\

3J2- ASTRONOMY.

equation vanishes, but the meridian of the place will come to thestar T six liours sooner than to the Sun . In the quadrant B =e=the meridian of the real Sun for the season above-mentioned isnearer =n= than the meridian of the fictitious Sun is, hence it isnoon by a true-going clock, before it is noon by the Sun . At =£=they come together again, and both shew equal June. Here themeridian of the places comes to the star at twelve liours beforeit comes to the Sun at In like manner the Sun is at t whentire fictitious'Sun lias come to o on the lower side, hence in thisquadrant the solar noon precedes noon hv the clock, till at thewinter-solstice th?y are on the same meridian at ]> and E, wherethey shew equal lime, but are nine hours later than tiie star at ty.Thus also frym E to <y> the meridian of the place comes to thefictitious sooner than to the real Sun , when at qr> they are togetheragain, having lost a day in respect of the time measured by therevolution of the meridian to a star, from this explanation itappears that at the cardinal points of the ecliptic, viz. at the firstdegree of the signs ly, S5, and yy, or on the 21st of March,21st of June,’23rd of September, and 21st of December, the SunMiews the time as measured by a well-regulated clock ; in thespring and autumn quarters, the solar time precedes the time by theclock, but in the summer and winter quarters the time by theclock precedes the solar. Here we have supposed the Sun ’s mo-tion equable, which is not the real case, for the Earth is in aphe-lion, or at its greatest distance from the Sun , outlie first of July,or when the Sun is in the 9th degree of Cancer, as at zu, wherehis motion is slowest; and in the opposite point at v, the Earth is at its least distance from the Sun , and moves with its greatestvelocity; at t o the Sun is said to he in apogee, at e in perigee,in which points the Sun ’s place is the same as it would he if hismotion were equable; blit from w to v, the true plaee is not soforward as the mean ; and from t to zv the true place is forwarderthan the mean ; hence when the above-mentioned fictitious Sun ,and tbe Sun moving equably in the ecliptic, are at <y, the Sun ’strue place will be forwarder than <y, and the clock will be beforethe Sun. At some distance from <y, suppose when tile Sun ’s meanplace is at it, the fictitious and real Sun will be on the samemeridian PtrsS, where the inequality from the Earth ’s motioncounter-balances that arising from the obliquity of the ecliptic.'Ellis takes place, on the 13th of April; trom this the Sim will bebefore the clock, till the 1 (3th of June, when lie is almost ad-vanced to B. The clock will be again before the Sun till the31st of August, when the mean place being d, the true place shallbe on the same meridian Pe AS with the fictitious Sun . Fromthis time the Sun will lie faster than the clock till the 24th ofDecember, when lie arrives at some point between E and r,where the inequalities from the Sun ’s apparent motion, and theobliquity of tiie ecliptic, are the same on contrary parts. Hencethe difference between tiie Sun ’s longitude ami right ascension,and also the difference between his true and mean motion beingfound, we have only to add or subtract these differences accord-ing to the situation of the Sun above explained, and we obtainthe true equation of time. On these principles the equation talliesare calculated.

(220.) The following concise Table for the noon of every oilierday in the year, adapted to the first, second, and third years afterBissextile, and also for leap-year,' will never vary from tiie truthmore than about five seconds of.time throughout tiie present ceu-turv ; and in a great majority of cases the error will not amountto fialf that quantity. N. B. The compound sign T shews thatthe tabular equation is to be subtracted irom equal time to reduceIt to'apparent ; and added to apparent, to reduce it to mean orclock-time. But the sign i denotes that the tabular equation mustbe add<'d to equal time to hud out the apparent, ami subtractedfrom tiie apparent to find out the mean. Or, in other words, theupper sign must he made use of in the reduction of mean time toapparent, and tiie under sign in the reduction of apparent to mean.'J 1ms, to regulate a clock or watcii on tiie noon ot tiie :1th ofJanuary, in leap-year, the cluck or watcii must be put 5m. 24s.before the instant marked by a true sun-dial: and if we wouldwish to know what apparent time correspond'd to tiie mean noon ofthe 27th oi October, m tiie first year after Bissextile,we find by the'l’able that lam. 58s. must lie added to twelve o’clock ; i. e. that15m. 53s. past noon, apparent time, is the same with tw elve o’clock,mean lime. But if the exact moment for which you want to knowthe dillbrence between the apparent and mean' time cannot ‘he

6 '

found in (lie Table, it may be readily obtained by tiie Rule ofThree, by saying, 48 liours, is to the difference of the equation ift48 hours, as tiie quantity that the required time is after tiiat in theTaiile immediately preceding it, is to a quantity which added orsubtracted according as tiie equation is increasing or decreasing,tiie sum or difference will he the true equation of time required.

