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No. 14.]
THE PLANETABY TABLES.
III. Txus LONGITUDE OF Tas Sok. Subtract mean Sun from San's Apeis, vis.
77° 16', or in case the Longitude is greater, from 437° 16'; the remisidder is the sun's anomaly. Take out the corresponding equation from the Anomalistid Table and add it to the mean Longitude. Result: true Longitude of the Sun. 8.g. for moan Long. of the Sun 20° 11', we find Anomaly 770 16-20° 11'= 57° 5', equation for the latter from Anomalistid Table + 1° 50'; 20° 11' + 1° 50' = 22° 1': true San; 2nd stamplo :-moan Long. 115° 6'; Anomaly 431° 18'-115° 6'= 392° 10°; equation -10 21'; true Long of the Stai: 115° 6' -1° 21'. = 113° 45'.
I now give examples for the Rules I and II. We have oslonlated the mean Longitudes of the planets for 12th April 1168 A.D., and shall new calenlate from them the true Longitudes of Venus (Rule I) and Saturn (Rule II).
First example.- Mean Venus = 196° 53'; Mean Ban 16° 23'; Apois of Venus 790 51' (bottom of Table IT). 1st step.-mean Venus 196° 53'; rabtract mean Sun
16° 23 result: Commntation=180° 30., corresponding equation from Commutation Table : l° 19'; half of equation 0° 40'; applied to mean Sun 16° 28' 0° 40' = 15° 48'. This is Venus once corrected. 2nd step.-From Venus Apsis 79° 51' subtract
Ventis onde corrected 15° 49'; tesult: Venus' Anomaly:
64° 8'; corresponding equation from Anomalistie: Table :+1° 36', half of it: +0°48'; added to Venas once corrected : 16°49'+0°49'
= 16° 31'. Result : Venus twice corrected. 3rd step.-From Venns' Apsis 79° 31' subtract
Venus twice corrected 16° 31'; rosalt: corrected Anomaly: 63° 20'; corresponding equation from Anomalistio Table : +1° 35'; add whole of it to mean San: 18° 23' +1° 35 = 17° 58'; Result:
Venns thrice corrected. 4th step.-From mean Venns. 196° 53' subtract
Venus thrioo corrected 17° 58'; result: corrected Commutation: 178° 55'; corresponding equation from Commutation Table : +2° 51'; add whole of it to Venus thrice corrdoted : 17 58' +2° 51'=30°
49, Final Result: true Venus. (Mosha 20°49'). Second example.—Mean Saturn : 302° 8'; mean Sun: 16° 23' or (adding 360°) 376° 23'; Saturn's Apsis 236° 27' (bottom of Tablo II) or 596° 87'. 1st stop.-From mean Sun: 376° 23'; subtract mean Saturn :
302° 8'; result: Saturn's Commutation : 74° 15'; corresponding equation from Commutation Table : +5° 55'; half of it: +2° 57' added to mean Saturn : 302° 8' + 2° 57'
805° 5'. Result: Saturn once corrected. 2nd step-From Saturn's Apsis: 596° 27' ; subtraet
Saturn once corrected : 305° 5'; result: Saturn's Anomaly : 291° 22'; corresponding equation from Anomalistio Table - 70 half of it -8° 84' added to Saturn Once corrected : 305° 3 90 84'=302° 31'. Result : Satura twise corrested.
