VOL. LXXXVII.] PHILOSOPHICAL TRANSACTIONS. \QQ 



that the same happens when the rays are refracted in a way similar, or analogous, 

 to that in which the other images were produced by reflexion and flexion. 



We are now to show, that this difference of size is not owing to the different re- 

 flexibilities and flexibilities of the rays. In order to this, we shall both demonstrate, 

 and then prove by experience, " that inflexion and deflexion do not decompound 

 heterogeneous rays, whose direction is such that they fall on the bending body." In 

 fig. 6, let ab be the body ; gh, ef, cd, the limits of its spheres of deflexion, in- 

 flexion, and reflexion, respectively ; and let ip be a white ray of direct light enter- 

 ing at p the sphere of deflexion : through p draw lk at right angles to gh ; ip will 

 be separated into pr red, and pv violet, and the 5 other colorific rays according to 

 their deflexibilities ; at r and v draw the perpendiculars st and qo ; then the alter- 

 nate angles prt, rpl ; and pvq, vpl, are equal each to each. But trp and avp 

 are the angles of incidence, at which the red and violet enter the sphere of inflexion: 

 and rpl, vpl are the angles of deflexion of the red and the violet ; therefore the 

 difference of the latter 2, that is rpv, is likewise the difference of the 2 former. 

 Suppose this difference equal to nothing ; or that pv and pr are parallel ; then rRs, 

 the angle of the red's inflexion, will be less than wo, the angle of the violet's in- 

 flexion, by the angle rpv : when not evanescent, add rpv to trs ; then trs will be 

 equal to wo : that is, the divergence will be destroyed, and the rays enter the 

 sphere of reflexion, parallel and undecompounded. It is evident therefore, that 

 the effect arising from the different deflexibilities of the rays is destroyed by the 

 equal and opposite effect produced by their different inflexibilities ; and the same 

 thing may in like manner be shown to happen in the return of the rays from the 

 body after reflexion. But let the rays be so reflected, that they shall pass by the 

 body without entering any more than one sphere of flexion ; then they will be 

 separated by their flexibilities, as we before described. It appears then, that if the 

 rays of light were not differently reflexible, flexion could never produce the coloured 

 images, by separating the compound light. And indeed this may be easily proved 

 by fact. At 144 feet from the bending body, the greatest fringes by flexion are 

 only half an inch in length, whereas the 4th or 5th images by reflexion are above 

 half an inch at 1 foot from the reflecting surface : the one sort is therefore more 

 than 144 times more distended than the other, whereas the flexion could, at the very 

 farthest, only double them. Also the distinctness, and brightness, and regularity 

 of the colouring, are quite different in the 2 cases ; the supposed cause would 

 neither account for the order of the colours, nor for their absence in common 

 specular reflexion, and refraction through two prisms joined together with their 

 angles the contrary ways. Lastly, if we suppose the images to be produced by 

 flexion, and then reflected from the body, it would follow, that light incident on a 

 prism should be decompounded, formed into several coloured images, and then re- 

 fracted, the violet being least and the red most bent ; all which is perfectly the re- 

 verse of what actually happens. I have multiplied the proof of this proposition 



