Astronomical and Nautical Collections. 201 



to conclude, on the contrary, that they are completely at 

 variance ; and, on the other hand, when the difference of the 

 paths would indicate a complete discordance, we must infer 

 that their oscillatory motions agree perfectly with each other. 

 Upon these principles it is easy to determine the position of 

 the dark and bright rings. 



In the first place, the point of contact, where the thickness 

 of the plate of air is evanescent, and produces no difference 

 in the length of the paths of the two systems, ought to exhi- 

 bit a perfect agreement in their oscillations : hence, from the 

 opposition of the signs, the reverse takes place, and they 

 destroy each other ; so that the point of contact, when seen 

 by reflection, exhibits a black spot. As we go further from 

 this point, the thickness of the plate becomes greater ; and at 

 a certain distance it becomes, for example, equal to half an 

 undulation, which would exhibit a complete discordance ; 

 but, from the change of signs, affords a perfect agreement, 

 so as to become the most luminous part of the first bright 

 ring. When the thickness of the plate of air is equal to half 

 the length of an undulation, the difference of the paths de- 

 scribed being a whole length, which answers to a perfect 

 agreement, there will again be a perfect discordance, and 

 the part will be the middle of a dark ring. It is easy to see, 

 in general, from the same mode of reasoning, that the black- 

 est points of the dark rings correspond to thicknesses of the 

 plate of air expressed by 0, J<i, |c?, 2d, ^d, and so forth ; 

 and the most brilliant points of the bright rings to thick- 

 nesses id, ^d, -5fl?, Id, 1^, V^?, and so forth ; d being the 

 length of a luminous undulation in air; or, if we take one 

 fourth of this length for our unit, the thicknesses of the plate 

 of air, answering to the maxima and minima of reflected light, 

 will be represented by the following numbers : 



Dark rings 0, 2, 4, 6, 8, 10 ... . 

 Bright rings 1, 3, 5, 7, 9, 11 . . . . 



It is evident that this unit, or the fourth part of a lumi- 

 nous undulation, is precisely the length of what Newton calls 

 the Jits of the particles of light : so that if we multiply by 

 4 the measures of them which he has given, for ** the seven'' 

 principal kinds of simple rays, we obtain the corresponding 



