TxRA 
to the other side. See Algebra and 
Equation. 
TRAPA, in botany, water caltrops, a 
genus of the Tetrandria Monogynia class 
and order. Natural order of Hydrochari- 
des, Jussieu. Essential character : calyx 
four-parted ; corolla four-petalled ; nut girt 
with four opposite spines, which were the 
leaves of the caly-x. There are two spe- 
cies, viz, T. nataus, four-horned water cal- 
trops; and T. biconis, two-horned Vvater 
caltrops. 
TRANSVERSE, something that goes 
across another, from corner to corner : thus 
bends and bars, in heraldry, are transverse 
pieces or bearings : the diagonals of a pa- 
rallelogram or a square, are transverse 
lines : lines which make intersections with 
perpendiculars, are also called oblique or 
transverse lines. 
TRAP, in mineralogy, is a Swedish term 
signifying stair. It was first applied to de- 
signate a certain class of mountains, com- 
posed of nearly horizontal strata, with per- 
pendicular breaks, which were supposed to 
give a rude resemblance to a flight of stairs. 
Hence many species of rock, differing very 
much from each other, were called by the 
same name, which caused much confusion. 
According to Werner, there are three dis- 
tinct classes or formations of rocks to which 
the term trap may be applied : of these the 
first class belongs to the primitive moun- 
tains, the second to the transition moun- 
tains, and the third to the secondary moun- 
tains. Primitive traps are composed essen- 
tially of hornblende, mingled with felspar, 
and sometimes with pyrites and mica. Of 
rocks belonging to this formation there are 
four distinct species, viz. the common horn- 
blende, the schistose hornblende, primitive 
griiustein, and schistose griinstein. Tran- 
sition traps are composed principally of 
granular griinstein, but the mixture of the 
ingredients is more intimate, the grain is 
finer, and the mass appears more homoge- 
neous. There are two principal varieties, 
viz. 1. The amygdaloid, which is a rock of 
schistose hornblende in a state of semi-de- 
composition resembling fine ferruginous clay. 
It contains a number of globular cavities, 
from the size of a pea to that of a small ap- 
ple : of these cavities some contain nothing 
but air, and are coated on the inside with a 
kind of varnish ; others contain balls of 
calcareous spar, quartz, chalcedony, &c. 
The toadstone of Derbyshire is considered 
by Werner as belonging to this variety. 
S. Globular trap, composed of schistose 
TRA 
griinstein, in a state of semi-decomposition, 
arranged in spheroids of various magni- 
tudes, and composed of thick concentric 
lamellar distinct concretions. Secondary 
or floetz traps are divided into those which 
are peculiar and characteristic of it, and 
those which are accidental. The former 
are basalt, porphyry, &c. Among the lat- 
ter may be classed rubble and sandstone, 
clay, coal, and bituminous wood. The pro- 
per base to the secondary trap formation, 
or in other words the .substance, which ap- 
pears to have immediately preceded it in 
the order of formation, is secondary lime- 
stone ; it is not, however, not unfrequently 
found resting on sandstone, on argillite, on 
gn' iss, and even on granite. The general 
order in which the strata of this formation, 
is the following, uiz. coarse sand, fine sapd, 
sandy clay, unctuous clay, wakke, basalt, 
amygdaloid, porphyry, and grunstein. It 
hardly ever happens that all these strata 
are met with in the same mass of mountain. 
No metallic veins are found in this class 
ot mountains, but the remains of vegetable 
and marine organized bodies are of frequent 
occurrence. See Rock. 
TRAPEZIUM, in geometry, a plane 
figure contained under four unequal right 
lines. 1. Any three sides of a trapezium 
taken together, are greater than the fourth. 
2. The two diagonals of any trapezium, 
divide it into four proportional triangles. 
3. If two sides of a trapezium be parallel, 
the rectangle under the aggregate of the 
parallel sides and one half their distance is 
equal to that trapezium. 4. If a parallelo- 
gram circumscribes a trapezium, so that 
one of the sides of the parellelogram be pa- 
rallel to a diagonal of the trapezium, that 
parallelogram will be the double of the tra- 
pezium. 5. If any trapezium has two of 
its opposite angles, each a right angle, 
and a diagonal be drawn joining these an- 
gles; and if from the other two angles be 
drawn two perpendiculars to that diagonal, 
the distances from the feet of these perpen- 
diculars to those right angles, respectively 
taken, will be equal. 6. If the sides of a 
trapezium be each bisected, and the points 
ot bisection be Joined by four right lines, 
these lines will form a parallelogram, which 
will be one half of the trapezium. 7. If 
the diagonals of a trapezium be bisected, 
and a right line joins these points, the aagre- 
gate of the squares of the sides is equal to 
the aggregate of the squaies of the diago- 
nals, together with four times of the square 
of the right line joining the point of bisec- 
