J38 On Halos. 



colours, as in the firft of thofe mentioned above; 

 the red of afecond was juft feen, and its diame- 

 ter, as far as could be determined by the naked 

 eye, was double the diameter of the firft. In at- 

 tempting to account for thefe appearances it will 

 be neceflary to lay down the following Lemmas. 



LEM. I. A ray of red light cannot pafs out of 

 water into air if the ang. of incidence exceed 

 48^ 35' 26". Nor a violet ray, if that ang. ex- 

 ceed 47° 59' 53'^ 



LEM. II. If a fmall pencil of parallel rays fall 

 upon a fpherule of water ABE (fig. i.) and 

 CD be drawn perpendicular to the refradted rays, 

 they will converge to a point F, which is found 

 by taking FB '• FD : : tang, of incid. : tang, of 

 refradlion. 



Cor. I. Let the angle of incidence approximate 

 to a right angle, and the tangent of incid. will ul- 

 timately be indefinitely greater than the tangent of 

 refraflion, and confequently F will coincide with D. 



Cor. 2. If a fmall pencil of rays diverging 

 from D be incident the contrary way, they will 

 be refrafted parallel. 



LEM. III. Let a fmall pencil of rays fall upon 

 the convex fpherical refledor BFG (fig. 2.) con- 

 verging to Fi from C its centre draw C D perpen- 

 dicular to BF, and CD to B/ the diredlion ofthc 

 rcflefted ray produced back; bifed BD, Bd In a 

 andi>, and take Fa '• aB ::Bl? '.bf: the rays after 

 refleftion will diverge from/. 



Cor^ 



