CAL 



CAL 



power, the exponent of which is varia- 

 ble, as xx\ ax. In order to difference an 

 exponential quantity, nothing else is re- 

 quired than to reduce ihe exponential 

 quantities to logarithmic ones, upon 

 which the differencing is managed as in 

 logarithmic ones. 



By the same method may be found the 

 difierential of an exponential quantity of 

 any power. This calculus was invented 

 by Mr. John Bournoulli, and is used in 

 . investigating the properties of exponen- 

 tial 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 differ- 

 entialis ; whence the English, who usu- 

 ally 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 differences to the sums, the 

 name of the inverse method of fluxions. 

 See FLUXIOW. 



CALEA, in botany, a genus of the Syn- 

 gynesia Polygamia JEqualis. Natural or- 

 der of Composite Oppositifolise. Corym- 

 biferae, Jussieu. Essential character : ca- 

 lyx imbricate ; down hairy, or none ; re- 

 ceptacle chaffy. There are seven species, 

 of which C. Jamaicensis has a shrubby 

 stem, six or seven feet high ; leaves hairy, 

 rugged, three-nerved ; flowers terminat- 

 ing, frequently three together; the pedi- 

 cles of the same length with the flowers ; 

 calyx coloured ; the pappus, or down, is 

 rugged, and as long as the flower. Native 

 of Jamaica, chiefly in the woods and in- 

 land parts of the island. 



CALENDAR, a distribution of time, 

 accommodated to the various uses of life, 

 but more especially such as regard civil 

 and ecclessiatical polity ; in which sense 

 it differs nothing from the modern al- 

 manacs. 



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 555 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 our nation 

 till the year 1752. This year is disposed 

 into quadrennial periods, of which the 

 three first years, which were called com- 

 mon, consisted of 365 days, and the fourth, 

 bissextile, of 366. See BISSEXTILE. 



The Julian account was afi erwards cor- 

 rected by Pope Gregory XIII., which on 

 that account obtained the name of the 

 Gregorian calendar, or new style, the Ju- 

 lian being called the old style: and though 

 the Gregorian calendar be preferable to 

 the Julian, yet it is not without its defects : 

 perhaps, as Tycho Brahe and Cassini ima- 

 gine, it is impossible ever to bring the 

 year to a perfect justness. 



CALENDAR, Julian 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 solor cycle ; and the new 

 and full moons, especially the paschal 

 full moon, with the feast of Easter, and 

 the other moveable feasts depending 

 thereon, by means of golden numbers, 

 rightly disposed through the Julian year. 

 See CTCLE, DOMINICAL LETTER, and GOLD- 

 EN 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 Gregorian calendar differs from the 

 Julian, both in the form of the year, and 

 in that epacts are substituted instead of 

 golden numbers. See EPACT. 



Dr. Playfair, in his " System of Chro- 

 nology," observes, that the method of in- 

 tercalation used in the Gregorian Calen- 

 'daris not the most accurate. Ninety-se- 

 ven days, or 100 3, are inserted in the 

 space of four centuries. This supposes 

 the tropical year to consist of 365 d , 5 h , 

 49', 12". On this supposition the inter- 

 polation would be exact, and the error 

 would scarcely exceed one day in 268,000 

 years. But the reformers of the calen- 

 dar made use of the Copernican year of 

 365d, 5''. 49', 20". Instead, therefore, of 

 inserting 97 days in 400 years, they ought 

 to have added, at proper intervals, 41 

 days in 169 years, or 90 days in 371 years, 

 or 131 in 540 years, &,c. Recent obser- 

 vations have determined the quantity of 

 the tropical year to be 365<J, 5*, 48', 45". 

 Admitting this to be the true quantity of 

 it, the intercalations ought to be made as 

 follows : 



-h - + h -f + + 4- + 



_4 17 33 _128_545 673 801 9_29 1057 1185 



T T 8 ' ~3? Ki2' 163' 199' 225' 256' 287* 



