9 
^une X. 45*46 7. fum 8; 449 7f<. 
5^«»^ 9. 44934. and 7^/»^ li. 44883, 
16. 44990. 7«»^ 16. 44990« 
In both which cafes the middle time is exadly io the 
middle between the extreams, and therefore io the for- 
mer three, ac=5'33, bc=477 and the time be- 
tween being 14 days, by the fir ft Rule, the time of the 
Tropick will be found by this Proportion, as 5-89 to 
817 I:: So f t or 7 days to 9 days 20^'- z\ whence the 
Tropick 1500 is concluded to have fallen ^/^/^^ ii^- 
zo^*z'. In the latter three, ac is = 107, and 50=15-, 
and the whole interval of Time is 8 days = to t; whence 
as 199 : to zo6.~ : : (b is 4 days to 4^•3^^•37^ which ta- 
ken from the i6th. day at Noon, leaves i i^-xo^^- 23'. for 
the time of the Tropick, agreeing with the former to 
the third part of an hour. 
Again, Amo 1636, Gajfendus at Marfeil/es ohihrvcd 
the Summer Solftice by a Gnomon of 55- Foot high, in 
order to determine the Proportion of the Gnomon to the 
Solftitial lhade, and he hath left us thefe Obfervations, 
which may ferve as an Example for the fecond Rule. 
^une 19. 5^. tJ. ftiadow 3 1 766 parts, whereof the Gnomon 
June zo. 3^753 (was 89428« 
June zx. 3^7 
June 22. 3^759 
Thefe being divided into two fetts of three Obferva- 
tions each, viz, the 19^^- 20^^* and 22^^- and the 19^^*^^ 
21^^' and 22^h- we fhall have in the firft three, 0=13 
and b = 7, t = 3 days, s = i, and in the fecond c — is 
and b= 7, t = 3 and s= 2. Whence according to the 
Rule, the 19th. day at Noon the Sun wanted of the Tro- 
pick a time proportionate to one day, as ttc — ssb to 
xtc — 2bs, that is, as no to 64 in the firft fetr, or 
