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XXXVII. On the Photography of Ripples. — Fourth Paper. 

 By J. H. Vincent, D.Sc, B.A., A.R.C.Sc.* 



[Plates V. & VI.] 



IT is proposed to bring this series f of articles to a close by 

 photographically recording some experiments on the 

 refraction of ripples. After seeking in vain for a more satis- 

 factory method of refracting ripples than that of using a 

 shallow portion of liquid to correspond to the optically denser 

 medium, this method was adopted. The use of mercury, in 

 reflexion methods, for the photography of ripples, leaves 

 nothing to be desired when dealing with most of the phenomena. 

 If, however, we wish to use mercury in refraction experiments, 

 it is necessary to employ waves whose length is large com- 

 pared with the smallest depth of mercury which can be 

 obtained in the trough. This depth appears to be fairly con- 

 stant in troughs made of different kinds of wood, and is at 

 ordinary temperatures very nearly 4 millim., when the mercury 

 is moderately pure and clean. The wave-length employed 

 would have to be large then, compared with 4 millim. 



If u, X, and v, \ be the velocity of propagation and corre- 

 sponding wave-length for frequency n, in deep and shallow 

 liquid respectively, we have, using the ordinary notation, 



j q\ 2ttt 

 2tt p\ 



and „ I q\ s 2irr > , , 2irh 



v — \ Q~ + T~ >tanh— — . 



The frequency is n in both cases, thus 

 o qu 2 t 2ttiit 



M 3 = f 1 + 



Z7T/i p 



and . ( qv 2 27rnT~) , , 2irh 

 v s = { — — + ■ \ tanh — — . 



If p. be the refractive index from the deep to the shallow 

 portion we have 



u A, 



M= % = x7 



thus 



f qu 2 , 27TWT ) 2irh 



1 o' 2 "• r anh t - ' 



s ^'=|(£:, + T)/(^ + 7)hv 



* Communicated by Prof. J. J. Thomson, F.R.S. 

 t Phil. Mag. June 1897, and Proc. Phys. Soc. July 1897 ; Phil Ma»- 

 Feb. 1898; Phil. Mag. Sept. 1898. * °' 



