( 88x ) 
draw the Line 4 y 7 parallel to the Tropick, and repre- 
(enting a Circle equal thereto then (hall the Tropick 
s So in Fig. 10. anlwer to the Circle NOPQ^, in Fig. 9. 
the Circle 457 (liall anfwer the Circle IKLM, T41 
fihall anfwer to the Elliptick Segment QIBKP, 6 R or 6 4 
fhall anfwer to SP, and 5 1 to BL, and the Arch s T, 
to the Arch LS, being the femidiurnal Arch in that La- 
titude and Declination ; the Sine whereof, though not 
expreffible in Fig. 10. mud be conceived as Analogous 
to the Line TS or UP in Fig. 9. 
The Relation between thele two Figures being wellun- 
derftood, it will follow from whac precedes, That, the 
Sum- of the Sines of the Meridian Altitudes of the Sun 
in the two fro picks, (and the like for any two oppofite 
Parallels) being multiplied by the Sine of the femidiur- 
nal Arch , will give an Area analogous to the Curve Sur- 
face R MSQj) P ; and thereto adding in Summer , or fub- 
ftratling in Winter ; the product of the length of the je- 
rnidiurnal Arch, (taken according to Van Ceulen'i Num- 
bers^) into the difference of the above-faid Sines of Me* 
vidian Altitude : the Sum in one cafe, and difference in the 
other fhall le as the Aggregate of all the Sines of the Sun s 
Altitude, during his appearance above the Horizon ; and 
confequently of all his Heat or Action on the Plain of the 
Horizon in the propofed Day. And this may alfo be ex- 
tended to the parts of the iame Day,- for if the afore- 
laid Sum of the Sines of the Meridian Altitudes, be 
multiplied by half the Sum of the Sines of the Sun's 
horary diftance from Noon, when the l imes are before 
and after Noon or by half their difference, when both 
are on the (ame fide of the Meridian • and thereto in 
Summer, or therefrom in Winter, be added or fubftracl- 
ed the produft of half the Arch anfwerable to the pro- 
ofed Interval of Time, into the difference of tlie Sines 
of Meridian Altitudes, the fum in one cafe, and diffe- 
rence 
