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Updated: June 11, 2025
We distinguish at a distance, by the eye only, trunks of trees insulated in a vast plain, though the subtended angle be under twenty-five seconds.
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.
What is needed in order to attain knowledge of the desired exactness is no less than this: to measure an angle about equal to that subtended by a halfpenny 2,000 feet from the eye, within a little more than a thousandth part of its value. The angle thus represented is what is called the "horizontal parallax" of the sun.
These circumstances are the more worthy of attention because vessels returning to Europe, sometimes wait impatiently for a sight of these mountains, to rectify their longitude; and think themselves much farther off than they really are, when in fine weather these peaks are not perceptible at distances where the angles subtended must be very considerable.
The site of Shuwak is a long island in the broad sandy Wady of the same name, which, as has been remarked, feeds the Damah. Its thalweg has shifted again and again: the main line now hugs the southern or left bank, under the slopes and folds of the Jebel el-Sani'; whilst a smaller branch, on the northern side, is subtended by the stony divide last crossed.
The flow of the tide, or rather the damming up of the lower waters between Porto da Lenha and the mouth, causes a daily rise, which we found to measure about a foot; thus it assists in forming a treble current, the rapid down-flow in the Thalweg being subtended by a strong backwater on either side carrying a considerable portion in a retrograde direction, and showing a sensible reflux; this will continue as far as the rapids.
When the globules were darker; when, instead of pins' heads, small globules of sealing-wax were used, their spherical form did not begin to be distinctly visible till the moment when the subtended magnified angles, that is, the moment when the natural angle multiplied by the magnifying power, amounted to five minutes.
During August, this branch was found almost dry; in mid-September, it was nearly full, and here the water breaks with the greatest violence. The right bank is subtended for some hundred yards by blocks of granite and greenstone, pitted with large basins and pot-holes, delicately rounded, turned as with a lathe by the turbid waters.
Now, subducting the diameter of the hole from the length and breadth of the image, there remains 13 inches the length, and 2 3/8 the breadth, comprehended by those rays, which, passing through the centre of the said hole, which that breadth subtended, was about 31', answerable to the sun's diameter; but the angle which its length subtended was more than five such diameters, namely 2 degrees 49'.
We won't shake it." While Morey took the time exposure, Arcot looked at the enlarged image in the telectroscope and tried to make angular measurements from the individual stars. This he found impossible. Although he could spot Betelgeuse and Antares because of their tremendous radiation, they were too close together for measurements; the angle subtended was too small.
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