CAL 
xler different names, the latter given by Sir 
Isaac Newton, and the former by Mr. Leib- 
nitz, who disputes with Sir Isaac the ho- 
nour of the discovery. There is, however, 
one difference between them, which con- 
sists in the manner of expressing the dif- 
ferentials of quantities ; Mr. Leibnitz, and 
most foreigners, express them by the same 
letters as variable ones, prefixing only the 
letter d : thus the differential of x is called 
d X, and the differential of y, dy : and d x 
is a positive quantity if x continually in- 
crease; and a negative quantity if x de- 
crease. We, on the other hand, following 
Sir Isaac Newton, instead of da;, write x, 
(with a dot over it), and instead of d y, y. 
But foreigners reckon this method not so 
commodious as the former, because if dif- 
ferentials were to be differenced again, the 
dots would occasion great confusion ; not to 
mention, that printers are more apt to over- 
look a point than a letter. See Fcuxtons, 
Calculus exponentialis, among mathe- 
maticians, a method of differencing expo- 
nential quantities, and summing up the dif- 
ferential^ of exponential quantities. By an 
exponential quantity is meant a power, the 
exponent of which is variable, as x”, a*. In 
order to difference an exponential quantity, 
nothing else is required than to reduce the 
exponential quantities to logarithmic ones, 
upon which the differencing is managed as 
in logarithmic ones. 
By the same method may be found the 
differential of an exponential quantity of 
any power. Tliis calculus was invented by 
Mr. John Bournoulli, and is used in investi- 
gating the properties of exponential curves. 
Calculus integralis is a method of sum- 
ming up differential quantities ; that is, from 
a differential quantity given, to find the 
quantity from whose differencing the given 
differential results. 
It is the inverse of the calculus differen- 
tialis ; whence the English, who usually call 
the differential method fluxions, give this 
calculus, which ascends from the fluxions to 
the flowing quantities ; or, as Wolfius and 
other foreigners express it, from the dif- 
ferences to the sums, the name of the in- 
verse method of fluxions. See Fluxion. 
CALEA, in botany, a genus of the Syn- 
gynesia Polygamia jEqualis. Natural or- 
der of Compositoe Oppositifoliae. Corym- 
biferae, Jussieu. Essential character ; calyx 
imbricate ; down hairy or none ; recepta- 
cle, chaffy. There are seven species, of 
which C. Janiaicensis has a shrubby stem, 
six or seven feet high ; leaves hairy, rugged, 
three-nerved ; flowers terminating, fre- 
CAL 
quently three together ; the pedicles of the 
same length witli the flowers ; calyx co- 
loured ; the pappus, or down, is rugged, 
and as long as the flower. Native of Ja- 
maica, chiefly in tlie woods and inland parts 
of the island. 
CALENDAR, a distribution of time, 
accommodated to the various uses of life, 
but more especially such as regard civil and 
ecclesiastical polity ; in which sense it dif- 
fers nothing from the modern almanacs. 
The first calendar was made by Romu- 
lus, who divided the year into 10 months 
only, beginning on the first day of March, 
and containing 304 days, in which time he 
imagined the sun performed his course 
through all the seasons. 
This calendar was reformed by Numa 
Pompilius, who added two months more, 
viz. January and February, placing them 
before March : his year began on the first 
of January, and consisted of 355 days. 
This was afterwards improved by Julius 
Caesar, and was by him called the Julian 
account, which reduced the year to 365 
days, 6 hours ; and was retained in most 
protestant countries, and in aur nation till 
the year 1752. This year is disposed into 
quadriennial periods, of which the three 
first years, which were called common, 
consisted of 365 days, and the- fourth bis- 
sextile, of 366. See Bissextile. 
The Julian account was afterwards cor- 
rected by Pope Gregory XIII., which on 
that account obtained the name of the Gre- 
gorian calendar, or new style, the Julian be- 
ing called tlie old style : and though the Gre- 
gorian calendar be preferable to the Julian, 
yet it is not without its defects : perhaps, 
as Tycho Brahe and Cassini imagine, it is 
impossible ever to bring the year to a per- 
fect justness. 
Calendar, JuKun Christian, that where- 
in the days of the week are determined by 
the letters A, B, C, D, E, F, G, by means 
of the solar cycle ; and the new and full 
moons, especially the paschal full moon, with 
the feast of Easter, and the other move- 
able feasts depending thereon, by means of 
golden numbers rightly disposed through the 
Julian year. See Cycle, Dominical Let- 
ter, and Golden Number. 
Calendar, Gregorian, that which, by 
means of epacts rightly disposed, through 
the several months, determines the new and 
full moons, and the time of Easter, with 
the moveable feasts depending thereon, in 
the Gregorian year. Therefore the Gre- 
gorian calendar differs from the Julian, both 
in the form of the year, and in that epacts 