Example I. Required the apparent time corresponding to half-past ten of the night of Sept. 2nd, 1830; it being tiie second afterBissextile.

In the 'Fable for Sept. !, in the second year after Bissextile, ((In;tabular time immediately preceding the required time,) the equa-tion of the mean time is -j- 0m. 2s. and two days after the equa-tion is increased to 0m. 40s. therefore 48 hours is to 38s. tilt-variation of the equation of time in two days, as 34J- liours, tiiespace that tiie proposed time is after the noon of Sept. 1, is to 27,3s.This quantity being added to2s. because the equation is increasing,the sum -j- 29,3s. will be tiie true equation of lime at the requiredinstant. Ilence Sept. 2, at 10{- liours mean time is tiie same withSept. 2, at lOh. 30m. 29,3s. apparent time. According to De LaLailde’s 'Fables the equation is found -j- 31,6s. so that the error oftiie 'Fable in this case is only — 2-jtjS. an ^ therefore sufficiently ac-curate for common clocks and watches.

Example 2. Required the apparent time corresponding to July2d, 1817,, at 10b. 15m. mean time, it being the first year afterBissextile.

in the Table for July 1, in the first year after Bissextile,(the tabular time immediately preceding tiie given time,) theequation of tiie mean time is — 3m. 18s. and 48 hours after tiieequation is increased to—3m. 4l)s. the difference of which is 22s.And 48 liours : 22s. : : 34h. 15m. the space that file given time isafter the noon ofJuly 1, : 15,69s. This quantity added to—3m.18s. because the equation is increasing, will give.— 3m. 33,69s.for the true equation of the mean time at the given instant. AndJuly 2, at lOh. 15m. — 3m. 33,69s. = July 2, at 10b. 1 lm. 26,31s.tiie apparent time required,

Example 3. Required the mean time corresponding to March12, 1819, at 1 hour, apparent time, it being tiie third year afterLeap-year.

In the Table for the noon of Marcii 11, in the year before Bis-sextile, (the tabular time immediately preceding the given time,)'the equation of apparent to meantime is-j-10m. 26s. and 48hours after-f 9m. 53s. tiie decrease of the equation of apparent tomean time in48h. is consequently 33s. And 48 hours : 33s. : : Id.lh. the space that tiie given time is after tiie immediately precedingtabular time, : 11,46s. This subtracted from + 10m. 26s. becausethe equation of apparent time is deereaisng the difference -f- 10m.14,54s. will be the true quantity of the equation of apparent timeat the given moment. And March 12, 1819, at 1 hour, -)- 10m.14,54s. = March 12, 1819, at lh. 10m. 14,54s. the meantimerequired.

Example 4. Required the mean time corresponding to June30, 1827, at 6J hours,'apparent time; it being tiie third afterBissextile.

In the 'Faille for the noon of June 30, in the third year after Bis-sextile, tiie equation of tiie apparent time is + 3m. 3s. and on tiienoon of the following day -f- 3m. 14s. the difference of which is +11s. And 24 hours : 11s. :: 6£ hours : 2,9Ss. 1 ins last quan-

tity added to -+- 3m. 3s. because the equation of time is increasing,die sum 3m. 5,98s. will he the true difference between tiie ap-parent and mean time. Hence June 30, 1827, at 6£ liours -|- 3m.5,98s. = June 30, 1827, at Oil. 33m. 5,98s. ihe mean time re-quired.

Example 5. Required tiie apparent time corresponding to Sept.7, 1820, at 50jj- minutes past 12 noon, mean time.

In tiie 'Fable for the noon of Sept. 7, 1820, (it being BissextileorJ.eap-year,) tiie equation of die mean time is -j- 2m. 8s. and twodays after -j- 2m. 49s. the difference of which is -|- 41s, And 48hours : 41s : : 50J minutes, tiie space that the immediately preced-ing tabular time is before the given time, : 0,72s.' This last foundquantity added to 2m. 8s. gives -j- 2m. 8,72s. the true quantity ofthe equation according to tiie 'Fable at the proposed time, lieneeSept. 7, 1820, at 50} minutes past 12 noon, mean time, is the samewith Sept. 7, 1820, at 52m. 48,72s. apparent time. From M. DeLa Lande’s 'Failles tile true quantity of the equation of mean totrue time for the given moment, is -j- 2m, 9,88s. Hence the errorof the '1 able in this instance is only— 1,16s.

(221.) Table