. C t5 ) 
Kepkr^ the Vernal being fo much later, and the Aiitum- 
nial fo much earlier than by the Calculus of thofe Fa- 
mous Authors. 
Now before we proceed, it will be ncccflary to pre- 
raife the following Lemmata^ (erving to demonftrate 
this Method, viz. 
X. That the motion of the Sun in the Ecliptick,about 
the time of the Tropicks, is fo nearly equable, that the 
difference from equality is not fenfible,from five days be- 
fore the Tropick, to five days after : and the differetice 
arifing from the little inequality that there is, never 
amounts to above ^ of a fingle Second in the Declina- 
tion, and this by reafon of the nearnefs of the Apogaon 
of the Sun to the Tropick of Cancer. 
%. That for five Degrees before and after the Tro- 
picks, the differences whereby the Sun falls fliort of the 
Tropicks, are as the Verfed Sines of the Sun's diftance 
in Longitude from the Tropicks, which Verfed ^ines in 
Arches under five Degrees, are beyond the utiboft ni- 
cety of fenfe, as the Squares of thofc Arches. From 
thefe two follow a Third : 
3. That for five days before and after the Tropicks, 
the Declination of the Sun falls fliort of the utmoft Tro- 
pical Dechnation, by Spaces which are in daplicfte pro- 
portion, or as the Squares of the Times by wHfeh the 
Sun is wanting of or paft the moment of the T^ipick. 
Hence it is evident that if the Shadows of ^he Sun, 
either in the Meridian or any other A2imuth,be>carefully 
obferved about the time of the Tropicks, the Spaces 
whereby the Tropical lhade falls fiiort of, or exceeds 
thofe at other times, are always proportionable to the 
Squares of the Intervals of Time between thofe Obfer- 
vations and the true time of the Tropick, and confe- 
quently if the Line, on which the Limits of the ftiadc 
is taken, be made the Axis, and the correfpondent times 
from the Tropick expounded by Lines, be erefted on 
D . their 
