On Halos. 341 



found : Rad. : S. of the angle CBE : : S.of ancid. 

 ; 3. pfrefraftionj and CE : CB : : S. of the angle 

 CBE : S. of the angle BEC, and the angles CBE, 

 CEB being known, the angle BCEisknown,which 

 meafures 4- of the dianaeter. And the converfe. 



The greateft halo will be formed when BE 

 touches the interior furface EI : in this cafe the 

 angle at E is a right angle j therefore the angle 

 BCE = 90° — 48° 2^' = 41° 24/, and the appa- 

 rent femidiameter 82° 48'. Alfo CB : CE :: 

 rad : S. of the angle CBE : : S. of the angle incid. 

 : S. of the angle of refradion. 



If we calculate the angle BCE for the red 

 and violet rays, and to twice the difference of 

 thefe angles add the moon's apparent diameter, 

 we get the breadth of the halo. 



Ex. If we fuppofe the radius of the halo to 



its outermoft edge i **, CE : CB :: . — l 



108 



: S. of the angle BED : : 75 : 7S-57o86 : : 131 

 : 132 nearly, and the angle BCE for the violet 

 rays will be about 29' 10" j confequently, the 

 breadth of the colours will be i' 40" + apparent 

 diameter of the moon. Hence it appears that the 

 rad. of the firft halo, mentioned above, could 

 not much exceed 30' if there w^re no interval 

 between the red and fucceeding violet. . 



If from the fame point in the luminous body 



M (fig. 5.) tangents, MA, MF, be drawn to 



the furfaces AB, FD, all the rays which fall be- 



Z 3 tyveen 



