Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/266

Table B (as well as Table D) consists of seventy-two different Tables, each of which is calculated for a particular value of ${\displaystyle L}$ taken in tens of degrees. Each of these little tables is a table with a double argument, giving the value of ${\displaystyle \gamma ''}$. The arguments are, vertically the latitude ${\displaystyle \phi }$, and horizontally the longitude ${\displaystyle \lambda }$ of the given place, the latter being stated in degrees from Greenwich and augmented by the value of ${\displaystyle \mu }$ given in Table A. The reader selects that table which is nearest to the value of ${\displaystyle L}$ given by Table A, and determines from it, by interpolation with the arguments ${\displaystyle \phi }$ and ${\displaystyle \lambda +\mu }$, the value of ${\displaystyle \gamma ''}$. If a greater degree of accuracy is desired, it is necessary to determine, with the arguments ${\displaystyle \phi }$ and ${\displaystyle \lambda +\mu }$, the value of ${\displaystyle \gamma ''}$ by both tables preceding and following the given value of ${\displaystyle L}$, and to interpolate between the two values of ${\displaystyle \gamma ''}$ so found.

The final value of ${\displaystyle \gamma ''}$ is added to the value of ${\displaystyle \gamma '}$ given by Table A, and this value of ${\displaystyle \gamma '+\gamma ''}$ serves as argument for Table C, which gives directly the magnitude of the greatest phase at the given place in digits, or twelfths of the sun's diameter.

Table D is arranged just like Table B, and gives, with the arguments ${\displaystyle \phi }$ and ${\displaystyle \lambda +\mu }$, the moment of the greatest phase at the given place in ghaṭikâs and their tenths, counted from true sunrise at the given place.

The first value in each line of Tables B and D corresponds to a moment before sunrise and the last value in each line to a moment after sunset. Both values are given only for pur- poses of interpolation. Therefore in both cases the greatest phase is invisible when ${\displaystyle \lambda +\mu }$ coincides exactly with the first or last value of the line, and still more so when it is less than the first or greater than the last value. But in both cases, when the difference between ${\displaystyle \lambda +\mu }$ and the last value given does not exceed 15 degrees, it is possible that in the given place the end of the eclipse might have been visible after sunrise, or the beginning of the eclipse before sunset. As the tables give only the time for the greatest phase this question must be decided by direct calculation.

EXAMPLES.

Example 1. Was the eclipse of the 20th June, AD. 540, visible at Jâlna, whose latitude ${\displaystyle \phi }$, is 19° 48' N., and whose longitude, ${\displaystyle \lambda }$, is 75° 54′ E.?

Table A gives: 540 VI 20, 7 h 57 m	L = 490	${\displaystyle \mu =314^{\circ }}$	${\displaystyle \gamma '=35{,}34}$
Jâlna has ${\displaystyle \phi =20^{\circ }}$, and		${\displaystyle \lambda =76^{\circ }}$
		${\displaystyle \lambda +\mu =30^{\circ }}$
Table B: L = 490 gives, with ${\displaystyle \phi =20^{\circ }}$ and ${\displaystyle \lambda +\mu =30^{\circ }}$,			${\displaystyle \gamma ''=0{,}86}$
			${\displaystyle \gamma '+\gamma ''=36{,}20}$

Table C gives, with ${\displaystyle \gamma '+\gamma ''=36{,}20}$, the magnitude of the greatest phase as nearly 8 digits.

Table D. L = 490 gives, with ${\displaystyle \phi =20^{\circ }}$ and ${\displaystyle \lambda +\mu =30^{\circ }}$, for the moment of the greatest phase, 24.8 ghaṭikâs or 24 gh. 48 pa. after true sunrise at Jâlna.

Example 2. Was the same eclipse visible at Multan, whose latitude ${\displaystyle \phi }$ is 30° 13′ N., and whose longitude, ${\displaystyle \lambda }$, is 71° 26′ E.?

Table A gives: A.D. 540 VI 20, 7 h. 57 m.	L = 490.	${\displaystyle \mu =314^{\circ }}$	${\displaystyle \gamma '=35{,}34}$
Multan has ${\displaystyle \phi =30^{\circ }}$ and		${\displaystyle \lambda =71^{\circ }}$
		${\displaystyle \lambda +\mu =25^{\circ }}$
Table B. L = 490 gives, with ${\displaystyle \lambda =71^{\circ }}$ and ${\displaystyle \lambda +\mu =25^{\circ }}$			${\displaystyle \gamma ''=0{,}76}$	(diff. between 0.80 and 0.72)
			${\displaystyle \gamma '+\gamma ''=36{,}10}$