730 PHILOSOPHICAL TRANSACTIONS. [aNNO 1672. 



Mr. Nejvton's Letter of April 13, 1672, O. S. written to the Editor, 

 being an Ansiuer to the foi^egoing Letter of F. Bardies. Translated 

 from, the Latin. N" 84, p. 4091. 



I received, Sir, the observations of the Kev. Father Ignatius Pardies, on my 

 letter concerning the refractions and colours of light: for which I acknowledge 

 myself much obliged to him ; and shall here clear up the difficulties he com- 

 plains of. In the first place, he says that the length of the solar image pro- 

 duced by the refraction of the prism, requires no other cause to account for it, 

 than the different incidence of the rays from opposite parts of the sun's disk; 

 and that therefore it does not prove a different refrangibility in the different 

 rays. And, to prove the truth of his assertion, he states a case, in which from 

 a difference of 30' in the incidence, the difference of the refraction may be 1* 

 13' y or rather more, as my experiment requires. But the Rev. Father is under a 

 mistake. For he has made the refractions by the different parts of the prism to 

 be as unequal as possible, whereas in the experiments, and in the calculation 

 from them, I employed equal refractions. Thus, let ABC (fig. 8, pi. 15,) be a 

 section of the prism perpendicular to its axis ; FL and KG two rays crossing 

 each other in x, the middle of the hole, and incident on the prism at G and L; 

 which let be first refracted into GH and Lm, and then into HI and mn. And 

 since I supposed the refractions at the side AC are nearly equal to those at the 

 side BC ; if AC and BC be equal, the inclination of the rays GH and Lm, to 

 the base AB of the prism, will be similar ; and therefore the angle CLm = the 

 angle CHG, and the angle CmL = the angle CGH. Therefore the refrac- 

 tions in G and m will be also equal, as well as those at L and H; consequently 

 the angle KGA = the angle nmB, and the angle FLA = the angle BHI; 

 and hence the inclination of the refracted rays HI and mn will be the same with 

 that of the incident rays FL and KG. Therefore let the angle FxK of 30' be 

 equal to the sun's diameter, then the angle made by HI and mn will be also of 

 30', provided the rays FL and KG be equally refrangible. But my experi- 

 ment gave that angle about 1° 49', which is constituted by the ray HI of the 

 extreme violet colour, and by the ray mn which gives the blue; and therefore 

 those rays were differently refrangible, or the refractions were necessarily pro- 

 duced according to the unequal ratio of the sines of incidence and refraction. 



The Rev. Father further adds, that to make a just calculation, it is sufficient 

 to subtract the magnitude of the window hole from the length of the image on 

 the paper ; since, even supposing the hole indivisible, yet there would be 

 formed as it were a broad hole in the posterior surface of the prism. But yet it 



