T E I 
T R I 
T R I 
S2<5 
sons who destroy sea-marks, and to get repa- 
ration of such damages ; and to take care of 
other things belonging to navigation. At 
present, many gentry and some nobility are 
members of that community. 
The master, wardens, and assistants of the 
trinity-house, may set up beacons, and marks 
for the sea, in such places near the coasts or 
forelands, as to them shall seem meet. By a 
statute of queen Elizabeth, no steeple, trees, 
or other things standing as sea-marks, shall 
be taken away or cut down, upon pain that 
every person guilty of such offence, shall tor- 
lei t TOO/. and- if the person offending is not 
possessed of the value, he shall be deemed 
convict of outlawry. 
Trinity, fraternity of, a religious so- 
ciety instituted at Rome by St. Philip Neri, 
in 1548. These religious were appointed to 
take care of the pilgrims who came to visit 
the tombs of St. Peter and St. Paul. r l be 
society originally consisted of only 15 re- 
ligious, who assembled on the lirst Sunday of 
every month, in the church of St. Saviour del 
Campo, to hear the exhortations of the 
founder; after whose deatli pope Paul IV. 
gave the fraternity the church of St. Bene- 
dict, near which they have since built a large 
hospital, for the reception of pilgrims. The 
fraternity is one of the most considerable in 
Home, and most of the nobility of both sexes 
have been members ol it. 
TRINOMIAL, or Trinomial root, in 
malhemathics, is a root consisting of three 
parts connected together by the signs + or 
— , as x -j- y -)- z, or a 4- b — c. See Bin o- 
mial and Hoot. 
TRIO, in music, a part of a concert 
wherein three persons sing ; or more pro- 
perly, a musical composition consisting of 
three parts. Trios are the iinest kinds of 
composition, and these are what please most 
in concerts. 
TIUOPTERIS, a genus of the decandria 
trigvnia class of plants, the corolla whereof 
.consists of six oval, erectopatulous, equal and 
permanent petals, surrounded by three others, 
smaller than themselves, but equal to one 
another; there is no pericarpium ; the seeds 
are three, erect, and carinulated at the back, 
each of them has externally at its base an ala, 
and at its apex two ; these ala are what in 
the flowering state of the plant appear to be 
petals, but they are not truly such. There 
are two species, shrubs oi the West Indies. 
TRIOSTEL1M, a genus of the pentandria 
monogyuia class and order of plants. The 
-calyx is the length of the corolla; corolla 
one-petalled, almost equal ; berry three- 
celled, unequal ; seeds solitary. There are 
three species, herbs of North America. The 
roots are said to be emetic. 
TRIPLARIS, a genus of the dioceia dode- 
candria class and order. The calyx is very 
large, three or six-parted; corolla three-pe- 
talied ; nect. threeTided. There are two 
species, trees of South America. 
TRIPLE, or Triple Time, in music, a 
time consisting of three measures in a bar; 
the two first of which are beaten with the hand 
or foot down, and the third marked by its ele- 
vation. There were formerly in use no less 
than six different triple measures: first, that 
of three breves in a bar, denoted by the figure 
3 ; secondly, that of three semibreves in a bar, 
3 
the sign of which was ^ ; thirdly, that of three 
minims in a bar, marked by ^ ; fourthly, that 
of three crotchets in a bar, implied by /( ’ 
fifthly, that of three quavers in a bar, sig- 
nified by g ; and, sixthly, that of three semi- 
quavers in a bar, expressed by But at 
present we only employ three different triples; 
that of three minims, that of three crotchets', 
and that of three quavers. The reader be- 
ing informed that the semibreve (which is 
now .the longest note in common use, and 
therefore made the common standard of 
reckoning), is equal in duration to two minims, 
or to four crotchets, or eight quavers, will 
readily comprehend the propriety of announ- 
cing these different measures by the above 
figures ; and will perceive that, to indicate a 
time of three minims in a bar (z. e. three 
halves, or second parts, of a semibreve), no 
method more concise or simple could be 
adopted, thanjthat of placing at the beginning 
3 
of the movement the figures 0 ; for a time 
of three crotchets (i. e. three-fourth parts of 
a semibreve), the figures \ ; and for a time 
of three quavers (i. e. three-eights of a semi- 
3 
breve), the figures g. 
The old musicians considered the triple, or 
three-timed measure, as superior to the 
binary, or two-timed, and for that reason 
called it the perfect time. 
Triple progression, an expression in 
old music, implying a series of perfect fifths. 
