134 M E M O I R S of the 
have in the firft three, <: = 13 and ^ = 7, / =: 5 days i — /j 
and in the iecond, ^ m 15, ^=: 7, ^ = 5, and/^m; 23 whence, 
accordino to the rule, the 19th day at noon the lun was fhort of 
the T'ropic a time proportional to one day, 2iS tt c z=l ssb to ztc 
- — 2^Jj that is, as iootod4inthe firft let, or 105 to 5 2 in 
the fecond fet^ that is, id. i7h. 15' in the firfl:, or id. 17 h. 
25' in the fecond fetj that is, id. 17 h. 1 5 ' in the firft, or i d. 
17 h. 25' in the Iecond fet; lb that we may conclude the Iblftitial 
moment to have been ^une 10 d. i7h. 20' in the meridian of 
Marfeilles. Now that thefe two folflitial times thus obtained, 
will be found to confirm each others exadtnefs from their near 
agreement, appears by the interval of time between them, viz, 
id. 2 h. 50' lels than 10^6 Julian years, whereof id. i h. 8' 
ariles from the defeat of the length of the tropical year from 
the Julian^ and the reft from the progreflion of the fun's apo- 
giEon in that time ; fo that no two obfervations made by the fame 
oblerver in the fame place can better anfvvcr to each other, and 
that without any the leaft artifice or force in the management of 
them. 
What were the methods of the ancients to conclude the mo- 
ment of the folftice, 'Ptolemy has no where mentioned 5 but it 
were to be wifiied, that they had been aware cf this, that io we 
might have been more certain of the moments of the folftices we 
have received from them 5 which would have been of fingular 
v.le to determine the queftion, whether the fun's apogxon be fixed, 
or, if it move, what its true motion is. It is certain that if we 
take the account of 'Ptolemy^ the folftice faid to be oblerved by 
JEu^emon and Meton, jfime 27th in the morning. An. 432 be- 
fore Chrift, can no ways be reconciled, without fuppofing the 
oblervation made the enfuing day, or jfiaie 28th in the morning j 
and the folftice oblerved hy Ptolemy himfelf, in the third year 
of j4/itoiiimis An. Chrifti 14.0, was certainly on the 23d, and 
not on the 24th of jfune-y as will appear to thoie that will duly 
confider and compare them with the length of the year deduced 
from the diligent and concordant obfervations of thofe two great 
aftronomical genii, Hlpparcbui and Albatani^ eftabli/hed and 
confirmed by the concurrence of all the modern accuracy; for the 
obfervations give the length of the tropical year, fuch as to anti- 
cipate the Jidian account only one day in 300 years; but we are 
now certain, that the faid period of the fun's revolution does an- 
ticipate very nearly 3 days in 400 years; fo that the tables of 
^Ptolemy , founded on that liippofition, do err about a whole day 
in the lun's place for every 240 years 3 which principal error, in 
lb 
