Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/267

Table C gives, with ${\displaystyle \gamma '+\gamma ''=36,10}$, the magnitude of the greatest phase as exactly 10 digits.

Table D. ${\displaystyle L=490}$ gives, with ${\displaystyle \phi =30^{\circ }}$ and ${\displaystyle \lambda +\mu =25^{\circ }}$, for the moment of the greatest phase, 24,0 ghaṭikâs, or 24 gh. 0 pa. after true sunrise at Multân.

Example 3. Was the eclipse of the 7th June, A.D. 913, visible at Trivandrum, whose latitude, ${\displaystyle \phi }$, is 8° 30′ N., and longitude, ${\displaystyle \lambda }$, 76° 56′ E.?

Table A gives: 913 VI 7, 8 h. 35 m. ${\displaystyle L=480}$ ${\displaystyle \mu =323^{\circ }}$ ${\displaystyle \gamma '=44,98}$

Trivandrum has, ${\displaystyle \phi =8^{\circ }}$ and ${\displaystyle \lambda =77^{\circ }}$ ${\displaystyle \lambda +\mu =40^{\circ }}$

Table B. ${\displaystyle L=480}$ gives, with ${\displaystyle \phi =8^{\circ }}$ and ${\displaystyle \lambda +\mu =40^{\circ }}$, ${\displaystyle \gamma ''=1,02}$

${\displaystyle \gamma '+\gamma ''=46,00}$

Table C shews, with ${\displaystyle \gamma '+\gamma ''=46,00}$, that the eclipse was total at Trivandrum.

Table D. ${\displaystyle L=480}$ gives, with ${\displaystyle \phi =8^{\circ }}$ and ${\displaystyle \lambda +\mu =40^{\circ }}$, for the moment of totality 26,2 ghaṭikâs or 26 gh. 12 pa. after true sunrise at Trivandrum.

Example 4. Was the same eclipse visible at Lahore whose latitude, ${\displaystyle \phi }$, is 31° 33′ N., and longitude, ${\displaystyle \lambda }$, 74° 16′ E.?

Table A gives: 913 VI 7, 8 h. 35 m. ${\displaystyle L=480}$ ${\displaystyle \mu =323^{\circ }}$ ${\displaystyle \gamma '=44,98}$

Lahore has ${\displaystyle \phi =32^{\circ }}$ and ${\displaystyle \lambda =74^{\circ }}$

${\displaystyle \lambda +\mu =37^{\circ }}$

Table B. ${\displaystyle L=480}$ gives, with ${\displaystyle \phi =32^{\circ }}$ and ${\displaystyle \lambda +\mu =37^{\circ }}$, ${\displaystyle \gamma ''=0,69}$

${\displaystyle \gamma '+\gamma ''=45,67}$

Table C gives, with ${\displaystyle \gamma '+\gamma ''=45,67}$, the magnitude of the greatest phase 4,8 digits.

Table D. ${\displaystyle L=480}$ gives, with ${\displaystyle \phi =32^{\circ }}$ and ${\displaystyle \lambda +\mu =37^{\circ }}$, for the moment of the greatest phase 26,9 ghaṭikâs, or 26 gh. 54 pa. after true sunrise at Lahore.

In all these examples the value of ${\displaystyle L}$ (Table A) was divisible by 10, and therefore a special table for this value was found in Table B. When the value of ${\displaystyle L}$ is not divisible by 10, as will mostly be the case, there is no special table exactly fitting the given value. In such a case we may take the small table in Table B for the value of ${\displaystyle L}$ nearest to that given. Thus for instance, if ${\displaystyle L}$ is 233 we may work by the table ${\displaystyle L=230}$, or when ${\displaystyle L}$ is 487 we may work by the Table ${\displaystyle L=490}$ and proceed as before, but the result will not be very accurate. The better course is to take the value of ${\displaystyle \gamma ''}$ from both the table next preceding and the table next following the given value of ${\displaystyle L}$, and to fix a value of ${\displaystyle \gamma ''}$ between the two. ^ Thus for ${\displaystyle L=233}$ we take the value of ${\displaystyle \gamma ''}$ both from Table 230 and from Table 240 and fix its truer value from the two. But where the only question is whether an eclipse was visible at a given place and there is no necessity to ascertain its magnitude, the first process is sufficient.

Example 5. Was the eclipse of the 15 January, A.D. 1032, visible at Karâchi, whose latitude, ${\displaystyle \phi }$, is 24° 53′ N., and longitude, ${\displaystyle \lambda }$, 66° 57′ E.?

Table A gives 1032 I 15, 10 h. 1 m. ${\displaystyle L=701}$ ${\displaystyle \mu =342^{\circ }}$ ${\displaystyle \gamma '=45,46}$

Karachi has ${\displaystyle \phi =25^{\circ }}$, and ${\displaystyle \lambda =67^{\circ }}$ ${\displaystyle \lambda +\mu =49^{\circ }}$

Table B. ${\displaystyle L=700}$ gives, with ${\displaystyle \phi =32^{\circ }}$ and ${\displaystyle \lambda +\mu =37^{\circ }}$, ${\displaystyle \gamma ''=0,63}$

Table B. ${\displaystyle L=710}$ gives,„ with„ phi x 25„ and„ l + mu x„ 49„ ${\displaystyle \gamma ''=0,69}$, or^[1] for L 701 ${\displaystyle \gamma ''=0,64}$

${\displaystyle \gamma '+\gamma ''=46,10}$