R A D R A D 217 closure, with or without one of the bodies present in it. For one of the fundamental equations gives dE dp 3Z ts *dt~ y> where t is the absolute temperature. If / be the pressure on unit surface, 3/ is the energy per unit of volume, and this equation becomes Hence it follows at once that, if the fundamental assump- tions be granted, the energy of radiation of a black body per unit volume of the enclosure is proportional to the fourth power of the absolute temperature. It is not a little remarkable that Stefan 1 had some years previously shown that this very expression agrees more closely with the experimental determinations of Dulong and Petit than does their own empirical formula. 27. It would appear from this expression that, if an impervious enclosure containing only one black body in thermal equilibrium is separated into two parts by an impervious partition, any alteration of volume of the part not containing the black body will produce a corresponding alteration of the radiation in its interior. It will now correspond to that of a second black body, whose tempera- ture is to that of the first in the inverse ratio of the fourth roots of the volumes of the detached part of the enclosure. 28. Lecher 2 has endeavoured to show that the distri- bution of energy among the constituents of the radiation from a black body does not alter with temperature. Such a result, though apparently inconsistent with many well- known facts, appears to be consistent with and to harmonize many others. It accords perfectly with the notion of the absolute uniformity (statistical) of the energy in an en- closure, and its being exactly that of a black body, even if the contents (as in 25) consist of a body which can radiate one particular quality of light alone. And if this be the case it will also follow that the intensity of radiation of any one wave-length by any one body in a given state depends on the temperature in exactly the same way as does the whole radiation from a black body. Unfor- tunately this last deduction does not accord with Melloni's results ; at least the discrepance from them would appear to be somewhat beyond what could fairly be set down to error of experiment. But it is in thorough accordance with the common assumption ( 14) that the percentage absorption of any particular radiation does not depend on the temperature of the source. The facts of fluorescence and phosphorescence, involving the radiation of visible rays at temperatures where even a black body is invisible, have not yet been dealt with under any general theory of radiation; though Stokes has pointed out a dynamical explanation of a thoroughly satisfactory character, they re- main outside the domain of Carnot's principle. (P. G. T.) RADIOMETER. See PNEUMATICS, vol. xix. p. 249. RADISH. See HORTICULTURE, vol. xii. pp. 286, 287. RADNOR, an inland county of South Wales, is situated between 52 5' and 52 25' N. lat. and between 2 57' and 3 25' W. long., and is bounded E. by Hereford and Shropshire, N. by Montgomery, W. by Cardigan, and S. by Brecknock. Its greatest length from north to south is about 30 miles, and its greatest breadth from east to west about 33 miles. The area is 276,552 acres, or 432 square miles. The greater part of the surface of the county is hilly, and the centre is occupied by a mountainous tract called Radnor Forest, running nearly east and west, its highest summit reaching 2163 feet. Towards the south and south-east the hills are much less elevated and the valleys 1 Sitzunysber. d. k. Ak. in Wien, 1879. 2 Wiedemann's Ann., 1882, xvii. widen out into considerable plains, abounding with small rivulets. The hills for the most part present smooth and rounded outlines, but the valley of the Wye is famed for its beauty. The higher ranges are covered with heath, but there is good pasturage on the lower slopes. The smaller elevations are frequently clothed with wood. The prevailing strata are the Lower Silurian rocks; but in the east there is a considerable area occupied by Old Red Sand- stone, and throughout the county felspathic ash and green- stone are found, while near Old Radnor there is a large patch of Silurian limestone. Lead and cor per are said to exist, but not in quantities sufficient to pay the working. There are saline, sulphurous, and chalybeate wells at Llan- drindod. The Wye enters the county in the north-west, 18 miles from its source in Plinlimmon, and flowing in a south-easterly direction divides it from Brecknock, until it bends north-east and reaches Hay, after which it for some distance forms the boundary with Hereford. Its prin- cipal tributary is the Ithon, which flows south-west and joins it 7 miles above Builth. The Teme, flowing south- east, forms the northern boundary of the county with Shropshire. The Llugw, rising in the northern part of the county, flows south-east into Hereford, a little below Presteigne. Agriculture. The climate is somewhat damp, and in the spring cold and ungenial. The greater part of the county is suitable only for pasturage, but there is some good arable land in the valleys in the southern and south-eastern districts, which pioduces excellent crops of turnips, oats, and Welsh barley, the soil being chiefly open shaly clay, although in the east there is an admixture of red sandstone soils. In 1884 there were 156,628 acres, or about five- ninths of the total area, under cultivation, and of these 114,242 acres, or about four-fifths, were in permanent pasture. Of the 21,356 acres under corn crops 12,245 acres, or more than half, were under oats, whilst wheat occupied 5200 acres and barley 3853. Green crops occupied only 7100 acres, of which 1107 were under potatoes and 5682 under turnips. Horses numbered 9249 (3755 used solely for agricultural purposes), cattle 30,917 (10,223 cows and heifers in milk or in calf), and sheep as many as 244,771. The inhabitants are dependent almost solely on agriculture, the manufactures being confined chiefly to coarse cloth, stockings, and flannel for home use. Railways. The county is intersected by several lines : the Central Wales Railway runs south-west from Knighton to Llan- dovery ; another line runs south-eastwards by Rhayaderand Builth and joins the Hereford line, which passes by Hay and Talgarth ; while another branch line passes by Kineton to New Radnor. Administration and Population. Radnor comprises six hun- dreds, but contains no municipal borough. It has one court of quarter sessions and is divided into six petty and special sessional divisions. The ancient borough of Radnor (population 2005) is governed by the provisions of an old charter, and has a commission of the peace. The county contains sixty civil parishes with part of one other, and is partly in the diocese of St David's and partly in that of Hereford. It returns one member to the House of Com- mons. The population in 1871 was 25,430 and in 1881 it was 23,528, of whom 11,939 were males and 11,589 females. ,The number of inhabited houses was 4775. The average number of persons to an acre was 0'09 and of acres to a person 11*75. History and Antiquities. During the Roman occupation the district was included in the province of Siluria. The Roman road from Chester to Caermarthen entered the northern extremity of the county near Newtown and, following the valley of the Ithon, crossed the Wye and entered Brecknockshire near the town of Builth. There are remains of a Roman station at Gym near Llan- drindod, and at Wapley Hill near Presteigne there is a very good example of a British camp. The district was afterwards included chiefly in Powis, but partly in Gwent and partly in Feryllwge. It was made a county by Henry VIII. Anciently it was called Maesy- fedd. The name Radnor is also of very great antiquity, and occurs in the Cambrian annals as early as 1196. There are no ancient castles claiming special notice, and the only ecclesiastical ruin of importance is that of the abbey of Cwm-Hir, founded for the Cis- tercians in 1143, and occupying a romantic situation in the vale of Clywedog. A considerable portion of the ancient building has been used as materials for the adjoining modern mansion. RADOM, a government of Poland, occupying a trian- gular space between the Vistula and the Pilica and bounded on the N. by Warsaw and Siedlce, on the E. by Lublin, on the S. by Austrian Galicia and Kielce, and on the W. XX. 28
