EUO 
arch B C. 2. The radius of the evolnte, 
CM, is perpendicular to the curve, AM. 
3. Because the radius, M C, of the evo- 
lute continually touches it, it is evident, 
from its generation, that it may be de- 
scribed through innumerable points, if the 
tangents in the parts of the evolnte are pro- 
duced until they become equal to their cor- 
responding arches. 4. The evolnte of the 
common parabola, is a parabola of the se- 
cond kind, whose parameter is §|, of the 
common one. 5. The evolute of a cycloid 
is another cycloid equal and similar to it. 
6. All the arches of evolute curves are 
rectifiable, if the radii of the evolute can be 
expressed geometrically. 
EVOLUTION. See Algebra. 
Evolution, in the art of war, the mo- 
tion made by a body of troops, when they 
are obliged to change their form and dispo- 
sition, in order to preserve a post, or occu- 
py another, to attack an enemy with more 
advantage, or to be in a condition of de- 
fending themselves the better. It consists 
in doublings, counter-marches, conversions, 
&c. A battalion doubles the ranks, when 
attacked in front or rear, to prevent its be- 
ing tlanked, or surrounded ; for then a bat- 
talion fights with a larger front. The files 
are doubled either to accommodate them- 
selves to the necessity of a narrow ground, 
or to resist an enemy which attacks them in 
flank ; but if the ground will allow it, con- 
version is much preferable, because, after 
conversion, the battalion is in its first form, 
and opposes the tile leaders, which are ge- 
nerally the best men to the enemy; and 
likewise, because doubling the files in a new 
or not well disciplined regiment, they may 
happen to fall into disorder. 
EVOLVULUS, in botahy, a genus of 
the Pentandria Tetragynia class and order. 
Natural order of Campanaceae. Convol- 
vuli, Jussieu. Essential character: calyx 
five-leaved; corolla five-cleft, rotate; cap- 
sule three-celled ; seeds solitary. There 
are seven species, all natives of the East or 
West Indies. 
EUONYMUS, in botany, English spin- 
dle-tree, a genus of the Pentandria Mono- 
gynia class and order. Natural order of 
Dumosas. Rhamni, Jussieu. Essential cha- 
racter : calyx five-petalled ; capsule five- 
sided, five-celled, five-valved, coloured ; 
seeds calyptred, or veiled. There are eight 
species. These are trees or shrubs ; the 
smaller branches or twigs four-cornered ; 
the leaves opposite ; peduncles axillary, so- 
EUP 
litary, opposite, one-flowered, sometimes 
inany-flow r ered, disposed in umbels. 
EUPAREA, in botany, a genus of the 
Pentandria Monogynia class and order. 
Essential character : calyx five-leaved ; co- 
rolla five or twelve petalled ; berry superior, 
one-celled ; seeds very many, adhering to a 
free receptacle. There is only one species, 
viz. E. amoena, a native of New Holland 
and Terra del Fuego. 
EUPATORIUM, in botany, English 
hemp agrimony, a genus of the Syngenesia 
Polygamia iEqualis class and order. Natu- 
ral order of Composite Discoideae. Corym- 
biferajj'Sussieu. Essential character : calyx 
imbricate, oblong; style cloven half-way, 
long ; down plumose ; receptacle naked. 
There are forty-nine species. These are 
mostly tall growing perennial herbaceous 
plants ; the greater part are natives of 
North America, many however from South 
America and the West Indies ; several are 
found wild in the East Indies, and one only 
in Europe. 
EUPHEMISM, in rhetoric, a figure 
which expresses things in themselves dis- 
agreeable and shocking, in terms implying 
the contrary quality : thus, the Pontus, or 
Black Sea, having the epithet i. e. 
inhospitable, given it, by reason of the sa- 
vage cruelty of those who inhabited the 
neighbouring countries, this name, by euphe- 
mism, was changed into that of Euxinus. 
In which signification nobody will deny its 
being a species of irony : but every euphe- 
mism is not irony, for we sometimes use im- 
proper and soft terms in the same sense 
with the proper and harsh. 
EUPHONY, in grammar, an easiness, 
smoothness, and elegance in pronunciation. 
Euphony is properly a figure, whereby we 
suppress a letter that is too harsh, and con- 
vert it into a smoother, contrary to the or- 
dinary rules : of this there are abundance of 
examples, in all languages. 
EUPHORBIA, in botany, English eu- 
phorbium, spurge, a genus of the Dodecan- 
dria Trigynia class and order. Natural 
order of Tricoce*. Euphorbias, Jussieu. 
Essential character: corolla four or five 
petalled, placed on the calyx ; calyx one- 
leafed, bellying ; capsule tricoceous. There 
are ninety-eight species.* These are milky 
plants, mostly herbaceous, a few shrubby, 
upright for the most part, very few of them 
creeping ; some are leafless ; stems angular 
or tubercled, or more frequently cylindric 
or columnar; unarmed, or in the angular 
