On Halos. 9jo 



Cor. I, If the rays converge to D they will, 

 after refleftion, diverge from/. 



Cor. 2. In the fame manner, if the rays diverge 

 from D upon the concave fide of the refleftor, 

 they will after reflexion converge to d. 



For the truth of thefe lemmas vid. Smith's 

 Optics, book 11, ch. 9. 



Let us fuppofe now with Dr. Halley that vapour 

 confifts of hollow fpherules of water, filled with 

 an elaftic fluid j and let BG? ( fig. 3. ) reprefent 

 fuch a Ihell. Take C its centre, and fuppofe 

 MB to be a fmall pencil of parallel homogeneal 

 rays, whofe angle of incid. is nearly 90' ; they will 

 be refraded to F the middle point of the chord 

 Bi or EI, ( Lem. II. Cor. i. ) and fince the ang. 

 BED is greater than EBC, or 48° ^^t, they fall 

 at E upon a convex fpherical refledor converging 

 to the middle of the chord EI j making then the 

 ang. D E G = to the angle DEB they will after re- 

 flexion diverge from/, the middle point of EK or 

 Gk (Lem. III. Cor. i.) they will therefore be 

 refraded at G in the direftion of the tang. GO, 

 and parallel to each otherj and if an eye be placed 

 any where in GO, they will excite the idea of 

 their proper colour. From O draw O M parallel 

 to BM, and fuppofe the whole figure to revolve 

 round OM as an axis, all the particles which 

 touch the furface defcribed by OG will refrad to 

 the eye a fimall pencil of parallel rays of the fame 

 c^r. 



Z 2 The 



