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Antwerp, then the commercial centre of the Netherlands and of Europe, stands upon the Scheldt. The river, flowing straight, broad, and full along the verge of the city, subtends the arc into which the place arranges itself as it falls back from the shore. Two thousand ships of the largest capacity then known might easily find room in its ample harbours.
We judge of a man by the angle he subtends to our eye only thus CAN we judge of him; and this angle depends on the relation his qualities and circumstances bear to our interests and sympathies. Bourgonef had charmed me intellectually; morally I had never come closer to him than in the sympathies of public questions and abstract theories. His story had disclosed hidden depths.
Ahead, where the front of the star-plough is clearing the way, the chaos is nearer at hand, and consequently there the rift subtends a broader angle, and is filled with primordial dust, which, having been annexed by the vanguard of the star-swarm, forms the nebulæ seen only in that part of the Milky Way.
As this group subtends an angle of three degrees only at the house where we dwelt, it long served me to compare the variations of the terrestrial refraction with the meteorological phenomena. Storms are formed in the centre of this Cordillera; and we see from afar thick clouds resolve into abundant rains, while during seven or eight months not a drop of water falls at Cumana.
Approaching, disparate, at relaxed walking pace they crossed both the circus before George's church diametrically, the chord in any circle being less than the arc which it subtends. Of what did the duumvirate deliberate during their itinerary?
The country, level and grassy, begins the region north of the great forest-zone which subtends the maritime mangrove swamps. It breeds horses and can command Moslem allies, equestrian races feared by the Ashantis. The Gyámans, according to their tradition, migrated, or rather were driven, southwards from their northern homes.
Crossing at six a.m. the broad pilgrim-track, we struck eastward at a place where the Secondary gypsum subtends the old coralline cliff. As we advanced, it became a rock-walled, stonesoled tunnel; winding, contracting and widening, rising and flattening, and generally interesting, compared with the dull flat breadth of such features as the Wady Salma.
In 1675 Cassini found the ring to be double, the concentric rings being separated by a black band a fact which was placed beyond dispute by Herschel, who also found that the thickness of the ring subtends an angle less than 0".3. Shroter estimated its thickness at 500 miles. Many speculations have been advanced to explain the origin and constitution of the ring.
Last night had a fine view of Alpha Lyrae, whose disk, through our captain's spy-glass, subtends an angle of half a degree, looking very much as our sun does to the naked eye on a misty day. Alpha Lyrae, although so very much larger than our sun, by the by, resembles him closely as regards its spots, its atmosphere, and in many other particulars.
The more complete this transparency, the more it seems to me that in the same conditions there must be a repetition of the same fact. Our inductions are certain, to our eyes, in the exact degree in which we make the qualitative differences melt into the homogeneity of the space which subtends them, so that geometry is the ideal limit of our inductions as well as of our deductions.
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