Maiichestet- Mcuioirs, Vol. xliv. (1900), No. JK 9 



Large Waves. 



From these tables it would seem that, for such waves 

 as Scott Russell experimented upon, if v gives the true 

 velocity, 71 is empirically a good representative of the 

 velocity, and that, on comparison, the experimental value 

 for the velocity seems to agree better with v than with ;/, 

 although the comparison is not decisive. 



Finally, ScottRussell's experiments show that although 

 a wave of depression could be propagated, it had a different 

 character from the wave of elevation, and especially failed 

 in those points which I have selected as typical of the 

 solitary wave. It is, therefore, essential to show that these 

 hypotheses would not allow of the propagation of a 

 similar wave of depression. 



For this purpose putting /3= 1-7, the three equa- 

 tions which we have to consider become 

 c^ =g tan 2!nyJ2»i , 

 A. 



1+9 



Ai 



(-^ ' 



I -t- cos 2W7 

 cos- 2/;/y - I 



') 



and 



cos 2my{l - 27t'')- + (l 



where w stands for mhij sin 2)ny. 



Writing this last equation in the form 



cos 2iny[l — 2ZV)^ + i(l - 27V) + \ = O. 



I iTT 



we find that co% 2 i)iy<i\, or (say) 7//-y>>--^ , while the 



greatest value of wy we have to consider is -^. More- 



4b 



over, within this interval, the equation would give positive 



