552 Trofv/iihii) ct'tctrii'iii^ the JJfj.P.ifiu ^ Light. 



prop. IV. Tlie rays of liglit may be made to revohc round a centre in a fpiral orbit. 



Prop. V. If the inficcling furfacc be of confiderablc extent, and a plane, then the curve 

 tlcfcribul may be foiiml by lielp of the Prop. X1,I. Uook I. of IVmcipia ; provided only the 

 jiroportion of the force to the dillanee be given. Thus, if the bending force be Inverfcly .is 

 I he clil'.ance, the curve cannot be found ; for, in order to obtain its equation, a curvilinear 

 ••.iTca muft be fq'.iared, whicli, in this cafe, is a conic hyperbola ; the relation, however, be- 

 tween its ordinares and abfcifTx may be obtained in fluxions, thus : v » -♦- i y = «-.«». 



If the force (which is rtioft probable) be inverfcly as the fvpiaTe of the diilance, the curve 

 to be fquarcdis the cubic hyperbola ; fptcies LXV. genus'KI. of Nevvton's F.nunienition ; 

 ai:d tliis being quadrablc, the curve dcferibcd by the liglit will be XM parabola campanifcrmu 

 fur.i ; Species LXIX of Newton. 



If tlie force beinvcrfely as the cube of the diftanec, the curve is a circular arch, and tlist 

 of defle-vton is a conic liyperbola *. If the inflefting body be a globe or cylinder, and titc 

 Icrce be inverfcly rts the fqunre of the diftance from t^-ie Jurface ; tlven, by Prop. 1, XXI. 

 Uook I. of Principia, the attr;!clion to the centre is invcifi-Iy as the fquare of the diftaiice from 

 that centre •, and therefore, by Prop. XI. and XIII. of the f.ime Book, tlic ray moves in an 

 cUipfe by the inflecling, and in an hyperbola by the defleifliiig force ; each having one focus 

 in the centre of the body. The truth of tliefe things mathematicians will eafdy determine. 



Vivp. VI. If a ray fall on a fpecul >r furface, it will be bent before incidence into a curyc 

 having two points of contrary flexure, and then will be bent back the contrary way into as 

 equal and fimilar curve, as in Fig. i. PI. XXIII. 



Ccrcllnry to thefe proportions. If a pencil of rays fall converging on an itrtcrpofed. 

 bodv, ths fliadow will be lefsthan the body by twice the fine of inflexion. 



And if a pencil fall diverging on the body, the (hadow will be greater tlian the body by 

 twice the fine of inflexion; but lefs than it flioiild be, if the rays had paflird without bcnd- 

 iiig, by twice the fine of the difference between the angles of infle£lion and incidence. The 

 fine or angle of incidence is greater than the fine or angle of inflexion, when the incident 

 rays make an acute angle with the body ; but, when they make an obtufe or right angle, 

 then the fine or angle of inflexion is lefs than that of incidence. The fine of incidence \i 

 greater than that of deflexion, if the angle made by the incident ray with the body is ob- 

 tufe ; but lefs, if that angle be acute or right. If a globe or circle be held in a beam of 

 light, the rays may be made to converge to a focus. 



Hitherto it has been fuppofed that the parts of which light eonfifts have all the fame dif- 

 pofition to be a^led upon by bodies which infleft and deflecl them ; but we fliall now fee 

 that this is by no means the cafe. 



Ohfirvat'icii I. Into my darkened chamber I let a beam of the fun's light through a hole 

 in a metal plate (fixed in the window-fhut) of -^^ of an inch diameter ; and all other light 

 being abfoibed by black cloth hung before the window and in the room, at the hole I 

 placed a prifm of glafs, whofc refra£ling angle was 45 degrees, and which was covered all 

 over with black paper, except a fmall part on each fide, which was free from impuritie!;, 

 and through which the light was refrafted, fo as to form a diftinft and tolerably homoge- 

 neous fpec\rum on a chart at fix feet from the window. In the ray?, at two feet from the 



• Principia, Lib. i. Prop. 8. 



prifm, 



