193 ]\Ir. A. J. Robertson on the Negative Wave of Translation. 

 whence 



and 



tan 'U^= ^ , tan = r =-, 



^ X—fiv ^ X + fiv 



l + v2 



which may be verified by means of the values of d, <p, ■^, \, fi, v 

 in terms of the nine direction cosines. 

 Oxford, Jan. 11, 1851. 



XXVI. On the Negative Wave of Translation. 

 By A. J. Robertson, Civil Engineer*. 



IN a paper on the Positive Wave of Translation, in the De- 

 cember Number of this Magazine, it was shown that the 

 distance the crest of the wave moves through, during the time 

 that an elementary column makes a A'ertical oscillation from rest 



V . V . 



to rest, IS Lh , — the quantity — beinghalf the absolute trans- 

 lation of the particles in space, — and that in consequence the 

 velocity of the wave is increased from \^{a + k)g to 



L+1 



-•(« + %= V^^"(» + 2%. 



In the negative wave of translation, which is generated by the 

 abstraction of a quantity of water from the Channel, and which 

 is a hollow instead of a swell, the translation of the particles is 

 in the direction contrary to the motion of the wave. Hence the 

 crest of the wave moves, during the vertical oscillation of a 



V 

 column, through a space less than L by a quantity — . 



Applying the same principles to the negative as to the positive 



E 



-N 



wave, retaining the same symbols, and remembering that k is ne- 

 gative, we obtain 



* Communicated by the Author. 



