From the spherical triangle PZS, we have
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cos. ZSv eq. cos. PS cos. ZP + sin. PS sin. ZP cos. ZPS but ZS eq. zenith distance eq. 90 - altitude ZP eq. 90-PR eq. 90 - latitude PS eq. polar distance eq. 90 - declination,
therefore, by substitution
sin. alt. eq. sin. dcd. sin. lat. +cos. dccl. cos. lat. cos. ZPS . . . (P>)
and ZPS is the hour-angle of the sun.
A comparison of the two formula? (A) and (P>) shows that the hour-angle given by the bead will be the same as that given by the sun, and proves the theoretical accuracy of the card-dial. Just at sun-rise or at sun-set, the amount of refraction slightly exceeds half a degree. If, then, a little cross m (see fig. 8) be made just below the sun-line, at a distance from it which would subtend half a degree at c, the time of sunset would be found corrected for refrac tion, if the central line of light were made to fall on cm.
The following list includes the principal writers on dialling whose works have come down to us, and to these we must refer for descriptions of the various constructions, some simple and direct, others fanciful and intricate, which have been at different times employed:—
Ptolemy, Analcmma, restored by Commandine ; Vitruvius, Architecture; Sebastian Munster, Horolorfiographia ; Orontius Fineus, De Ilorologiis Solaribus; Mutio Oddi da Urbino, Horologi Solari; Dryandcr, De Horologiorum Compositions ; Conrad Gesner, Pamleetce ; Andrew Schoner, Gnomonicce; F. Comraaudine, Horolo giorum Descriptio ; Joan. Bapt. Benedictus, De Gnomonum Usu ; Georgius Schomberg, Exegesis Fundamcntorum Gnomonicomm ; Joan. Solomon de Caus, Horologes Solaircs ; Joan. Bapt. Trolta, Praxis Horologiorum; Desargues, Maniere Univcrselle pour poser I Essieu, &c. ; Ath. Kircher, Ars magna Lucis et Umbra ; Hallum, Explicatio Horolorjii in Horto Regio Londiin ; Joan. Maik, Tracta- tus Horologiorum ; Clavius, Gnomonices de Horologiis.
Also among more modern writers, Deschales, Ozanam, Schottus, "Wolfius, Picard, Lahire, "Wai per ; in German, Paterson, Michael, Miiller ; and among English writers, Foster, Wells, Collins, Lead- better, Jones, Leybourn, Emerson, and Ferguson. See also Meikle a article in former editions of the present work.
DIAMANTE. The Italian fresco painter, commonly known as Fra Diamante, was born at Prato about 1 400. He was a Carmelite friar, a member of the Florentine com munity of that order, and was the friend and assistant of the more celebrated Filippo Lippi. The Carmelite convent of Prato which he adorned with many works in fresco has been suppressed, and the buildings have been altered to a degree involving the destruction of the paintings. He was the principal assistant of Fra Filippo in the grand frescoes which may still be seen at the east end of the cathedral of Frato. In the midst of the work he was recalled to Florence by his conventual superior, and a minute of proceedings of the commune of Prato is still extant, in which it is determined to petition the metropolitan of Florence to obtain his return to Prato, a proof that his share in the work was so important that his recall involved the suspension of it. Subsequently he assisted Fra Filippo in the execution of the frescoes still to be seen in the cathedral of Spoleto, which Fra Diamante completed in 1470 after his master s death in 14G9. Fra Filippo left a son ten years old to the care of Diamante, who, having received 200 ducats from the commune of Spoleto, as the balance due for the work done in the cathedral, returned with the child to Florence, and, as Vasari says, bought land for himself with the money, giving but a small portion to the child. The accusation of wrong-doing, however, would depend upon the share of the work executed by Fra Diamante, and the terms of his agreement with Fra Filippo. Fra Dia mante must have been nearly seventy when he completed the frescoes at Spoleto, but the exact year of his death is not known.
See Relazione delle Pitture di Fra, Filippo nel coro di Prato, by the Canon Baldanzi, Prato ; also the last edition of Vasari, Florence, 1848.
DIAMANTINA, formerly Tejuco, a town of Brazil, in the province of Minas-Geraes, is situated at an altitude of 5700 feet above sea-level, in a valley watered by affluents of the Jequitinhonha. Its streets are broad, and the houses are mostly of wood. The public structures include several churches, a theatre, barracks, three hospitals, and a school. The surrounding district is sterile, but is rich in minerals. The discovery of diamonds there was made in 1729. Population about 7000, or, with that of the neighbouring villages, 15,000. See Brazil, vol. iv. p. 224.
DIAMANTINO, a town of Brazil, in the province of Matto-Grosso, is situated close to the Diamantino river, about six miles from its junction with the Paraguay, at the foot of a high range of country, in 14" 24 33" S. lat. and 56 8 30" W. long. The neighbourhood, which is infertile, yields diamonds and gold. Population about 5000.
DIAMOND. This gem, the most highly valued and brilliant of precious stones, is also remarkable for its history and its peculiar physical and chemical properties. Though not always accurately distinguished from other similar stones, it seems to have attracted notice at a very early period, especially in India, the chief source of supply in ancient times. The old Jewish doctors regarded the jahalom, the third in the second row of stones in the breast-plate of the high priest (Exod. xxxix. 11), as the diamond, and it is thus translated in the English and other versions. But as each stone bore the name of one of the tribes, and there is no reason to believe that any method of polishing such hard stones, still less of engraving letters on them, was then known, the identification cannot be accurate. Among the Greeks it is first mentioned about three centuries B.C. under the name of adamas ([ Greek ]), " the unsubduable," referring to its hardness and power of resisting fire. The same name was previously given to a metal highly valued from its extreme hardness for armour and weapons, and the twofold. use of the term continued long both in Greek and Latin. The name of the gem in our own and most modern languages is derived from this old name, occurring in the form diamas in Albertus Magnus and other authors of the 13th century. Curiously enough, the French aimant, applied to the magnet, comes from the same term in its other signification of an ore or metal.
Pliny, who says it exceeds in value all human things, and its use was confined to kings, and to few even of them. He mentions six varieties, the most remarkable being the Indian and Arabian, of such unspeakable hardness that when struck with a hammer even the iron and anvil were torn asunder " ita respuentes ictum, ut ferrum utrinque dissultet, incudesque etiam ipsi dissiliant." It also resisted the fire, and could only be subdued and broken down when dipped in fresh warm goat s blood. Similar fables con tinued to prevail during the Middle Ages, and even yet have hardly vanished from popular belief. As an ornamental stone it was highly esteemed during the early times of the Roman empire, as some scandalous stories recorded by Juvenal testify, though only stones with naturally polished faces could be used. This fact is proved not only by the words of Seneca—" nec secari adamas ant csedi vel deteri potest"—and others, but fr.om specimens of diamonds set in gold, with no artificial polishing, which have come down both from classic times and from the Middle Ages. This unworkable character long greatly limited both its use and its value ; and the more highly coloured rubies, and even emeralds and sapphires, were often preferred to it. It was only after Ludwig van Berquen (or Berghem, as he is often
named) in 147G discovered the mode of cutting and polish-
