obtained by Combinations of Different Interferometers. 133 



The difference in wave-lengths amounts to 21*0609 A.U. 

 according to Fabry and Perot, and also by our measurements 

 with crossed spectra, at 15° and 760 mm. pressure. The 



(/9 2 \ 

 1 — -— J mm., 



and as it can be accurately observed, there is no difficulty in 

 measuring the thickness of an air- plate to within a few 

 microns. When the Fabry-Perot interferometer is used 

 singly, the accuracy in deciding the exact coincidence of the 

 two systems of rings is rather limited, even if these lines are 

 sharp and pure. In case of mercury lines, the immersion of 

 satellites on one side of the principal line causes an apparent 

 shift of the principal to that side and causes illusion. But if 

 we place another interferencei apparatus such as a Lummer- 

 Gehrcke plate or an echelon grating, and open the slit widely 

 so that the interference points, instead of being dots, are 

 small portions of circular arcs, the coincidences are easier to 

 observe, and we are free from the error caused by satellites. 

 Knowing <?, we can calculate P and P', which are whole 

 numbers. It must not, however, be forgotten that the 

 optical thickness varies with wave-length, so that we cannot 

 use the value of e found by the yellow lines for red or violet 

 lines. According to Fabry and Perot, the difference in e 

 amounts to a few millimicrons within the visible spectrum, 

 so that by making the air-plate sufficiently thick, we can 

 neglect this small difference in e. 



Thus far the discussion does not differ much from the 

 method introduced by Fabry and Perot, or that modified 

 by Lord Rayleigh* and others. The advantage of crossed 

 spectra consists in the accuracy with which we can measure 

 the position of interference points; consequently, the distance 

 between the plates e and the values of e and e' are exactly 

 known. This is due to the separate appearance of inter- 

 ference points for different lines, even in the position of 

 coincidence in the rings, when observed with interferometer 

 only. When the centre of the ring is known, the coordinates 

 of the interference points will determine at once the values 

 of e and e' . The coincidence of the rings observed with the 

 interferometer only may be perfect, but on interposing the 

 echelon, and measuring the numerous points, we generally 

 find a slight deviation, which we can detect from the dif- 

 ference in the values of e and e . So far as our experience 

 goes, the position of the centre of the system of rings is more 

 difficult to measure than the coordinates of interference 

 * Rayleigh, Phil. Mag-, xi. p. 685 (1906). 



