( i6 ) 
107 to 6x In the fccond fet ; that is, i^- ly^- ij'. in the 
firft, or 1^' 17^ 25'. in the fccond fett : So that wc may 
conclude the Moment of the Tropick to have been 
Jufie 10^' if''- 20'. in the Meridian of Marfeilles. 
Now that thefe two Tropical times thus obtained , 
will be found to confirm each others exaftnefi from their 
near agreement, appears by the interval of time be- 
tween them ; viz. 1^ x^- 30'. lefs than 11,6 Julian years: 
whereof I i>* 8'. ari(es from the defeft of the length 
of the Tropical Year from the Julian, and the reft from 
the Progreffion of the Smu's Apogaon in that time; fb 
that no two Obfervations made by the fameObferver 
in the fame place, can better anfwer each other, and that 
without any the leaft Artifice or Force in the manage- 
ment of them. 
What were the Methods ufed by the Ancients to con- 
clude the hour of the Tropicks, Ptolemy has no where 
delivered ; but it were to have been wilhed that they 
had been aware of this, that fo we might have been 
more certain of the moments of the Tropicks we have 
received from them, which would have been of fingular 
ufe to determine th« Queftion, Whether the Sun's ApO' 
ga^on be fixt in the Starry Heaven ; or if it move, what 
IS the true motion thereof? It is certain, that if we take 
the Account of Ptolemy, the Trcpick (aid to be obfer- 
ved by Eudemon and Met on, Junii 17. mani, A?nio 431 
ante Chriftum, can no w^ays be reconciled without lup- 
pofing the Obfervation made the next day, or June i.Zth, 
iq the Morning. And Ptolemy's own Tropick obfer- 
ved in the Third Year of Antoninus, Anno Chrifli 140, 
was certainly on the 13//^. and not the ^4^/;. day of 
June ; as will appear to thofe that (hall duly confider 
zni compare them with the length of the Year dedu- 
ced from the diligent and concordant Obfervations of 
I hofe two great Aftronomical Geniiy Hipparchus and Al^ 
htini * eftablilhed and confirmed by the concurrence 
of 
