On the Mechatiifm of the Eyt, 4^27, 



according to the direflion and quality of the vibration. Whether or no, ftri(ftly fpeaking, 

 wc can hear two founds, or fee two objefts, in the fame inftant, cannot eafily be deter- 

 mined :, but it is fufEcient, that we can do both, without the intervention of any interval of 

 titne perceptible to the mind ; and indeed we could form no idea of magnitude, without a 

 comparative, and therefore ne;irly cotemporary perception of two or more parts of the fame 

 obje(n:. The extent of the field of perfciH; vifion for eaph pofition of the eye, is certainly 

 not very great ;' but it will appear hereafter, that its refradivc powers arc calculated to take 

 in a moderately diftinfl: view of a whole hemifphere: the fenfe of hearing is equally per- 

 fe^ in almoft every direflion. 



IV. DIOPTRICAL PROPOSITIONS; 



Propofition I. Phenomenon. 



In all refra£tions, the ratio of the fine of the angle of incidence to the fine of the angle 

 of refradtion is conftant* (Newton's Opt. I. Ax. 5. Smith's Opt. 13. Wood's Opt. 24.) 



Scholium i. "^e. (hall c^U. it the ratio of m to m -f 1, and m T i, n. In refradliops 

 out of air into water, m ~ 4 and « — 3, very nearly ; out of ait into glafs,- the ratio is 

 nearly that of 3 to 2. 



SchQlium 2. According to '&ixxovf, ( Le£l. Opt. ii. 4.) Huygens, Euler, (ConjeSi. ph;jf. 

 circa prop, font et luminis. Opufc. t. ii.) and the opinion which I lately fubmitted to the Royal 

 Society, (Phil. Tranf. for 1800. p. 128,) the velocity of light is the greater the rarer the 

 medium : according to Newton, (Schol. Prop. 96. 1. i. Princip. Prop. 10. p. 3. 1. ii. Opt.) 

 and the doftrine more generally received, the reverfe. On both fuppofitions, it is always the! 

 fame in the fame medium, and varies in t-he ratio of the fines of the angles. This circum- 

 ftance is of ufe in facilitating the computation of fome very complicated refractions. 



Propofition II. Phemmenon. 



If between two refra£l:ing mediums, a third medium, terminated by parallel furfaces, be 

 interpofed, the wHole refradlion will remain unchanged. (Newton's Opt. 1. i. p. 2. 

 Prop. 3. Smith, r. 399. Wood, 105.) 



GaroUary. Hence, when the refraftions out of two mediums into a third are given, the 

 refraction at the common furface of theie mediums may be thus found. Let the refractions 

 given be as m :n, and as «»':«' 5 then: the ratio fought will be that of m «' : m' n. For 

 inftance, let the three mediums be glafs, water, and air-, then tn~ 3, nzz 2, m' ~: 4^ 

 «' zz 3,.« /iVz;; 9* and m' n ~- 8. If the ratios be 4 : 3, and 1 3 : 14, w? have tn »' : tn' n 

 :: 39:56; and, dividing by 56 — 39, wc obtain 2.3 and 3.3 for m and~w -f i, in 

 Schol. I, Prop. I. 



Propofiiton 



