ASTRONOMY. 
455 
of the Sun's centre. If the altitude of the upper limb 
be obferved, the femi-diameter mud be fubtracied, The 
mean femi-diameter of the Sun is fixteen minutes, which 
for common obfervation may be taken as a conftant quan¬ 
tity, for the greated deviations from this quantity fcarcely 
exceed a quarter of a minute. When greater accuracy is 
aimed at, the femidiameter may be taken from the Nau¬ 
tical Almanac. The obferved altitude of the Sun’s lower 
limb being i8°4i', add thereto 16' for the Sun’s femidia¬ 
meter, and you obtain i8° 57', the central altitude. 
The apparent altitudes of all the heavenly bodies are 
increafed by refraction, except when they are fituated in 
the zenith. An obferved angle of a dar, or any other ob¬ 
ject in the heavens, mud be diminifhed by a fmall quanti¬ 
ty, to be taken from the table of refractions. Where 
greater exaCtnefs is required, a fmall quantity is to be add- 
en for the error occafioned by parallax, or the difference 
between the altitude of an object as feen from the centre 
and the furface of the Earth. That from the centre is 
the true altitude, and the greated, except at the zenith, 
where parallax vanilhes; confequently the apparent alti¬ 
tude of the Sun is to be augmented by a fmall quantity 
taken from the table of the Sun’s parallax. 
June 6, 1788, the apparent altitude of the Sun’s lower 
limb was obferved to be 62° 19^; required the true alti¬ 
tude of the Sun’s centre, as leen from the centre of the 
Earth ? 
Obferved altitude 
Semidiameter 
SubtraCf for refraction 
Add for parallax 
True central altitude 
62° 
19' 
16 
62 
35 
3 ° 
62 
34 
3 ® 
4 
62 
34 
34 
If it is a fixed dar that has been obferved, there is no 
correction for femidiameter or parallax ; you have only to 
fubtraCt for refraction, in order to obtain the true altitude. 
To find the Time by equal or correfponding Altitudes. This 
problem is of extenfive ufe, for the bads of all adronomi- 
cal obfervation is the determination of the exaCt time of 
any appearance in the heavens ; which cannot be attained, 
unlefs you are allured of the going of your watch or 
clock. A mean folar day is always conlidered as of the 
fame determinate length ; but the length of an apparent 
day is variable, being lometimes longer, fometimes lhort- 
er, than a mean day. The indant, therefore, of apparent 
noon will fometimes follow, at others precede, that of the 
mean noon. The interval between apparent and mean 
time is called the equation of time. To find, then, the 
time of apparent noon, obferve the Sun’s altitude in the 
morning, and alfo the time by a clock or watch. Leave 
the quadrant in the fame duration, taking care that its po¬ 
rtion be not altered by any accident; and in the afternoon 
direCt it to the Sun, by moving the index of the horizontal 
circle only, and obferve the time when the Sun’s altitude 
correfponds with that to which the quadrant was fet in 
the morning. Add the times of obfervation together ; 
the middle indant between thofe times of obfervation is 
that of apparent noon: this being corrected, J^y adding 
.or fubtraCling the equation of time, gives the time of true 
noon. If it be precilely twelve, the clock Is right; but, 
if it differ, the clock is fader or dower by the quantity of 
the difference greater or lefs than twelve. 
Thus, fuppofe the time in the 
Tliat in the afternoon 
The time of noon by watch 
Equation of time 
Mean noon by watch 
tiling to be 
2ih.35 
'. 8" 
- 
2 55 
43 
24 3 ° 
5 1 
12 15 
2 5 i 
- 
13 
29 
- 
I 2 I 
564 
too fad. 
To be 
more 
particular and accurate; In our latitude, the altitudes 
3 
fhould be taken when ths Sun is at lead two hours didant 
from the meridian. The bed time is when the Sun is on 
or near the prime vertical, or ead and wed point of the 
compafs; becaufe his motion perpendicular to the hori¬ 
zon is greated at that time. About this time, in the fore¬ 
noon, take feveral altitudes of the Sun, writing down the 
degrees and minutes fhewn on the arch, and alfo the exaCt 
time fhewn by the clock at each obfervation: the obfer- 
vations to be written one below the other, in the order 
they were made; the time of each obfervation being pre- 
vioufiy increafed by twelve hours. In the afternoon fet 
the index to the fame degree and minute as the lad obfer¬ 
vation, note exaCtly the time Ihewn by the clock when the 
Sun is come down to the fame altitude, and write down 
the time oppolite to the lad morning altitude ; proceed in 
the fame manner to note the time of all the altitudes cor¬ 
refponding to thofe taken in the morning, writing down 
each of them oppofite to that morning one with which it 
correfponds. 
Half the fum of any pair of correfponding altitudes 
will be the time of noon by the watch uncorreCled. Find 
the mean of all the times of noon thus deduced from each 
correfponding pair of obfervations; which correCt for the 
change in the Sun’s declination, and you obtain the exaCf 
time fhewn by the clock at folar noon. This, correded 
by the equation of time, gives the time of mean noon ; 
and the watch will be too fad or too Oow, according as the 
time of noon thus found is more or lefs than twelve hours. 
Ex. Equal altitudes taken, June 17S2. 
Morning. 2ch. 55'. 46". Afternoon. 3ft. S'. 44". 
20 57 41 3 6 48 
20 59 27 34 5 S 
Fird Pair. Second Pair. Third Pair. 
aoh. 55'. 46". 20I1.57'. 41". 20b. 59'. 27". 
_3 _8_44 _j_6_ 3 4 5 8 
Sum 24 4 30 24 4 29 24 4 25 
5 Sum 12 2 15 12 2 14! 12 2 i2§ 
As the feconds differ, add them together, and divide the 
fum by 3 (the number of pairs), which gives a mean of 
fourteen feconds. 
Therefore the mean obferved time is 
Equation for 6h. difference in declination 
Time of apparent noon by the watch 
Equation of time 
Time per watch of mean noon 
The watch is nineteen feconds feven thirds too fad for 
mean time. 
To find the Error of a Clock or Watch , by correfponding or 
equal Altitudes of a Fixed Star. Rule, i. Add half the 
time elapfed between the obfervations to the time when 
the fird altitude was taken, and you have the time of the 
dar’s tranfit over the meridian by the watch. 
Rule 2. Subtraid the Sun’s right afeenfion from the 
dar’s, increafed by twenty-four hours, if neceffary. Take 
tlje increafe of the Sun’s right afeenfion in twenty-four 
hours, and add it to twenty-four hours ; then fay, As this 
fum : twenty-four hours :: fo is the difference between the 
Sun and dar’s right afeenfion : the true time of the dar’s 
tranfit. If the watch be regulated to folar time, the dif¬ 
ference between the true time of the dar’s tranfit and the 
time fhewn by the watch will be the error. 
If your meridian be different from that of Greenwich, 
fay, As twenty-four hours : the daily difference of the 
Sun’s right afeenfion :: the longitude in time : a propor¬ 
tional part, which mud be added to the true time of the 
dar’s tranfit if the longitude be ead, but fubtradled if wed. 
If the watch be regulated to mean folar time, that is, if it 
divides the time equally, apply the equation of time as di- 
recled in p. 2 of the Nautical Almanac, to the true ap¬ 
parent time of the dar’s tranfit, before you fubtradf. 
Ex. On the 6th of November, 1787, at nh. 10'. 9'h 
P. M. and at 1611,4'. 15". folar time, the dar Aldebaran 
had 
12h. 
14” 
12 2 
14 
8 
1 
55 
I 
12 0 
19 
7 