A progression of sounds thus explained by 
theorists : let any sound be represented by 
unity, or the number 1 ; and as the third 
part of a string has been found to produce 
the twelfth, or octave of the fifth above the 
whole string, a series of fifths may be repre- 
sented by a triple geometric progression of 
numbers, continually multiplied by 3 ; as 1, 
3, 9, 27, 81, 243, 729 ; and these terms may 
be equally supposed to represent twelfths, or 
fifths, either ascending or descending: for 
whether we divide by 3, or multiply by 3, 
the terms will either way be in the proportion 
of a twelfth, or octave to the fifth. 
TRIPLICATE ratio, the ratio which 
cubes bear to one another. 
This ratio is to be distinguished from triple 
ratio, and may be thus conceived. In the 
geometrical proportions 2, 4, 8, 16,32, as the 
ratio of the first term (2) is to the third (8) 
duplicate of the first to the second, or of the 
second to the third, so the ratio of the lirst to 
the fourth is said to be triplicate of the ratio 
of the first to the second, or of that of the 
second to the third, or of that of the third to 
the fourth, as being compounded of three 
equal ratios. See Ratio. 
TRIPOLI, a mineral found sometimes in 
an earthy form, but more generally indurated. 
Its texture is earthy. Specific gravity 2to2.5. 
It absorbs water, feels harsh and dry. Scarce- 
ly adheres to the tongue; takes no polish 
from the nail ; does not stain the fingers. 
Colour generally pale yellowish grey ; also 
different kinds of yellow, brown, and white. 
According to Klaproth, a species of this mi- 
neral contained 
66.5 silica 
7.0 alumina 
2.5 oxide of iron 
1.5 magnesia 
1.25 lime 
19.0 air 
§7.75. 
TRIPSACUM, a genus of the moneecia 
triandria class and order of plants. The male 
calyx isa glume, four-flowered; corolla, glume 
membranaceous ; female calyx, glume per- 
forated sinuses ; corolla, glume two-valved; 
sty les two ; seed one. There are two ‘spe- 
cies, grasses of she West Indies. 
TRISECTION, or Trissection, the dividing 
a thing into three. The term is chiefly used in 
geometry, for the division of an angle into three 
equal parts. The trisection of an angle geome- 
trically, is one of those great problems whose 
solution has been so much sought by mathema- 
ticians for these two thousand years, being in 
this respect on a footing with the quadrature of 
the circle, and the duplicature of the cube angle, 
The cubic equation by which the problem c 
trisection is resolved, is as follows : Let c denote 
the chord of a given arc, or angle, and x the 
cord of the 3d part of the same, to the radius 1 : 
then is x 3 — Sx — — c, 
by the resolution of which cubic equation is 
found the value of x, or the chord of the 3d 
part of the given arc or angle, whose chord is 
c ; and the resolution of this equation, by Car- 
dan’s rule, gives the chord 
m _ 3 / -c + yT-4 1 
2 3 j £-|-yV 4 
_ V ~~ 2 ' 
or x = lJ~ C+Vc2 .-^+ 3 /r-lZA /7 =J 
V 2 ~ f 2 
TRTSETOUS, in entomology, three- 
bristled, applied chiefly to the tail of insects, 
as in the ephemera. 
TRISPAST, in mechanics, a machine witl 
three pullies, or an assemblage of thief 
pullies for raising of great weights. 
TRITICUM, wheat, a genus of plants o 
the class triandria, and prder digynia, and ir 
the natural system ranging under the fourtl 
order, gramina. The calyx is bivalve, soli 
tary, and generally containing three florets 
the corolla is bivalve, one valve being blunt 
ish, the other acute. There are 19 species 
the sestivum, summer or spring wheat; by 
bernum, winter, Lannnas, or common wheat 
compositum, turginum, or cone wheat ; polo 
nicum, or Polish wheat; spelta, or spel 
wheat ; monococcum, or one-grained wheat 
prostratum, or trailing wheat-grass ; pumi 
lum, or dwarf wheat-grass : junceum, or nisi 
wheat-grass ; repens, or couch-grass ; tenellum 
or tender wheat-grass; maritimum, or sej 
wheat-grass ; unilaterale, or spiked sea-wheat 
unioloides, or linear-spiked wheat-grass ; dis 
tichum, loliaceum, caninum, hispanicum. O 
what country the first six species are natives 
cannot now be derermined: the prostratul 
is a native of Siberia ; the junceum, repens 
unilaterale, and maritimum, are natives o 
Britain ; the tenellum is a native of Spain 
and the unioloides is a native of Italy. It ma- 
also be observed, that the first nine are aii 
nuals, the rest are perennials. 
Linnaeus comprehends the different kind 
of wheat cultivated at present under six spe 
cies ; but cultivation has produced a grea 
many varieties from these. 
