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If the unification of nature were complete sense would evidently fall within it; it is to subtend and sustain the sensible flux that intelligence acknowledges first stray material objects and then their general system. The elements of experience not taken up into the constitution of objects remain attached to them as their life.
Such was the labour of that indefatigable astronomer, of which I am going to give a compressed abridgment. The author relates first, that in 1774, he endeavoured to ascertain experimentally, with the naked eye and at the distance of distinct vision, what angle a circle must subtend to be distinguished by its form from a square of similar dimensions.
English officers traversed the interior in all directions, and their reports throw vivid light upon the position, the extent, and the value of the auriferous grounds which subtend the Gold Coast and which supply it with the precious metal.
Of all regular polygons it is the simplest: its three equal sides subtend equal angles, each of 60 degrees; it trisects the circumference of a circle; it is the graphic symbol of the number three, and hence of every threefold thing; doubled, its generating arcs form the vesica piscis, of so frequent occurrence in early Christian art; two symmetrically intersecting equilateral triangles yield the figure known as "Solomon's Seal," or the "Shield of David," to which mystic properties have always been ascribed.
It is customary to speak of peaks as towering in the air, which yet subtend an angle of very few degrees; of almost precipitous ascents, which, when measured, are found to be slopes of 18 degrees or 20 degrees; and of cliffs as steep and stupendous, which are inclined at a very moderate angle.
As usual, the garments do not fit you, you are lost in the garments, or you cannot get into them at all; this is not your suit of clothes, it must be another's: alas, these are not your dimensions, these are only the optical angles you subtend; on the whole, you will never get measured in that way! Another time, of date probably very contiguous, I remember hearing Sterling preach.
The lesser Congo delta is bounded north by the Banana or Malela stream, whose lower fork is "Pirates' Creek;" and south by the mangrove-clad drains, which subtend the main line: the base measures 12-15 miles. At the highest station, Boma, I shall have something to say about the greater delta.
It is clear that if the forces that hold an organism together are mechanical, and therefore independent of the ideal unities they subtend, those forces suffice to explain the origin of the organism, and can have produced it. Darwin's discoveries, like every other advance in physical insight, are nothing but filling for that abstract assurance.
The reason why, to our sight, an object becomes apparently smaller and smaller as it is withdrawn from the eye, until it at last disappears entirely, is that the eye is a very imperfect instrument for viewing objects at a great distance; it can only form an image of an object when that object is near enough to subtend a certain angle, or, in popular language, to show itself a certain size the rays of light must converge in fact, the eye cannot single out and appreciate parallel rays: could it do this, objects would not appear to grow smaller as they are removed.
Clearly the actual number of multiple stars is beyond all present estimate. The elder Herschel's early studies of double stars were undertaken in the hope that these objects might aid him in ascertaining the actual distance of a star, through measurement of its annual parallax that is to say, of the angle which the diameter of the earth's orbit would subtend as seen from the star.