446 Astronomical and Nautical Collections, 



stripes belonging to the different colours, which prevents 

 their existing at any one point, in the proportions required 

 for constituting white light. The situation of these stripes, 

 being known for each species of rays, as well as the laws, 

 according to which their intensities vary in their different 

 parts, it will be possible to calculate the proportions of 

 their mixtures, and then to determine the tints that they 

 compose, by means of the empirical formula of Newton, 

 which enables us to find the tint corresponding to any 

 given mixture of coloured rays. Thus it is sufficient to 

 study the optical phenomena in any homogeneous light, 

 which presents them in their simplest form, and it will 

 always be easy to infer from them the appearances which 

 must be produced, under similar circumstances, in white 

 light. Henceforwards, therefore, it will always be supposed 

 that we employ a homogeneous light, except when the re- 

 sults of experiments made with white light are expressly 

 mentioned. 



It may easily be inferred, from the very simple law of the 

 influence of the luminous rays, which has been explained, 

 that the breadth of the fringes [in order to preserve the same 

 value of] d, must be in the inverse ratio of the interval 

 which separates the two images of the luminous point, and 

 in the direct ratio of their distance from the micrometer, or, 

 in other words, must be in the inverse proportion of the angle 

 under which the observer would see this interval, if he 

 placed his eye at the point where the fringes are reversed. 



The same geometrical law is applied to the fringes pro- 

 duced by two very narrow slits cut in a screen. The 

 breadth of the fringes, which they exhibit, is in the inverse 

 proportion of the interval comprehended between the middle 

 points of the two slits. 



This law is also true, in an approximate degree, of the 

 fringes which are observed in the shadow of a narrow sub- 

 stance, at least until they approach near to the limits of the 

 shadow; for when this is the case, they are governed by a 

 more complicated law, which nevertheless depends on very 

 simple principles, although it can only be represented by a 

 transcendental function, containing, besides the breadth of 



