NATURAL PHILOSOPHY. 153 



hundred-and-first of this set. Consequently, at about this part of 

 the phenomenon, the bright spaces of one set of rings will occupy 

 the same position as the dark spaces of the other sot, and they 

 will mutually obliterate each other. But since the thousandth ring 

 of one set is nearly the same size as the thousand-and-first of the 

 other, the two sets of rings will appear to fit each other again 

 about this point ; the fifteen-liundredtli of the first set, however, is 

 larger than the fifteen-hundredth-and-first of the second set, but 

 not so large as the fifteen-hundred-and-second, and hence, at 

 about the position of the ring, the rings of the two sets will over- 

 lap each other, and mutually efface each other's outlines. And, 

 carrying such considerations further, it is evident that the appar- 

 ent coincidence and overlapping of the two systems of rings 

 would occur alternately at regular intervals. 



In order to simplify this explanation, we have tacitly assumed 

 the lens to be so large that several thousand rings could be seen 

 between its centre and its circumference, Practically, this would 

 be impossible ; but by gradually separating the lens from the 

 plane glass, we can, as it were, draw in towards the middle the 

 rings which, with a larger lens, would be formed at a great dis- 

 tance from the centre. 



Now, according to the explanation which the undulatory theory 

 gives of the foundation of " Newton's Rings," the distance by 

 which the interval between the glasses must be increased, in 

 order that a given ring may come into the position previously 

 occupied by the next smaller ring, must be equal to half the 

 wave-length of the kind of light used for the experiment; and 

 the distance of 0.28945 millimetres which, as M. Fizeau found by 

 actual measurement, it was necessary to vary the space between 

 the glasses, in order to make the rings go through one of "the re- 

 current periods above described, that is to say, pass from sharp- 

 ness to confusion and become sharp again, must contain just one 

 more half wave-length of one portion of the light by which the 

 rings are formed, than it does of the other. 



This brings us to the point of contact between M. Fizeau's 

 observations and those of Prof. Angstrom, to which we referred 

 at the beginning. According to the latter, the wave-lengths of 

 the two principal constituents of the light emitted by a flame 

 containing the vapor of sodium (such as the flame employed by 

 M. Fizeau) are respectively 



0.000589513 millimetres. 

 0.000588912 



Now, if we divide 0.28945 by half the former of these numbers, 

 we get, as the quotient, 982 ; and if we divide it by half the 

 second, we get, as the quotient, 983. That is to say, we find 

 precisely as the undulatory theory requires, that the distance 

 measured by M. Fizeau contains exactly one more half wave- 

 length of the more refrangible constituent of the light of a 

 sodium-flame than it does of the less refrangible part. And, 

 moreover, if we calculate from Angstrom's determination of the 

 wave-lengths, the number of rings which must intervene between 

 the positions of greatest confusion and greatest distinctness, we 



