TRI 



TRI 



origin, and negative yrhen on the opposite 

 side. 



4. Trigonometrical Tables. There are 

 two kinds of trigonometrical tables. The 

 first kind contains the sines, cosines, &c. 

 of angles, calculated to the radius unity ; 

 the sines, cosines, tangents, and secants 

 in these tables to radius 1, are called 

 natural, to distinguish them from those 

 of the second kind, which are called arti- 

 ficial or logarithmic. By aid of the latter 

 tables, instead of multiplying natural 

 sines, &c., we need only add the loga- 

 rithmic sines, &c. ; and, instead of di- 

 viding a natural sine or cosine, &c. by 

 another, we need only subtract the loga- 

 rithmic sine, &c., which represents the 

 dividend. By these operations much 

 time and labour are saved. 



5. Trigonometrical Canon. This is a 

 table, which, beginning from one second 

 or one minute, orderly expresses the 

 lengths which every sign, tangent, and 

 secant have, in respect of the radius, 

 which is supposed unity; and is con- 

 ceived to be divided into 10,000,000 or 

 more decimal parts. And so the sine, 

 tangent, or secant of an arc, may be had 

 by the help of this table ; and, contrari- 

 wise, a sine, tangent, or secant being 

 given, we may find the arc it expresses. 



6. Trigonometrical Curves and Series. 

 The former are curves having such equa- 

 tions as ^ = sin x, y = cos x, y = a cos 

 X + bcos 2x, &c. The latter are infinite 

 series of the form a sin a: + b sin 2x + c 

 sin 3x + &c., and a cos x + b cos 2x + c 

 cos 3a; + &c. 



7. Trigonometrical Survey. The appli- 

 cation of trigonometry to geodetic opera- 

 tions, for topographical purposes, and 

 for measurements connected with gene- 

 ral geography and with the figure of the 

 earth. 



TRIGY'NIA (rpelf, three, '^wrj, a 

 ■woman). The name given by Linnaeus 

 to those orders of plants which have 

 three pistils. 



TRILLION. A million of billions, or a 

 million of million of millions. 



TRI'LOBITE (rpel?, three, \o/36r, a 

 lobe). An extinct crustacean animal, al- 

 most the sole representative of its class 

 in the periods which intervened between 

 the deposition of the earliest fossiliferous 

 strata and the end of the coal formation. 

 It ic named from the upper surface of 

 its body being divided into three lobes. 



TRI'MERA (rpelf, three, /xepof, a 

 part). A section of coleopterous insects, 

 in which only three ordinary- sized joints 

 346 



exist in the tarsi, the fourth being mi- 

 nute and indistinct. Latreille. 



TRIMYA'RIANS (rpel?, three, juuf, a 

 muscle). A designation of those bi- 

 valves which present three muscular im- 

 pressions on each valve. 



TRI'NGIDiE. A group of birds, dis- 

 tinguished from all others by the great 

 length, the slenderness, and the flex- 

 ibility of the bill, no less tbaii by the 

 delicacy of the legs and the smallness of 

 the hinder toe. The tringa, or sand- 

 piper, is the type of the group. They 

 belong to the family Scolopacidae. 



TRINO'MIAL. An algebraical name 

 for an expression consisting of three 

 terms, as o + b + c, or ax — bx^ + bx^. 



TRIPHANE. Spodumene. A silicate 

 of lithia and alumina, first discovered in 

 the island of Uton in Sudermannland, 

 where it is associated with red felspar 

 and quartz, and lately by Dr. Taylor in 

 the vicinity of Dublin. 



TRIPHYLINE. A phosphate of iron, 

 manganese, and lithia. 



TRIPl'NNATE ; TRITE'RNATE. 

 \. The former of these terms is applied 

 by botanical writers to a leaf in which 

 there are three series of pinnation, as 

 when the leaflets of a bipinnate leaf are 

 themselves pinnate. 2. The latter term 

 denotes a leaf in which there are three 

 series of ternation, as when the leaflets of 

 a biternate leaf are themselves ternate. 



TRIPLE SALTS. A term sometimes 

 applied, in chemistry, to salts in which 

 two bases are combined with one acid, as 

 soda and potassa with tartaric acid in 

 Rochelle salt. These compounds are, 

 however, more commonly viewed as 

 double salts, Rochelle salt being consi- 

 dered as composed of single equivalents 

 of the tartrates of soda and potassa. 



TRI'PLICATE RATIO. The compo- 

 sition of a ratio with itself twice : thus 

 the ratio of a^ to 63 is the triplicate of 

 the ratio of a to b. In other words, the 

 triplicate of a given ratio is found by 

 taking the cube of each of the terms of 

 the ratio. Thus, when it is said that 

 two similar solids, whose linear dimen- 

 sions are as 6 to 9, are in the triplicate 

 ratio of 6 to 9, it is meant that the con- 

 tents of these solids are in the ratio of 

 6 X 6 X 6 to 9 X 9 X 9, or 216 to 729. 



TRIPLITE. Phosphate of manga- 

 nese, found at Chanteloube, near Li- 

 moges, in the department of Haute 

 Vienne in France, where several other 

 mineral substances have lately been 

 found, the essential constituents of which 



