Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/265

${\displaystyle L'}$	=	longitude of sun and moon.
${\displaystyle P}$		(only indication if ${\displaystyle P}$ is near 0° or near 180°).
${\displaystyle u'_{a}}$	=	radius of shadow.
${\displaystyle \gamma }$	=	shortest distance of shadow's centre from earth's centre.
${\displaystyle \mu }$	=	Sun's hour-angle at Greenwich at the moment of this shortest distance.

(There is no necessity for attempting any further explanation of all the other elements and formulæ noted above, which would be impossible without going into the whole theory of eclipses. Such an attempt is not called for in a work of this kind.)

These elements are given in Table A in the following form:—

Column 1.	Date of eclipse,—year, month, and day; Old Style till 2 September, 1752 A.D., New Style from 14 September, 1752.
Column 2.	Lanka time of conjunction in longitude, counted from mean sunrise in hours and minutes.
Column 3.	${\displaystyle L=}$ longitude of sun and moon in degrees, when ${\displaystyle P}$ is near 0°; or longitude of sun and moon plus 400°, when ${\displaystyle P}$ is near 180°; so that numbers in this column under 360° give directly the value of this longitude, and indicate that ${\displaystyle P}$ is near 0°, or that the moon is in the ascending node, whilst numbers over 400° must be diminished by 400 when it is desired to ascertain this longitude. At the same time these last indicate that ${\displaystyle P}$ is near 180°, that is that the moon is in the descending node.
Column 4.	${\displaystyle \mu =}$ Sun's hour-angle at Greenwich at the moment of shortest distance of shadow's centre from earth.
Column 5.	${\displaystyle \gamma '=}$ ten times the second decimal cipher of ${\displaystyle u'_{a}+5+\gamma }$. So the tenths of the numbers of this column give the last cipher of ${\displaystyle u'_{a}}$ whose first ciphers are 0.5, and the rest of the number diminished by 5 gives the value of ${\displaystyle \gamma }$.

For instance; the line 975 II 14, 0 h 52 m, 730°, 202°, 74.66 shows that on the 14th February, A.D. 975, the conjunction took place at 0 h 52 m after mean Lanka sunrise, that the longitude of sun and moon was 330° (the moon in the descending node), ${\displaystyle \mu =202^{\circ }}$, ${\displaystyle u'_{a}=0{,}57}$, and ${\displaystyle \gamma =-0{,}34}$.

Table A gives, in the first column, the year, month, and day of all eclipses visible in any part of India, or quite close to the frontiers of India. The frontiers are purposely taken on rather too large a scale, but this is a fault on the right side. The letters appended shew the kind of eclipse; "a" stands for annular, "t" for total, "p" for partial. Eclipses of the last kind are visible only as very slight ones in India and are therefore not of much importance.^[1] When the letter is in brackets the meaning is that the eclipse was only visible quite on the frontiers or even beyond them, and was without importance. When the letter is marked with an asterisk it shews that the eclipse was either total or annular in India or close to it, and is therefore one of greater importance. The second column shews, in hours and minutes counted from mean sunri.se at Lanka, the time of conjunction in longitude. This column serves only as an indication as to whether the eclipse took place in the morning or afternoon; for the period of the greatest phase at any particular place may differ very sensibly from the time thus given, and mu.st in every case be determined from Table D, if required. The third, fourth, and fifth columns, headed respectively ${\displaystyle L}$, ${\displaystyle \mu }$, and ${\displaystyle \gamma }$ furnish the arguments for the following Tables B, C, and D, by which can be found the magnitude and the moment of the greatest phase of the eclipse at a particular place.