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 86 TWICKENHAM burg, 1826-'37), and Grundriss der analyti- schen Logik (Kiel, 1834). II. Karl, a German author, son of the preceding, born in Kiel, April 22, 1820, died in Berlin, Oct. 14, 1870. He became connected with the judicial service, and was one of the founders of the progres- sive party, which in 1861 involved him in a duel with Gen. Manteuffel, in which he lost his right arm. In the same year he was elected to the Prussian chamber of deputies, and he was one of the founders of the national-liberty party and an early member of the North Ger- man Reichstag. Persecuted for advocating the fullest parliamentary freedom, he retired in 1868 after being fined. His works include Schiller in seinem Verhdltniss zur Wissen- schaft (Berlin, 1863), Machiavelli (1868), and the posthumous Die religiosen, politischen und sodalen Ideen der asiatischen Culturvolker und derAegypter in ihrer historiscnen Entwickelung (edited by M. Lazarus, 1873). TWICKENHAM, a village and parish of Middle- sex, England, on the left bank of the Thames, opposite Richmond, with which it is connected by a handsome bridge, about 10 m. "W. S. W. of St. Paul's, London; pop. in 1871, 10,533. It is celebrated as the residence of Pope, whose villa has been destroyed ; but his grotto is still standing, and his monument is in the parish church, where he was buried. Walpole's seat, called Strawberry Hill, is about 1 in. distant. At Twickenham is also Orleans house, occu- pied by Louis Philippe while a refugee in Eng- land before his accession to the throne, and still belonging to his family. In 1874 the large church of St. Stephen was completed, and a new quarter between the old village and Rich- mond bridge was added to the parish. TWIGGS, a central county of Georgia, bounded W. by the Ocmulgee river ; area, 400 sq. m. ; pop. in 1870, 8,545, of whom 5,632 were col- ored. The surface is moderately hilly and the soil fertile. The Georgia Central railroad crosses the N. border, and the Macon and Brunswick railroad intersects the W. part. The chief productions in 1870 were 164,145 bushels of Indian corn, 18,163 of sweet potatoes, and 6,189 bales of cotton. There were 473 horses, 1,046 mules and asses, 1,172 milch cows, 2,583 other cattle, 794 sheep, and 6,991 swine; 5 flour mills, and 1 saw mill. Capital, Marion. TWILIGHT, the faint light which appears in the sky a little before sunrise, and again for some time after sunset, the amount and dura- tion of the light varying materially in different latitudes and at different seasons. The light is caused by the reflection of the sun's rays, when below the horizon, from the vapors and minute solid particles floating in it, and per- haps from the material atoms of the air itself. To this property of reflection possessed by the atmosphere its illumination is due beyond the direct reach of the rays proceeding from the sun, as under the shadow of clouds and behind opaque objects upon the surface, where, unless the light were directed upon some principle TWILIGHT of general diffusion, intense darkness would prevail. So also a sudden illumination would attend the rising of the sun and instantaneous darkness accompany his setting. As the sun sets to any point upon the surface of the earth, the atmosphere above this point all around the horizon is illuminated by direct rays, and the reflection from so broad an illuminated sur- face brings to the earth a large amount of light ; but as the dark shadow of the earth, in consequence of the continued sinking of the sun, rises higher and higher into the atmos- phere at this locality, the reflected light stead- ily diminishes, and finally disappears when no direct rays from the sun reach the higher regions of the atmosphere above the horizon- tal line extended toward the sunset. By ob- serving the time after the setting of the sun to the disappearance of the reflected rays, data are afforded upon which an approximate esti- mate may be made of the height of the atmos- phere, or at least of that portion of the atmos- phere which is capable of being illuminated in the manner above described ; and it is on this method chiefly that this calculation is based. On the equator, Avhen the sun is in the equi- noctial, and apparently descending vertically, and occupying as much time below as above the horizon, the duration of the twilight is an hour and 12 minutes, or one tenth of the semi- circumference, equal to 18; whence it is con- cluded that such must be its depression below the horizon at any place before the twilight can end ; and it is reckoned from this that the height of the atmosphere is a little over 52 m. But this cannot be otherwise than a rude ap- proximation, the calculation proceeding on the supposition of there being but one direct re- flection, whereas the rays may be reflected again and again, and no account being made of the refraction the rays must experience in their direct passage through the dense stratum of air near the surface, and entering it again when turned back from the upper strata. By a different calculation, founded on observations of the progress of the edge of the dark shadow (known till it reaches the zenith as the anti- crepuscular, and afterward as the crepuscular curve), made in the pure and transparent air at the summit of high mountains, the height of the atmosphere has been found by French astronomers (whose observations are recorded in the Annuaire meteorologique de France, 1850) to be 71-46 m. This curve they found set when the sun was 17 below the horizon. The variable length of the twilight at the same place in different seasons results from the vary- ing declination of the sun and the consequent difference of time required to sink 17 or 18 below the horizon, as his course is vertical or more or less approaching it. Near the poles, where the sun attains at noon no great height above the horizon, it also keeps near it after disappearing each night ; and if its depression does not exceed 18, the twilight is continuous into the dawn. This is the case in some por-