Astronomical and Nautical Collections, 447 



the body and its distance from the micrometer, its distance 

 from the luminous point. 



With respect to the exterior fringes which surround the 

 shadows, their breadth depends always on both these dis- 

 tances : the former remaining constant, they are so much the 

 broader as the second is smaller. 



When, on the contrary, the respective positions of the 

 luminous point and tlie screen are invariable, and the dis- 

 tance of the micrometer only from the screen is changed, 

 we observe that the breadth of the external fringes is not 

 proportional to it, as that of the internal fringes was. This 

 fact may be expressed in a more geometrical manner by con- 

 ceiving a right line drawn through the luminous point, in 

 the direction of a tangent of the opaque body, so as to con- 

 stitute the limit of the geometrical shadow, and saying that 

 if we follow in space the middle of the same dark or bright 

 stripes, and let fall from this point, at each distance, a per- 

 pendicular on the tangent, we find indeed that this little 

 perpendicular increases as we go further from the opaque 

 body, but in a less proportion than that of the distance 

 from that body. Hence it follows that the same point of a 

 dark or light stripe, belonging to the external fringes, does 

 not describe a right line, but a curve, of which the convexity 

 is turned outwards. This may be demonstrated by a pre- 

 cise measurement, made by means of the micrometer that 

 has been described : and the result being a very remark- 

 able one, it will be worth while to describe one of the 

 experiments by which it has been exhibited : an experi- 

 ment which was made with light apparently homogeneous, 

 that was transmitted through the red glass already men- 

 tioned. 



The opaque body being at the distance of 118.53 E. I. 

 from the luminous point, I measured the successive inter- 

 vals between the edge of the geometrical shadow, and the 

 darkest point of the dark band of the third order: first 

 at the distance of .067 i. from the opaque body ; secondly 

 at 39.49 i.; and thirdly at 157.28 i.; and I found for the 

 first interval .00315 i., for the second .0866; and for the 

 third .2296. Now if we join the two extreme points by a 



