and their Magneto-optic Properties. 267 



addition to N, its octave 2N as the next frequency, then 3N, 

 «tc, while the lines * of Wood's iodine spectra, excited 

 by green or yellow light, follow upon one another in intervals 

 of 60 to 85 A.U. only. What we require is a fractional 

 power of js, but little differing from unity. 



Let us write, therefore, /(#) = «. x* 9 where p is a real, 

 positive, constant, whose value is for the moment undeter- 

 mined. Then (2) will become 



x + kx + Nx 2 = c Q e im -ax p (4) 



Whatever the value of p, the difference 1—p will be a 

 certain measure of departure of the resonator from Hookean 

 elasticity, and it will be responsible for the series of lines 

 accompanying the fundamental one. The coefficient a is a 

 real constant. If symmetry around the position of equi- 

 librium is required, then x p is to be taken as + | xP | , according 

 as x>0 or x<0. 



As to c , if the exciting agent be (polarized) light, c is 

 the product of the amplitude of the electric force in the 

 incident wave, and of q/m, the ratio of the charge and mass 

 of the resonator. 



Now, proceeding by the well-known method of successive 

 approximations, write, first, 



x = be , 



and neglect ax p . Then 'x-\-T$x 2 = 0, and 



6 =-*Hf (5) 



Substitute the first approximation in x p , so that (4) will 

 become 



w + kx + Wx = c e^ - ab p e lpm : 

 thus, as a second approximation, 



x = be im + b 1 e ipm , 

 where b is as above, and b\ is determined by 



b l [W(l-p 2 )+iWp'] = -ab p . . . . (5J 



Thus, b x is a complex magnitude, say b 1 = pie %dl ; 6\ is the 

 phase-difference with respect to the exciting oscillation, and 

 p 1 the amplitude of the oscillations of frequency n 1 =pN. 

 The former is of no interest here, and as regards the latter 



* To speak only of the chief lines of groups or " orders," each of 

 which contains in addition a number of fainter lines. 



T2 



^^m^^^^^^m^am 



