770 Prof. H. Rubens and Mr. H. Hollnajrel 



on 



of damped sine waves of wave-lengths Ai and logarithmic 

 decrement y lt As was first pointed out by Bjerknes *, such 

 a train of waves, at normal reflexion on a fixed wall, causes 

 stationary waves which can be proven to take the form of a 

 damped sine wave ; this by the utilization of an energy 

 measuring instrument to record the various intensities which 

 are plotted as ordinates against the corresponding distances 

 from the stationary wall as abscissae. In this curve the 

 wave-length is one-half as great, but the logarithmic decre- 

 ment has the same value as in the component waves. The 

 interference curves, as recorded by the previously described 

 interferometer, and the intensity curves of the stationary 

 waves just considered are of entirely similar formf. It is 

 therefore permissible to take the value of 7 as given by the 

 interference curves, considering them from the above stand- 

 point, i. e. as damped sine waves with a logarithmic decre- 

 ment y. But one difficulty in the case of figs. 3, 4, and 5 

 presents itself, that of the two bands, i. e. we have to deal 

 with two damped sine waves which produce the fluctuations 

 shown. To obviate this difficulty a further assumption is 

 made: the damping in both stripes referred to the same length 

 shall be the same, that is, the logarithmic decrements shall 

 be in the same ratio as the mean wave-lengths of the two 

 radiations : — 



Yi : 72 = Ai :A 2 . 

 This agrees very approximately with the experimental 

 results, since the fluctuations appear at various positions in 

 the interference curves almost equally strong. Under this 

 assumption the logarithmic decrements can be easily cal- 

 culated, for one only considers those maxima and minima of 

 the curves which appear the most intense, t. e. in which both 

 damped-sine waves are in phase. This is the case, for 

 example, in fig. 4 in the maximum a, the minimum i', and the 

 maximum s. The ordinate difference (h aa <) for the points a 

 and a! is 6'0 mm., for i' and k (Jim) 3*1 mm., and for s and 

 s' (hg S <) 1*8 mm. The logarithmic decrements as calculated 

 from these values are accordingly : — 



7l = - log. nat.^' =0'078, 

 n tii K 



71= -log. nat. 7^ =0'071. 



* V. Bjerknes, Wied. Ann. xliv. p. 517 (1891). 



f This holds true only when the reflectivity on the boundaries of the 

 air-film is small. The approximation in the present case is a good one. 



