On the Injiexhn, Rcjlcxion, mid Colours of Light. 591 



9pd' by what rays formed. Then I joined the p^rts that I Iiad marked, and 'obtnined a 

 eorve, which I took to be, either nearly or accurately, an hyperbola of the fourth order. I 

 next meafured the ordinates (the axis of the fpcclrum and ihadow being the axis of the 

 curve) at the confines of each colour; firft, the ordinate at the extremity of the redilinear 

 red, then that at the confine of the red and orange, and fo on to that at the extreme reft?- 

 linear violet. To each of thefe ordinates I added the greateft one, or that in the violet, 

 which (in fig. 10 ) is W; that is, I produced vV to V, fo that vV is equal to vV ; and 

 through V I drew V'R' parallel to the axis V R, and produced gG to G', and rR to R' ; 

 then from V'l fet ofFV'g' equal to G'g, and VV equal to R'r, and the other ordinates m 

 like manner ; and I found, according to the method before defcribed *, that VV was di- 

 vided inverfely, after the manner of the mufical intervals. It is therefore evident that the 

 inflexibilities of the rays are diretlly as their deflexibilities and reflexibilities, but inverfely 

 as their refrangibilities. The fame may be proved by meafuring aiul dividing the images 

 made in the inCde of the fliadows. Thefe 1 have found to be at equal incidences and dif- 

 tanccs, equal to the images on the outfide, both in breadth, in diflance from the edge of 

 the fhadow, and in the relation which their divifions bear to one another ; wherefore what- 

 ever be the ratio of the angle of intlexion to that of incidence, the fame is the ratio of 

 the angle of deflexion to that of incidence ; fo that the angle of deflexion is equal to the 

 angle of inflexion. If farther proof of this propofition be defired, the following experiment 

 and obfervations, which from the importance of the thing I do not fcruple to add, may be 

 fufficient. 



Obf. 14. Wlien two knife blades were placed by one another in a beam of light which 

 entered the dark room, fo that the one might form and the other diilend the images, I 

 made in one of the blades (with a file) a fmall denr, which, on the chart, call an elliptic or 

 femicircular outline ; then I obferved that the images of both blades were diflurbed by it, 

 and wound round the edges of the femicircle ; and they were all afFefted in precifely the 

 fame manner and degree. So then the firft knife deflected the images formed by the fpcond 

 in precifely the fame degree that it inflefted thofe images which itfelf formed, and To of 

 tlie other knife; otherwife the efFe<S of the dent would have been (lifferent upon the two 

 fets of images. We may therefore conclude that the angles, or fines of inflexion and de- 

 flexion, bear the fame ratio to the angle or fine of incidence, and that they are equal to one 

 another. My next obje£l was to determine this ratio in one of thefe cafes, ;and confe- 

 quently in both ; and it vras very agreeable to find data for the folution of this problem in 

 1 Newton's meafurement of the images and (hadow ; fince this philofopher's well-known ac- 

 curacy in fuch matters, befides the fingular ingenuity of the methods he employed, made 

 me more fatisficd with thefe than any experiment I could make on the fubjei^. In fig. 11. 

 CS is the line perpendicular to the chart SU, and pafllng through the centre of the body, 

 whofe half is CD or SE. EB is parallel to CS, and AI a ray incident at D. ADH or 

 EDI is the angle of incidence, EDIl that of the red's deflexion, EDV that of the violet'si 

 and EDG that of the intermediates. According to Newton f, CD was -, 5-j,th of an'incli, 

 ■DE fix inches, SI t-^-j'^ of an inch, RV -pic'^' ^'"* confequently, RG -jj-ijtli ; GS 'Wns 

 •/,th; whence the angles IDE, EDV, EDG, and EDR,willbc found to be 4', 30"! 5 '; 7 ', aad 



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• Page 5*0. 1 Opticf, Bo^>l' HI. Olif. 5. 



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