6)3 
T II I 
T R I 
]ar from the angle upon the base. 33. In 
the same triangle, viz, having one angle equal 
to 120', the difference ot’ the cubes of the 
sides about that angle, is equal to a solid con- 
tained by the difference of the sides and the 
square of the base ; and the sum of the cubes 
of the sides is equal to a solid contained by the 
sum of the sides and the difference between 
the square of the base and twice the rectan- 
gle of the sides. 
TRIANGULAR COMPASSES, are such 
as have three legs, or feet, whereby to take 
off any triangle at once ; much used in the 
construction of maps, globes, &c. 
TRIANGULAR NUMBERS, are a kind of 
polygonal numbers . being the sums of arithme- 
tical progressions, which have 1 for the common 
difference of their terms. 
Thus, from these arithmetical 1 2 3 4 5 6, 
are formed the triang. numb. 1 3 6 10 15 21, 
or the third column of the arithmetical triangle 
abovementioned. ■ 
The sum of any number n of the terms of the 
triangular numbers, 1,. 3, 6, 10, &c, is — 
n' . n 2 n n n -4- 1 n -4- 2 
J or — X — - — X — - — 
6' 2 ' 3 1 2 3 
which is also equal to the number of shot in a 
triangular pile of balls, the number of rows, or 
the number in each side qf the base, being n. 
The sum of- the reciprocals of the triangular 
series, infinitely continued, is equal to 2 ; viz., 
1 + j i + To J r tV & c = 2 - 
For the rationale and management of these 
numbers, see Simpson’s Algebra, sect. 15. 
TRIANGULAR CAN ON, the, tables of 
artificial sines, tangents, secants, See. 
TRIANGULAR QUADRANT, is a 
sector furnished with a loose piece, whereby 
to make it an equilateral triangle. 
The calendar is graduated thereon, with 
the sun’s place, declination, and other useful 
lines; and by the help of a string and a plum- 
met, and the. divisions graduated on the loose 
piece, it may be made to serve for a qua- 
drant. 
TRIANTHEMA, a genus of the class and 
order decandria digynia. The calyx is mu- 
cronate below the tip ; no corolla ; stamina 
5 or 10; germ, retuse ; capsule cut round. 
There are seven species. 
TRIBULUS, caltrops, a genus of the de* 
eandria-monogynia class of plants, the corolla 
of which consists of five oblong, obtuse, and 
patent petals: its fruit is of a roundish figure 
and aculeated, being composed of five cap- 
sules, gibbous- on one side, and armed with 
three or four points on the other, angulated 
and convergent ; and containing numerous 
seeds, turbinated and oblong. There are 
four species. 
TRICEPS. See Anatomy. 
TRICERA, a genus of the class and or- 
der inonoecia tetrandria. There is no co- 
rolla ; the male is four-leaved; filaments four, 
ovate; female calyx five-leaved; styles co- 
nical ; capsules three, horned, three-celled. 
There is one species, a shrub of Jamaica. 
TRICHECHUS, walrus, a genus of qua- 
drupeds of the order bruta. The generic 
character is, fore-teeth (in the full-grown 
animal) none either above or below ; tusks 
solitary, in the upper jaw ; grinders with 
wrinkled surfaces ; lips doubled; hind feet at 
the extremity of the body, uniting into a fin. 
The genus trichechus vs entirely marine, 
5 
T R l 
and contains but three species, besides varie- 
ties : of these the principal is the trichechus 
rosmarus, or, as it is sometimes called, the sea- 
horse, or walrus. 
1 . Trichechus rosmarus, arctic walrus. This 
animal inhabits the northern seas, and is prin- 
cipally found within the arctic circle. It 
grows to a very large size, having been some- 
times seen of the length of eighteen feet, 
and of such a thickness as to measure twelve 
feet round the middle of the body. The 
walrus is oi an inelegant form ; having a small 
head, short neck, thick body, and short legs: 
the lips- are very thick, and the upper lip is 
indented or cleft into two large rounded lobes: 
over the whole surface of this part are scat- 
tered numerous semitransparent bristles, of a 
yellowish tinge, and of such a thickness as 
almost to equal a straw in diameter: they 
are about three inches long, and are slightly 
pointed at their extremities; the eyes are 
small : instead of external ears there are only 
two small, round orifices ; the skin on the 
whole animal is thick, and more or less wrinl> 
led and is scattered over with short brownish 
hair: on each foot are five toes, all connect- 
ed by webs, and on each toe is a small nail: 
the hind feet are considerably broader than 
the fore feet: the tail is extremely short. In 
the upper jaw are two large and long tusks, 
bending downwards: there are no cutting- 
teeth ; but in each jaw, both above and below, 
are four roundish grinders with fiat tops: the 
tusks are'sometimes upwards of two feet in 
length, but are more generally of about one 
loot long : and it sometimes happens that the 
two tusks are not perfectly equal in length, 
d lie chief resorts of the walrus are the seas 
about the northern parts of America. They 
are found in the gulph of St. Laurence accord- 
ing to Mr. Pennant, between latitude 47 and 
48. They are also found in Davis’s Straits and 
within Hudson's Bay, lat. 62. They inhabit 
the coast of Greenland ; and are found in 
great numbers about Spitsbergen, and on the 
Boating ice in those parts.. They occur like- 
wise on the coasts of Nova Zem’bla, and on 
the headlands stretching towards the north 
pole. 
