions of the secondary age, subtended east and west by ghats, or containing mountains mostly of palaeozoic or primary formation, the upheaval of earthquakes and volcanoes. These rims must present four distinct water-sheds.
Our first anxiety, of course, was to ascertain whether we were gaining upon the chase, or whether she was maintaining her distance from us; as soon, therefore, as we had secured our morning altitude of the sun for the determination of the longitude, we measured as accurately as we could the angle subtended by that portion of the barque's main-mast which showed above the horizon.
In a subsequent series of experiments, some globules of silver placed very far from the observer, allowed their globular form to be perceived, even when the magnified angle remained below two minutes. Under equality of subtended angle, then, the telescopic vision with strong magnifying powers showed itself superior to the naked eye vision. This result is not unimportant.
This spot was a favourite one with Clement Hicks, and a fortnight after the incidents last related he sat there smoking his pipe, while his eyes roved upon the scene subtended before him. The hill fell abruptly away, and near the bottom glimmered whitewashed cots along a winding road.
It was my watch below from eight o'clock until noon, and I was consequently off duty; but although I had been on deck for eight hours of the twelve during the preceding night, I was much too fidgety to turn in and endeavour to get a little sleep; I therefore routed out a small pocket sextant that had been presented to me by a friend, and, making my way up into the fore- topmast cross-trees from which the strangers could be seen I very carefully measured with the instrument the angle subtended by the mast- head of the brig and the horizon, so that I might be able to ascertain from time to time whether or not that craft was increasing the distance between her and ourselves.
The largest links of these West-Arabian Ghats are of white-grey granite, veined and striped with quartz; and they are subtended inland by the porphyritic traps of the Jibal el-Shafah, which we shall trace to the parallel of El-Hamz, the end of Egypt. All are maritime, now walling the shore, like the Tayyib Ism; then sheering away from it, where a broad "false coast" has been built by Time.
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