Manchester Memoirs, Vol. xlii, (1898). No. 3. 13 



y=\\i.x becomes steeper, and the intervals of total reflection, 

 which are indicated by the heavier portions of the axis 

 of X in the figure, widen out at the expense of those of 

 partial transmission. 



In interpreting these results we must remember that 

 the quantity ka is inversely proportional to the wave-length, 

 and therefore directly proportional to the frequency, 

 of the incident vibrations. 



To estimate the maximum amplitude of the transmitted 

 waves, in any interval of partial transmission, we remark 

 that the value of in any such interval ranges between 

 the limits o and tt. If we put 6 = ^77, the formula (59) of 

 § 3 gives 



/= I sini^rt I . . . (74) 



Also, putting = j7r in (11), we have 



Xsccika 



2 



(75). 



Hence, near the centres of the intervals of higher order 

 we have 



ka = s-K -^ €, 

 where e is small, and 



approximately. We infer that in the successive intervals 

 of partial transmission the amplitude of the transmitted 



