202 Astronomical and Nautical Collections, 



lengths of their respective undulations : and we obtain in 

 this manner precisely the same results as when we deduce 

 the lengths of the undulations from the measurement of the 

 fringes produced by two mirrors, or from the diversified 

 phenomena of diffraction. This numerical identity, which 

 was first pointed out by Dr. Young, establishes between 

 the coloured rings and the diftraction of light, an intimate 

 connexion, which, before his time, had escaped the notice of 

 natural philosophers, who had been guided by the system of 

 emanation ; this connexion being a natural consequence of 

 the theory of undulation only. 



According to the experiment of Mr. Arago, on the dis- 

 placement of the fringes produced by the interference of two 

 luminous pencils, when one of them has passed through a 

 thin plate of some refractive substance, we have seen that the 

 luminous undulations are shortened within the plate, in the 

 proportion that the sine of refraction of the substance bears to 

 the sine of incidence out of air. This principle is universally 

 true, and extends to all refractive substances, whatever their 

 nature may be : for example, the length of an undulation of 

 light in water, is to its length in air, as the sine of the angle 

 of incidence of rays passing obliquely from [water into 

 air], is to the sine of the angle of refraction. Consequently, 

 if we put some water between the glasses in contact, which 

 exhibit the coloured rings, the plate of air being replaced by 

 a plate of water, in which the undulations of light become 

 shorter, in the proportion which has been stated, the thick- 

 nesses of the two plates, which reflect the same rings, will be 

 to each other in the proportion of the sines of incidence and 

 refraction, at the passage of light from air into water. This 

 is precisely the result obtained by Newton from observation, 

 when he compared the diameters of the rings exhibited in 

 both cases, and deduced from them the respective thicknesses. 

 This remarkable relation between the phenomena of difirac- 

 tion, refraction, and coloured rings, which have no connexion 

 in the system of emanation, might have been very accu- 

 rately predicted from the theory of undulation, since, in this 

 theory, the sines of the angles of incidence and refraction 

 niust necessarily be proportional to the velocities of propa- 



