TIME. 



to owf iti own itnmatcrial being to the creation of materia 

 order ; to have all iis portions meafnred l.y the periodical 

 motion, of matter, and yet to be diftind from, and inde- 

 pendent of, thofc motions for its exilK-nce, though it couM 

 not exill until they exiiLd : alfo that it operates upon every 

 thing, yet touclios nothing. Many other contradiftory 

 prop.'rties might be mentioned, but fuch tend t., darken 

 rather tlian to elucidate the fubjeit. Some philofophera 

 have gone even fo far as to deny the exiftence of time ; for 

 if there be no profent, there cannot be any future, and the 

 paft certainly has no exiftence. 



We now come to confider the application of mathe- 

 matics to time, asconneAed with allronomical computations, 

 where the fubjedt is accurately calculated, and rendered 

 fubfcr\-ient to tlie important purpofes of meafuring fpace, 

 by which the longitude is determined both in the heavens 

 and on earth. 



jljlronomical lime is diftinguiflied into folar or apparent 

 time, mean time, and fidereal time. 



Apparent time, alfo called true folar and ajlronomical time, 

 it regulated by the apparent motions of the fun. Mean or 

 mean folar time, alfo called equated time, is a mean or average 

 of apparent time : iaAfiJereal time is fhewn by the diurnal 

 revolutions of the fixed ftars. 



An apparent rlay is the interval between two fuccedive 

 tranfits of the fun's centre over the fame meridian, which 

 interval is fubjcft to continual variations, owing to the ec- 

 centricity of the earth's orbit, and the obliquity of the 

 ecliptic to the equator. Thefe variations are computed in a 

 table, for which fee Equation of Time. 



A mean day is the interval that would be obferved be- 

 tween two fuccedive tranfits of the fun's centre over the 

 fame meridian, if the earth's orbit were circular, and the fun 

 always in the equinoftial. Thus the intervals or tranfits 

 would be all equal, fuch as are fhewn by a clock that goes 

 exaftly 24 hours in a day, and 365* 5 ■■ 48"' 48' in a 

 year. A clock thus fet is faid to be adjufted to mean 

 time. 



KJidereal day is the interval between two fuccedive tran- 

 fits of a ftar over the fame meridian ; which interval is uni- 

 form, becaufe all the fixed ftars make their revolutions in 

 equal times, owing to the uniformity of the earth's diurnal 

 rotation on its axis. 



The fidereal day it fhorter than the mean folar day by 

 3" 56'. 55 fidereal time. Tliis difference arifes from 

 the fun's apparent annual motion from weft to eaft, which 

 leaves the ftar as it were behind. Thus, if the fun and a 

 ftar be obferved on any day to paft the meridian at the fame 

 inflant, the next day, when the ftar returns to the meridian, 

 the fun will have advanced about a degree eafterly (his 

 daily portion of the ecliptic) : and, as the earth's diurnal 

 rotation on its axis is from weft to eaft, the ftar will come to 

 the meridian before the fun, infomuch that at the end of the 

 year it will have gained a day on the fun, that is, it will 

 have paffed the meridian 366 times, while the fun will have 

 paffed it but 365 times. Now as the fun appears to per- 

 form his revolution of 360° in a year, fay, as 365 <i ^ >• 

 48"" 48' : 360° :: i" : 59' 8".3, which is the fpace the 

 fun would dcfcribe in a day, if all the days were of an equal 

 length ; and this fpace reduced to time, = 3' S^"-S5 = the 

 ticefs of a mean day above 3. fidereal day, in fidereal time, or 

 3' 55".9i in mean folar time. 



It therefore appears that the earth defcribes about its axil 

 M arc of 360° 59' 8".3 in a mean folar day, and an arc of 

 360° in 2. fidereal day ; therefore, as 360° 59' 8" : 360* :: 

 »4'' : »3 j6' 4".o9 = the length of a fidereal day in mean 



folar time, or the interval between two fuccefTive tranfits of 

 a ftar over the fame meridian. 



Hence the following general rule for converting fidereal 

 to mean time, and the contraiy : 



As 24'' : 23'' 56' 4".09 :: any portion of fidereal time 

 to its equivalent in meantime. And as 23'' 56' 4".09 : 

 24'' :: any portion of mean time to its equivalent in fidereal 

 time. Thus Tables I. and II. in our article Chronometbr 

 are computed. 



From what has been faid, it is evident that apparent and 

 mean time are tlic fame, with refpcft to the length of the 

 hour, minute, and fecond of each, as well as of the year } 

 but the hour, minute, and fecond of fidereal time are refpec- 

 tively lefs in the above proportion. It is only the folar and 

 mean days that differ, and this variation is marked by the 

 times of commencement. Thus the apparent day always 

 begins when the fun's centre is on the meridian ; but the 

 mean day commences fometimes fooner and fometimes later, 

 as computed in the tables of the equation of time. See 

 Equation of Time. 



The reduaion of time, that is, to turn apparent, mean, and 

 fidereal time into each other, may be performed by the fol- 

 lowing theorems, taken from Kelly's Spherics, p. 208, ed. 4. 



Let A = apparent time. 

 M = mean time. 

 S = fidereal time. 



E = the equation of time at apparent noon. 

 e r= the daily difference of the equation of time. 

 R = the fun's right afcenfion at apparent noon. 

 r = the daily increafe of the fun's right afcenfion. 

 N = the fun's mean right afcenfion at mean noon, 



;. e. the fidereal time at mean noon. 

 m = the reduction of fidereal time at the rate of 



3' 55".9i for 24 hours fidereal time. 

 3 = the reduction of mean to fidereal time, at the- 

 rate of 3' S&'-SS ^°^ ^4 lioui"S mean time. 

 And let + fignify that addition or fubtraftion which is to 

 be ufed according as the quantity under coa- 

 fideration is increafing or decreafing. 

 Alfo let A' = M + E, as applied in cafe 2. 



Formulae for the Reduftion of Time. 



Cafe, 



. M 



Given. 



A 



M 



Req". 



Solution. 



M 



M 



M = A+E -(- 



A X < 



24 



A'4- 



A'x 



— 24±f 



S = N4- M-f-/ 



M=S-N 



S = A+^^^^+R 



A A=S-R- 



S- R X r 



24 + r 



The 



