TIIA 
tions, and form him to an amble. Tt is a:so 
taken in many places for an iron moveable 
instrument in cliimnies, to hang pots ovet 
the tire. ' 
Tramei. net, is a long net wherewith to 
take fowl by night, in champaign cmmtries, 
much like the net used for the low bell, 
both in shape, bigness, and mashes. To use 
it, they spread it on the ground, so as the 
nether, or further end, fitted with small 
plummets, may lie loose thereon ; then the 
other part, being borne up by men placed 
at the fore ends, it is thus trailed along the 
ground. At each side are carried great 
blazing lights, iy which the birds are rais- 
ed, and as they rise under the net they are 
taken. 
TRAMMELS, in mechanics, an instru- 
ment used by artificers for drawing ovals 
upon boards. It consists, on one pat t, of 
a cross with two grooves at right angles ; 
the other is a beam carrying two pins which 
slide in those grooVes, and also the describ- 
ing pencil. Engines in general, intended 
for turning ovals, are constructed on the 
same principles with trammels : the only 
ditference is, that in the trammels the board 
is at rest, and the pencil moves upon it : in 
the turning engine, the tool which supplies 
the place of the pencil is at rest, and the 
board 'moves against it. See Lathe, and 
Turning., 
TRANSACTIONS, philosophical, a kind 
of journal of the principal things that come 
before the Royal Society of London. See 
Society. It appears, that the printing of 
these transactions was always, from time to 
time, the single act of the respective secre- 
taries of the Society, till the publication of 
the 47th volume, in 1753, notwithstanding 
it has been the common opinion, that they 
were. published by the authority, and under 
the direction, of the Society itself. The 
truth is, that the Society, as a body, never 
did interest themselves further in their pub- 
lication, than by occasionally recommend- 
ing the revival of them to some of their se- 
cretaries, when, from the particular circum- 
stances of their affairs, the transactions had 
happened for any length of time to be in- 
termitted, and this seems principally to 
have been done with a view to satisfy the 
public, that their usual meetings were then 
continued for the improvement of know- 
ledge, and benefit of mankind, the great 
' ends of their first institution ; but the So- 
ciety being of late years greatly enlarged, 
and their communications more numerous, 
tliey thought it advisable, that a commit- 
TRA 
tee of their members should be appointed 
to reconsider the papers read before them, 
and select out of them such as they should 
judge proper for publicalion in the future 
transactions, which was accordingly done 
upon the g6th of March, 1752. 
The tiansactions are now usually publish- 
ed in half volumes twice a year, and each 
member is entitled to receive one copy gra- 
tis, of every part published after his admis- 
sion into the Society. The volumes have 
lately been abridged by Ur. Hutton and 
others. Those published before the year 
1750, were abridged in eleven volumes, 
quarto, by Mr. Jones, Mr. Eames, and 
Mr. Martyn. 
TRANSCENDENTAL, or Transcen- 
DANT, something elevated or raised above 
other things ; which passes and transcends 
the nature of other inferior things. Trans- 
cendental quantities, among geometricians, 
are indeterminate ones, or such as cannot 
be fixed or expressed by any constant equa- 
tion : such are all transcendental curves, 
which cannot be defined by any algebraic 
equation ; or which, when expressed by an 
equation, one of the terms thereof is a va- 
riable quantity. Now whereas algebraists 
use to assume some general letters or num- 
bers, for the quantity sought in these trans- 
cendental problems, Mr. Leibnitz assumes 
general or indefinite equations for the lines 
sought ; e. gr. putting x and y for the ab- 
sciss and ordinate, the equation he uses for 
a line sought, is a-j-6a!-j-c2/-|-exy-f- 
fxx-\-gyy, &c. = 0 , by the help of which 
indefinite equation, he seeks the tangent; 
and by comparing the result with the given 
property of tangents, he finds the value of 
the assumed letters, a, h, c, d, he. and thus 
defines the equation of the line sought. 
If the comparison above-mentioned do 
not proceed, he pronounces the line sought 
not to be an algebraical, but a transcendeuc 
tal one. This supposed, he goes on to find 
the species of transcendency: for some 
transcendentals depend on the general di- 
vision or section of a ratio, or upon the lo- 
garithms ; others, upon the arcs of a circle ; 
and others, on more indefinite and com- 
pound enquiries. He therefore, besides the 
symbols, x and y, assumes a third, as v, 
which denotes the transcendental quantity ; 
and of these three, forms a general equation 
for the line sought, from which he finds the 
tangent, according to the differential me- 
thod, which succeeds even in transcenden- 
tal quantities. The result he compares with 
the given properties of the tangent, and s» 
