Astronomical and Nautical Collections, ~ 40S 



tions only, and consequently no colours, because there are 

 no interferences. 



Both images, on the contrary, are distinguished by the 

 brightest colours, when the coefficient of the variable term 

 is equal to unity, which hapj^ens when s = o, and i = 45° ; 

 and then the two expressions become 



« «-« 



Ord. im. . . . 1— sin '^r-r-, or cos -y . . 



A A 



Extr. im. ... sin tt — -. 



A 



It must be remarked, that the second expression is similar 

 to that which indicates, for the common coloured rings, the 

 result of two systems of undulations reflected perpendicu- 

 larly at the first and second surface of a plate of air, when 

 its thickness is equal to i (p—e), which makes the difference 

 of the paths described equal to o — e. In fact, if we repre- 

 sent the velocity of oscillation for each system of undulations 

 by J, and remark that these velocities must be taken with 

 contrary signs, because one of them is reflected within a 

 denser medium, and the other without it, which occasions an 

 opposition of signs, as we have seen in the explanation of the 

 phenomena of coloured rings, we may proceed to find for 

 the intensity of the resulting light, by the formula already 



employed, J+ J— 2 . J . J cos 29r -r— , or | — J cos 2 5r-r-; 



A A 



or lastly, sin " ^~t~. 



Thus the tints of the extraordinary image, produced by 

 crystallized plates, must resemble those of the reflected 

 rings, as the observations of Mr. Biot had demonstrated; at 

 least while the difference o—e produced by the crystal does 

 not vary sensibly with the nature of the rays : for, in the 

 coloured rings, this difference being twice the distance of 

 the thickness of the plate of air, in a perpendicular direc- 

 tion, is rigorously the same for all kinds of rays. 



The formulas which Mr. Biot has derived from this resemr 

 blance represent, with great fidelity, the colour produced 

 by a single plate. Instead of giving immediately the inten- 

 sities of each species of coloured rays, like those which are 

 here calculated, they refer to the table of Newton, which 

 contains the tints of the reflected rays, and they show, at the 



