ON WAVES. 351 



(2.) That it is a wave of translation, the direction of which is opposite to 

 the direction of transmission. 



(3.) Tliat its anterior form is that of the positive wave reversed. 

 (4f.) That the path of translation is nearly that of the positive wave reversed. 

 (5.) That its velocity is, in considerable depths, sensibly less than that due 

 by gravity to half the depth reckoned from the lowest point, or the velocity 

 of a positive wave being the same total height. 



(G.) That it is not solitary, but always carries a train of secondary waves. 

 It is important to notice that the positive and negative waves do not stand 

 to each other in the relation of companion phsenomena. They cannot be con- 

 sidered in any case as the positive and negative portions of the same phae- 

 nomena, for the following reasons : — 



(1.) If an attempt be made to generate or propagate them in such manner 

 that the one shall be companion to the other, they will not continue together, 

 but immediately and spontaneously separate. 



(2.) If a positive wave be generated in a given channel and a negative 

 wave behind it, the positive wave moving with the greater velocity, rapidly 

 separates itself from the other, leaving it far behind. 



(3.) If a positive wave be generated and transmitted behind a negative 

 wave, it will overtake and pass it. 



(4'.) Waves of the secondary class which consist of companion halves, one 

 part positive and the other negative, have this peculiarity, that the positive 

 and negative parts may be transmitted across and over each other without 

 preventing in any way their permanence or their continued propagation. It is 

 not so with the positive and negative waves of the first order. 



(5.) If a positive and negative wave of equal volume meet in opposite 

 directions, they neutralize each other and both cease to exist. 



(6.) If a positive wave overtake a negative wave of equal volume, they also 

 neutralize each other and cease to exist. 



(7.) If either be larger, the remainder is propagated as a wave of the larger 

 class. 



(8.) Thus it is nowhere to be observed that the positive and negative wave 

 coexist as companion phsenomena. 



These observations are of importance for this reason, that it has been sup- 

 posed by a distinguished philosopher that the positive and the negative wave 

 might be corresponding halves of some given or supposed wave. 

 On some Conditions which affect the Phcenoniena of the Wave of the First Order. 

 — It has not appeared in any observations I have been able to make on the 

 subject, that the wave of the first order retains the stamp of the many pe- 

 culiarities that may be conceived to affect its origin. In this respect it is 

 apparently diiferent from the waves of sound or of colour, which bear to the 

 ear and the eye distinct indications of many peculiarities of their original ex- 

 citing cause, and tlms enable us to judge of the character of the distant cause 

 which emitted the sound or sent forth the coloured ray. It is not possible 

 always to form an accurate judgement from the phsenomena of the wave of the 

 first order, of the nature of the disturbing cause, except in peculiar and small 

 number of cases. 



I have not found that waves generated by impulse by a fluid column of 

 given and very various dimension, by immersion of a solid body of given 

 figure, by motion in given velocity or in different directions ; I have not 

 found in the wave obtained by any of the many means any peculiarity, 

 any variation either of form or velocity, indicating the peculiarity of the 

 original. In one respect therefore the wave of translation resembles the sound 

 wave ; that all waves travel with the velocity due to iialf the deptli, whatever 

 be the nature of their source. 



