377 



TRINODA NECESSITAS. 



TRISECTION OF THE ANGLE. 



378 



suggested to Smeaton in 1759, and they had actually been employed 

 in the Portland lighthouse about 1789; but from some mismanage- 

 ment they had fallen into disfavour until Augustin Fresnel, on 26th 

 July, 1822, read a paper at the Academic des Sciences of Paris, 

 describing a lighthouse apparatus on the dioptric system executed 

 under his orders. In 1825 the French government undertook the 

 comprehensive scheme for lighting their coast, which has since then 

 been so carefully carried into execution ; and as they began almost de 

 they have been able to adopt, throughout, the dioptric apparatus, 

 whereas in the English lighthouses there were already numerous and 

 costly catoptric lights of a very perfect nature in operation. The 

 other nations of Europe have adopted the dioptric lights ; and there 

 seems to be little reason to question that the latter will ultimately 

 replace the other known systems. The Fresnel's dioptric lamps may 

 be popularly described as consisting of a mechanical, four-wicked, oil 

 lamp placed in the centre of an octagonal glass prism ; the centre part of 

 each of the sides being formed of a plano-convex lens of about 15 

 inches in diameter, which is surrounded by a series of glass rings of a 

 spherical triangular form, so as to produce the same effect upon the 

 rays of light as the central lens does. Messrs. Leopold Fresnel, A. 

 Stevenson, Arago and Faraday, have in turn contributed to the 

 perfection of Augustin Fresnel's invention ; and it is to the distin- 

 guished philosopher, Faraday, that we are indebted for the efficient 

 means of ventilating the lamps of lighthouses now adopted an 

 apparently insignificant, but really a most important detail in their 

 working. 



The only other events of importance connected with the history of 

 lighthouses, are the establishment of light vessels about the end of the 

 last century ; the erection of the screw-pile lighthouses aud beacons, 

 on Mitchell's plan, the first of the former erected on the Maplin sand, 

 having been lighted for the first time on February 16, 1841 ; and the 

 erection of the first cast-iron lighthouse at Morant Point, in Jamaica, 

 under the orders of Mr. A. Gordon : it was lighted for the first time 

 on November 1, 1841. Many valuable papers have from time to time 

 been published on the scientific questions involved in this branch of 

 the engineering art in addition to those previously noticed ; amongst 

 which attention is particularly called to the report by M. Rossel, 

 ' Sur le Systeme General d'Eclairage des Cotes ' ; to a memoire by L. 

 Freanel in the ' Annales Des Fonts et Chaussees,' for 1831, on the 

 stability of lofty towers ; to another me'moire by the same author on 

 the mode of treating the dioptric apparatus, in the ' Annales Maritimes 

 et Coloniales,' 1836 ; and a description of the scaffolding and machinery 

 used at the lighthouse at Br<!hat, inserted by M. Potel in the 

 ' Annales des Fonts et Chaussees,' for 1835. 



It may be as well to add that the French authorities class the lights 

 on their shores hi four divisions, according to the power, and the 

 range of visibility, of their lights. The " I'hares ' of the first class are 

 from a distance of 30 miles ; those of the second class, from 

 a distance of 25 miles ; those of the third class, from a distance of 15 

 miles ; whilst the phares of the fourth class, or the harbour lights, are 

 only visible at distances of about 6 miles. In addition to the harbour 

 lights, the French authorities frequently place bells, with reflectors at 

 the extremities of their piers ; these bells are rung in foggy weather, 

 but they are not considered to be of much service. 



TK1NODA NECESSITAS. This term, in Anglo-Saxon times, 

 signified the three services due to the king in respect of tenures of 

 lands in England for the repair of bridges, the building of fortresses, 

 and expeditions against his enemies. All the lands within the realm 

 were bound to contribute to these three emergencies, on the principle 

 of their necessity for general convenience or safety ; and for this 

 reason every roan's estate was subject to the trinoda necfMitas, whatso- 

 ever other immunities he might enjoy. Even in royal grants to the 

 Church of privileges and exemptions from secular sen-ices, the right of 

 requiring contribution for these purposes was almost always reserved 

 to the king. (Selden's Janut Anglm-um, i. 42; Cowell's Interpreter, ad 

 vocatn.) 



TRINOMIAL, the algebraical name for an expression which consists 

 of three terms, as a + k + c, orazbaP + bx'. [TERM.] 



TRIOXYPROTEIN. A substance said to be obtained from albumi- 

 nous substances. Its existence is very problematical. 



TRIPHOSPHETHYLAMINE. Synonymous with trict!<ylj,ho*phine. 

 [OROAHIC BASES. Organic phntphorout bates.] 

 i TRIPLE ALLIANCE. [TREATIES, CHRONOLOGICAL TABLE OP.] 

 TRIPLETS. [DOUBLETS.] 



TRIPLICATE. [R.VTIO.] In the common arithmetical sense, the 

 triplicate of a given ratio is found by taking the cube of each of the 

 terms of the ratio. Thus, when we say that two similarly formed 

 solids, whose linear dimensions are as 4 to 7, are in the triplicate ratio 

 of 4 to 7, it is meant that the bulks of those solids are in the ratio of 

 4x4x4to7x7x7, or of 64 to 343. 



