( ) 
itnder CMN, that is equal to the Complement of half 
the Diftance of the exterior Rainbow from the Point 
oppofite to the Sun. Then putting a for the Radius 
A K, and b for the Sine of the Angle under C K Y, 
the Sine of the Angle under A K V will be the Root 
of this Equation ^ by ^ — %aaby-\-^aabb — o. 
But the Angle of Incidence and Refraction may alfb 
be found as follows. ' 
Let two mean Proportionals between the Radius 
and the Sine of the Angle under C K Y be found, then 
take the Angle, whofe Cofine is the firfl: of thele mean 
Proportionals, counting from the Radius ; and alfo the 
Angle, whofe Sine together with the lecond mean 
Proportional fhall be to the Radius as the Cofine of 
the Angle under C K Y to the Sine of the Angle before 
found. The Sum of thefe three Angles is double the 
Complement to a right one of the Angle under A KL, 
the Angle under K M L, or the refradted Angle, being 
equal to half the Sum of this Angle under A K L and 
the Angle under C K Y ; as in the lad Place the Angle 
under K LV, that is the Angle of Incidence, equal to 
the Sum of the Angles under K M L and under M KL. 
I need not obferve, that the geometrical Methods of 
deducing thefe Angles of Incidence and Refraction 
from the Angle meafiiring the Didance of each Rain- 
bow from the Point oppofite to the Sun, adbrd very 
expeditious mechanical Condrud'ions. 
T 
7art 
