COLORS OF THIN PLATES. 119 



the prismatic spectrum whose n-frangibility and color are sensibly the same. 

 Then very many more bright rings will be observed, separated by intcirraediatc 

 rings entirely dark. ]3ut what is of most importance at present is that those 

 which are i'ormed by the least refrangible rays arc larger than any others, and 

 that the diameters of rings of the same order regularly diminish as the refran- 

 gibility increases. This difference of magnitude between the rings of different 

 tints occasions the overlapping of one color upon another when white light is 

 used, so that the colors observed are not simple but resultant colors, determined 

 in their tints by the simple colors which happen to be predominant at any point. 

 The other components serve, with some portion of the predominant tint, to pro- 

 duce white light, by which the tint is diluted and rendered more feeble than it 

 would otherwise be. The truth of this explanation will be made apparent by 

 viewing the rings through a prism. The effect will be to make the overlajj- 

 ping on one side more complete than before, and, on the other side, less. The 

 rings Avill be less highly colored but more numerous and better separated on the 

 side of greatest refraction, and more confused on the other. 



From a careful measurement of the diameters of all the bright rings, Sir 

 Isaac Newton ascertained that the squares of these diameters form a regular 

 arithmetical p^-ogressiou, corresponding to the natural series of odd numbers, 1, 

 3, 5, 7, &c. And the squares of the diameters of the hitermediate dark rings 

 were found to constitute another similar progression, corresponding to the series 

 of even numbers, 2, 4, 6, &c. From the law xozif, it therefore follows that 

 the bright rings appear where the thickness of the plate is once, thrice, fire times, 

 &c., some constant value, and that the dark rings appear Avhere the thickness is 

 twice, four times, six times, &c., the same constant value. The next question 

 to be determined is, therefore, what is that constant ? 



In order to ascertain this, Sir Isaac Newton measured with great precision 

 the absolute diameter of the fifth dark ring. This, with the known radius of the 

 spherical surface of the lens, enabled him to compute the thickness of the plate 

 at that ring, this thickness being the versed sine in a great circle of the sphere 

 of an arc of which the measured diameter is the chord. The result gave him 

 ■g^^ of an inch, very nearly, for the thickness of the plate at the fifth dark 

 ring. But the fifth number in the series 8, 4, 6, &c., is 10. Hence, the con- 

 stant sought for is one-tenth of -gg^^o" ^^ ^^ ruf^h, or xnuHTo' ^^'^^ this is the 

 thickness of the plate at the point where the greatest brightness of the first 

 bright ring is seen. Reduced to a decimal, it gives a little more than fifty-six 

 ten-millionths of an inch. If the value of this constant be sought for the several 

 homogeneous rays, it will be found to be, for the violet, a littlemore than thirty- 

 nine ten-millionths, and, for the red, not quite sixty -nine ten-millionths. As, in 

 the space occupied by the colors of the first order, the thicknesses vary slowly, 

 and as there is a certain range of variation in thickness within which each color 

 may appear, though its greatest intensity is in the middle of this range, it 

 happens that the colors of the first order are dilute, especially toward the centre 

 of the system, and that the middle of the series is white. In the succeeding 

 orders, the differences tell in such a manner that the bright rings of some colors 

 fall more or less exactly upon the dark rings of others, and the tints become 

 stronger. But, as the thicknesses soon begin to vary rapidly, every system of 

 rings becomes crowded, and the separating dark intervals groAV narrower and 

 narrower, until there is a complete blending of tints at every point and the 

 resultant is sensibly white. When water is introduced between the glasses, the 

 rings become immediately smaller. If the thickness at which a given tint now 

 appears is compared with that at which the same tint appeared in air, it is found 

 to be reduced in the ratio of n to I, n being the index of refraction between air 

 and water. This law admits of being generalized. In fact, whatever be the 

 substance of the thin plates in which these tints appear, the thicknesses Avhich 

 produce them are inversely proportional to their index(.'S of refraction. 



