UNDULATION LENGTHS AND NUMBERS. 



171 



obtuse vertex in two intcrfi'rinp; waves. The effects correspond in all respects 

 ■with those produced by Frcsnel's mirrors. 



Mr. Arago also introduced a modification of the experiment, which, though 

 simple, is very interesting in the bearing upon theory, of its results. In the 

 path of one of the interfering rays he interposed a thin lamina of mica. As 

 mica is transparent, it was to be expected that fringes would continue to ap- 

 pear after the interposition as well as before ; and this expectation is realized. 

 But as the undulation length cannot be the same in the mica as in the air, since 

 the refracting power of mica exceeds that of air, it was also to be expected that 

 the fringes would change their place; and this expectation also is fulfilled. The 

 direction of the displacement will depend upon the question, which of the two 

 waves, after the lamina is interposed, will be found, when they reach the position 

 of the originally luminous central stripe, to be advanced beyond the oth(>rin its 

 phase of undulation. This will of course be true of that which has the least 

 average length of undulation. If the undulations in mica are of less length 

 than in the air, (a necessary supposition, as we have already seen,) the average 

 length of undulation on the side of the )nica will be less than that on the other side ; 

 and accordingly the phase at the central line of meeting Avill be most advanced 

 on the side of the mica. We must therefore assume a line upon the screen par- 

 allel to the central line, such that the length of path from the radiant on the side 

 of the mica shall be as much less than the length of path from the other radiant 

 to the same line, as the thickness of the lamina of mica is less than that of a 

 lamina of air embracing the same number of vindulations would be, in order to 

 find the position of the bright stripe which is central in the displaced system. 

 The whole system is of course moved toward the side of the mica. 



If homogeneous light be employed in the experiment with Fresnel's mirrors 

 or Arago's prism, equation [7.] or [8.J furnishes the means of measuring the 

 undulation lengths in different parts of the spectrum. In the following table 

 are embraced the results of such a measurement, made by Fraunhofer and 

 expressed in decimals of an inch, for fourteen different positions determined by 

 their relations to the colors or to the fixed lines of the spectrum. The undulation- 

 lengths in this tabic are taken from Fraunhofer : the niunbers per second are 

 computed on the supposition of a velocity of light of 192,700 miles to the 

 second. 



Undulation-hngfJis and nu tubers per second. 



Place iu spectrum 



Line B 



Line 



Middle red 



Line D 



Middle oratigo 

 Middle yellow 



]^iue E 



Middle green.. 



Line F 



Middle blue... 

 Middle indigo. 



l^iue G 



Middle violet. 

 Line H 



Length of un- 

 dulations iu 

 parts ot inch. 



. 00002708 

 . 00002.583 

 . 00002441 

 .00002319 

 , 00002295 

 .00002 J 72 

 . 00002072 

 .00002016 

 .0000] 900 

 .00001870 

 . 00001 703 

 .00001689 

 .00001 OOf) 

 . 00001547 



Number of un- 

 dulations iu 

 an inch. 



Number of undulations 

 per second. 



no, 918 

 ;{S,7J9 

 40, 949 

 415, 12:5 

 4:*>, 507 

 46,0:54 

 48, 286 

 49, 609 

 52, 479 

 53, 472 

 56, 569 

 59, 205 

 60, 044 

 64, 631 



451,000,000, 

 473, 000, 000, 

 500, 000, 000, 

 527,000,000, 

 532,000,000, 

 562, 000, OOt), 

 59,), 000, 000, 

 606,0(10,000, 

 641,000,000, 

 653, 000, tlOO, 

 691 , 000, 00(», 

 72:5, 000, 000, 

 733, 000, 000, 

 789, 000, 000, 



000, 000 

 t)00, 000 

 000, 000 

 000, 000 

 000, 000 

 OOt), 000 

 000, 000 

 t)00, 000 

 OtiO, 000 

 000,000 

 000, 000 

 000, 000 

 000, 000 

 000, 000 