They are gregarious animals, and are some- 
times seen in vast multitudes on the masses of 
floating ice so frequent in the northern seas. 
4 hey are said to produce their young- early in 
the spring, and rarely bring more than one 
at a birth : their food consists of sea-plants, 
shell-fish, &c. 
The wal rus is a harmless animal, unless pro- 
voked or attacked, in which case it becomes 
furious, and is extremely vindictive. When 
surprised upon the ice, the female is said first 
to provide for the safety of the young, by 
Hinging. it into the sea, and immediately pre- 
cipitating itself after it ; carrying it to” a se- 
cure distance, and then returning, with great 
rage, to revenge the injury. They will some- 
times attempt to fasten "their teeth on the 
boats, with an intent to sink them ; or rise in 
numbers under them to overset them ; at the 
same time shewing all the marks of rage, by 
roaring in a dreadful manner, and gnashing thei r 
teeth with great violence ; if once thoroughly 
irritated, the whole herd will follow the boats 
till they lose sight of them. They are 
strongly attached to each other ; and it is said 
that a wounded walrus has been known to 
sink to the bottom, rise suddenly up again. 
and bring with it multitudes of others, which 
have united in an attack upon the boat whence 
the insult came. 
'The teeth of the walrus are used as ivory ; 
but on this subject authors seem to' vary con- 
siderably ; some representing them as supe- 
rior to common ivory, and others greatly in- 
ferior, and more subject to turn yellow. 
The. animals are now killed chiefly for the 
sake of the oil ; and it is said thata very strong 
and elastic leather may be prepared from the 
skin. See Plate Nat.’Hist. fig. 4C4. 
2. Trichechus dugong, Indian walrus. Tins , 
species is a native of the seas about the Cape 
of Goad Hope and the Philippine islands. It 
does not, however, seem to be very clearly*] 
known to naturalists'. The grinders differ 
from those of the walrus, being broader hi pro- 
portion : ot these there are four on each side 
m lire upper jaw, and three in the lower. The 
head is said to be of a sharper or nar- 
rower form. This species, in the Philippine 
Islands, is said to be called by the name of 
dugung. 
3. Trichechus borealis, manate or whale- 
tailed trichechus. This animal seems to ap- 
proach so nearly to the cetaceous or whale 
tribe, as scarcely to deserve, according to Air. 
Pennant, the name even of a biped ; what are' 
called the feet being little more than pectoral 
fins, which serve only for swimming, and are ne- 
ver used to assist the animal either in walking 
or landing; for it never goes ashore, nor e- . 
ver attempts to climb the rocks like the walrus ’ 
and the seal. It brings forth in the water, 
and, like the whale, suckles its young in that 
element. Like the whale, it is also destitute 
qf voice ; and has also a horizontal tail, which 
is broad, and of the form of a crescent, with- 
out even rudiments of hind feet. 
So complete is the account given by Mr. 
Pennant ot this animal, that we shall here deli- 
ver the most material parts of that author’s, 
description, rather than attempt a new one. 
It inhabits the seas about Berings. and the 
other Aleutian islands, which intervene be-, 
tween Ivamtschatka and America, but never 
appears off Kamtschatka, unless blown ashore 
by . a tempest. It is probably the same spe- 
cies which is found above Mindanao, but is 
certainly that which inhabits near Rocliguez, 
vulgarly called Diego Keys, an island to the 
east of.Mauritius, or the Isle of France, near' 
which it is likewise found. It is also probable- 
that it extends to New Holland. They, live 
perpetually in the water, and frequent the 
edges of the shores; and, in calm weather,, 
swim in great droves near the mouths of ri- 
vers: in the time of flood they come so near 
the land that a person may stroke them with 
his hand: if hurt, they swim out to the sea, 
but presently return again. They live in fa- 
milies, one near another; each consists of a 
male, a female, a half-grown young one, and 
a very small one. The females oblige the 
young to swim before them, while the other 
old ones surround, and, in a manner, guard 
them on all sides. The affection between the 
male and female is very great ; for if she is at- 
tacked, he will defend’ her to the utmost ; and 
if she is killed, will follow her corpse to the 
very shore, and swim for some days near the 
place it has been landed at. 
They are vastly voracious, and feed not 
only on the fuci that grow in the sea, but such 
as are flung on the edges of the shore. When 
