UND 
UNDECAGON, in geometry, is a po- 
lygon of eleven sides. If the side of a re- 
gular undecagon be 1, its area vvill be 
9.36564 nearly = ~ X 
4 
grees ; and therefore if this number be 
multiplied by the square of the side of aiy 
other regular undecagon, the product will 
be the area of that undecagon. 
UNDER currents, currents distinct from 
the upper or apparent currents of the seas. 
Some naturalists conclude that there are in 
divers places under currents which set or 
drive a contrary way from the upper cur- 
rent, whence they solve the remarkable 
phenomena of the sea’s setting strongly 
through the Streights into the Mediterra- 
nean, with a constant current twenty 
leagues broad ; as also, that running from 
the Eiixine throirgh the Bosphorus into the 
Hellespont, and thence into the Archipe- 
lago ; they conjecture, that there is an 
under current whereby as great a quantity 
of water is carried out as comes in. To 
confirm this, it is observed, that between 
the North and South Foreland, it is either 
high or low water upon the shore three 
hours before it is so off at sea; a certain 
sign, that though the tide of flood runs 
aloft, yet the tide of ebb runs under foot, 
or close by the ground. Yet Dr. Halley 
solves the currents setting in at the Streights 
without overflowing the banks, from the 
great evaporation, without supposing any 
under current. 
UNDERSr AN DING or June ment, in 
the Hartleyan acceptation ofthe terra, is that 
faculty by which w e contemplate mere sen- 
sations and ideas, pursue truth, and assent to, 
or dissent from, propositions. In this article, 
and in Words, we shall, as we proposed in 
Philosophy, mental, § 104, lay before 
our readers a view' of the highly important 
principles of Hartley respecting the under- 
standing, occasionally making in his state- 
ments such alterations as will 'best adapt 
them to our object. 
Whatever be the precise nature of assent 
and dissent, they must class with ideas, 
being only those very complex internal 
feelings which are connected by association 
with those groups of words which are called 
propositions |n general, or affirmations and 
negations in particular. — Assent (and conse- 
quently its opposite, dissent) may be distin- 
guished into two kinds, rational and practi- 
cal. Rational assent to any proposition 
niay be defined a readiness to affirm it to 
be true, proceeding from a close a.ssociation 
UND 
of the ideas suggested by the proposition, 
with the idea or internal feeling belonging 
to the word truth ; or of the terms of the 
proposition with the word truth. Rational 
dissent is the opposite to this. — Practical 
assent is a readiness to act in such a manner 
as the frequent vivid recurrency of the ra- 
tional assent disposes us to act and prac- 
tical dissent the contrary. 
Practical assent is then the natural con- 
sequence of rational assent, when suffici- 
ently impressed. It must liowever be ob- 
served, first, that some propositions, mathe- 
matical ones for instance, admit only of a 
rational assent, the practical not being ap- 
plied to them in common cases : secondly, 
that the practical assent is sometimes gene- 
rated, and arrives at a high degree of 
strength, wdthout any previous rational as- 
sent, and by methods which have little or 
no connection with it ; yet still is in general 
much influenced by it, and, conversely, ex- 
erts a great influence upon it : thirdly, prac- 
tical assent may be in opposition to rational 
assent, and in consequence of its having 
been long and firmly cultivated, may alto- 
gether prevent the latter from influencing 
the conduct. 
Let us next inquire into the causes of ra- 
tional and practical assent, beginning, I. 
with that given to mathematical conclu- 
sions. — Now the original cause that a per- 
son affirms the truth of the proposition, 
twice two are four, is the entire coincidence 
ofthe visible or tangible idea of twice two, 
with that of four, as impressed upon the 
mind by various objects. We see every 
where that both are only different names 
for the same impression ; and it can only 
be in consequence of association that the 
word truth, its definition, or internal feel- 
ing, becomes -appropriated to this coinci- 
dence — Where the numbers are so large 
that we cannot form any distinct visible ideas 
of them, as when wesay 12 times 12 are equal 
to 144 , rational assent is founded (if not on 
the authority of a table or a teachei-) on a 
coincidence of w'ords -arising from some me- 
thod of reckoning up 12 times 12, so as to 
conclude with 144, and resembling the co- 
incidence of words which attends the be- 
fore-mentioned coincidence of iijeas in the 
simpler numerical propositions.^Tlie ope- 
rations of addition, subtraction, multiplica- 
tion, division, and extraction of roots, with 
all tlie most complex operations relating to 
algebraic quantities considered as the de- 
notements of numbers, are no more than 
methods of producing this coincidence of 
