EPI 
orb, or sphere, which being fixed in the 
deferent of a planet, is carried along with 
it ; and yet, by its own peculiar motion, 
carries the planet fastened to it round its 
proper centre. 
It was by means of epicycles, that Pto- 
lemy and his followers solved the various 
phenomena of the planets, but more espe- 
cially their stations and retrogradations. 
The great circle they called the excentric 
or deferent, and along its circumference 
the centre of the epicycle w as conceived to 
move ; carrying with it the planet fixed in 
its circumference, which in its motion down- 
wards proceeded according to the order of 
the signs, but, in moving upwards, con- 
trary to that order. The highest point of 
a planet’s epicycle they called apogee, and 
the lowest perigee. 
EPICYCLOID, in geometry, a curve 
generated by the revolution of the peri- 
phery of a circle, ACE (Plate V. Mis- 
cel. fig. 4.) along the convex or concave 
side of the peripiiery of another circle, 
DGB, 
The length of any part of the curve, 
that any given point in the revolving circle 
has described, from the time it touched the 
circle it revolved upon, shall be to double 
the versed sine of half the arch, which all 
that time touched the circle at rest, as the 
sum of the diameters of the circles, to the 
semidiameter of the resting circle, if the 
revolving circle moves upon the convex 
side of the resting circle ; but if upon the 
concave side, as the difference of the dia- 
meters to the semi-diameter of the resting 
circle. 
In the Philosoph. Transactions, No. 218, 
we have a general proposition for measuring 
the areas of all cycloids and epicycloids, 
viz. The area of any cycloid or epicycloid 
is to the area of the generating circle, as the 
sum of double the velocity of the centre 
and velocity of the circular’ motion to the 
velocity of the circular motion : and in the 
same proportion are the areas of segments 
of those curves to those of analogous seg- 
ments of the generating circle. 
EPIDEMIC. A contagious disease is so 
termed that attacks many people at the 
same season, and in the same place ; thus, 
putrid fever, plague, dysentery, &c. are 
often epidemic. Dr. James Sims observes, 
in the Memoirs of the Medical Society of 
London, that there are some grand classes 
of epidemics which prevail every year, and 
which are produced by the various ciianges 
nfj the seasons. Tims, spring is accompa- 
nied by inflammatory diseases; summer by 
EPI 
complaints in the stomach and bowels ; au- 
tumn by catarrhs ; and winter by inter- 
mittents : these being obviously produced 
by die state of weather attendant upon 
them, other epidemics are supposed analo- 
gous to them, and obedient to the same 
rules, which, on examination, not being 
the case, all further scrutiny is laid aside, 
perhaps too hastily. 
The most natural and healthful seasons 
in this country are a moderately frosty win- 
ter, showery spring, dry summer, and rainy 
autumn; and whilst such prevail, the wet 
part of them is infested by vastly the great- 
est proportion of complaints, but those not 
of the most mortal kind. A long succes- 
sion of wet seasons is accompanied by a 
prodigious number of diseases ; but these 
being mild and tedious, the number of 
deaths arc not in proportion to the co- 
existent ailments. Ou the other hand, a 
dry season, in the beginning, is attended 
witii extremely few complaints, the body 
and mind botli seeming invigorated by it ; 
if, however, this kind of weather last very 
long, towards the close of it a number of 
dangerous complaints spring up, which, as 
they are very short in their duration, the 
mortality is much greater than one would 
readily suppose from the few persons that 
are ill at any one time : and as soon as a 
wet season succeeds a long dry one, a pro- 
digious sickness and mortality come on uni- 
versally. So long as this wet weather con- 
tinues, the sickness scarcely abates, but 
the mortality diminishes rapidly ; so that in 
the last number of rainy years the number 
of deaths is at the minimum. The change 
of a long dry season, whether hot or cold, 
to a rainy one, appears to bring about the 
temperature of air favourable to the pro- 
duction of great epidemics. 'Some, how- 
ever, seem more speedily to succeed the 
predisposing state of the air, others less so ; 
or it may be that the state of air favourable 
to them exists at the very beginning of the 
change, whilst the state favourable to others 
progressively succeeds : of this last, how- 
ever, Dr. Sims is very uncertain. 
Two infectious diseases, it appears, are 
hardly ever prevalent together ; therefore, 
although the same distemperature of air 
seems favourable to most epidemic disor- 
ders, yet some must appear sooner, otiiers 
later. From observation and books, the 
Doctor describes the order in which these 
disorders have a tendency to succeed each 
other, to be plague, petechial fever, pu- 
trid sore throat, with or without scarlatina, 
dysentery, small-pox, measles, simple scar* 