TRIPOD (tripra, rplirovi) is any article of furniture resting upon 

 three feet, whence the name is given to tables, chairs, moveable altars, 

 and other articles of the same kind. (Athen. ii. p. 49.) A chair or 

 an altar of this kind must be understood when wo read that the Pythia 

 of Delphi gave her oracles from a tripod. We find also mention of 

 tri|xls containing a certain measure of fluid (Horn., ' II.,' xxiii. 264), 

 and in this cam: we lirvvc to understand a bowl resting upon a | 

 with three feet. The crater, or the vessel in which the wine was 



mixed with water at the banquets of the ancients, was very frequently 

 a tripod of this description. 



The ancients made much more frequent use of tripods than we, and 

 from their descriptions, as well as from the numerous representations 

 of tripods on medals, and from the specimens still extant, we see that 

 they were often most tastefully ornamented and of the most exquisite 

 workmanship. They were usually of metal, but sometimes also of 

 marble, and appear to have been made as much for mere ornament as 

 for use. A tripod seems to have been at Athens a usual reward to a 

 successful choragus. The tripod was connected with the worship of 

 several gods, and was one of their attributes ; but there is no deity in 

 whose worship tripods occur so frequently as in that of Apollo. 

 Accordingly the Pythia gave her responses from a tripod, tripods were 

 the most common presents (donaria) to his temples, tripods were given 

 to the victors in the games which were celebrated in honour of Apollo, 

 and tripods appear on innumerable coins which have any relation to 

 the worship of that god. Several fine tripods have been found at 

 Pompeii. (Mazois, Donaldson.) In the accompanying cut of a bas- 



relief on an altar found in the forum at Pompeii an altar tripod is 

 represented. Some tripods are preserved in the British Museum. 



TRIPTYCH, an altar-piece in three divisions. As mentioned under 

 RETABLE, altar-pieces were originally small and portable ; they being 

 carried with the other ecclesiastical utensils to the altar for the per- 

 formance of the service, and removed at its conclusion. The altar-pieco 

 usually comprised a representation of some event in the history of Christ, 

 or of an incident in the life of the saint to whom the altar was dedi- 

 cated. In their oldest form, these portable altar-pieces seem to have 

 consisted of two leaves or tablets of ivory or wood, like the larger 

 two-leaved tablets carried by the Roman consuls and other superior 

 officers, and like them they were called Diptychs. It is supposed that 

 this in fact was their origin ; the emperors having, when Christianity 

 was recognised and protected, sent to the bishops, as to other high 

 officers of the government, official diptychs, which, when they presided 

 at the mass, were displayed open at the altar as the insignia of their 

 office ; but if so, the practice probably early fell into desuetude, and 

 altar-pieces came to be commonly the gift of pious individuals or com- 

 missioned by wealthy communities, and they soon began to be made in 

 various forms and of very different materials. The most frequent 

 form was that of the Triptych, which consisted of a large central 

 division, in which the principal circumstance was set forth, and two 

 wings, fastened to the centre by hinges, so as when not in use to fold 

 over it like shutters. On the insides of these wings were usually repre- 

 sented circumstances subsidiary to] that shown in the central division, 

 or portraits of saints or of the donors of the altar-piece, &c. ; whilst 

 on the outside was the Annunciation, the Baptism, or some event sym- 

 bolising the initiation of the Christian religion, if the Crucifixion or 

 other crowning event were shown inside ; or, if the central picture 

 related to a saint, the exterior was commonly made in some way 

 correspondent. Sometimes there were more than three divisions, 

 when it was called a Polyptych. Most frequently these portable 

 altar-pieces are framed pictures ; but they are very commonly, espe- 

 cially the earlier ones, bas-reliefs carved in wood or ivory. Often they 

 are of inlaid-work, or marquetry, or of metal-work and enamel, the 

 latter being sometimes richly inlaid with gems. Of all these kinds, 

 and extending over a long range of years, there are many, and somo 

 very exquisite, examples in the South Kensington Museum, as well as 

 of those large carved and painted triptych retables which so generally 

 prevailed at a somewhat later date in Germany and the Low Countries. 

 [RETABLE.] When the altar-piece came to be treated as an important 

 architectural feature, and the paintings were much larger in size and 

 more important in character, the triptych form was long retained, 

 though, at least in Italy, the wings were no longer made to close over 

 tho centre, and certain supplementary parts were added. Of these, 

 examples, either entire (as in that of Jacob Casentius) or portions (as 

 those by Francia, Andrea Orcagna, &c.), may be seen in the National 

 Gallery. 



T1USECTION OF THE ANGLE. In the articles DUPLICATION 

 and QUADRATURE, we have given a slight outline of tho history of two 

 of those remarkable problems the solutions of which at one time 

 engaged the attention of the learned, and have not yet ceased to be the 

 ambition of a certain class of geometrical students. The trisection of 

 the angle is the third problem of this kind. 



The difficulty of cutting an angle into three equal parts is entirely 

 of that geometrical nature which has been alluded to in the articles 

 above cited. Euclid, who confines himself to the description of right 

 linen aud circles, could not by these only trisect an aa^le ; but a very 



