386 Frederick Guthrie on Stationary Liquid Waves. 



on the water, inasmuch as it causes the more rapid loss of am- 

 plitude, might be supposed to effect a retardation in the wave's 

 progress. Such is not the case, apparently ; for a layer of olive- 

 oil 5 millims. in thickness undulated with the water beneath it 

 in the trough B at such a rate as to give in three experiments 

 the numbers 123, 122-5, 122*5. 



§ 31. Viscosity. — Glue added in varying quantity up to lib. 

 of the solid in the trough B did not change the rate from 123. 



§ 32. Images on wall. — It can readily be imagined that the 

 sun shining on water or, better, water covered with oil in one 

 of the states of motion above described, gives most elegant 

 figures on the wall. The circular binodal, for instance, shows 

 lateral and vertical loop-exchange; the cross binodal circular shows 

 a collapsing and expanding parallelogram ; the binodal rectan- 

 gular exhibits bars of light which approach and recede with a 

 pause and slight regression. From the distribution of light in 

 the images, the kind and, to some extent, the degree of curva- 

 ture can be ascertained. Thus, when the circular binodal has 

 nearly subsided, the only alteration visible is the change of lumi- 

 nosity in the centre, due to the alternating convexity and con- 

 cavity. 



§ 33. Recent contributions to the subject. — On the occasion of 

 the communication of my experiments to the Physical Society, 

 I invited the Members to offer suggestions regarding the ratio- 

 nale of some of the stationary waves which were there exhibited. 



Mr. 0. Lodge has been good enough to point out how com- 

 pletely the phenomenon depends upon the relationship between 

 wave-length and rate of wave-progress. I regard the results as 

 being of value, in a great measure because they show, I believe, 

 more conclusively than can be shown by the wave-progress on 

 open sheets of water, that this law, that the velocity of progress 

 is directly proportional to the square root of the wave-length, is a 

 true one. This they do by reason of the conservation of wave- 

 length. 



In 'Nature' of July 28th Lord Rayleigh discusses the theo- 

 retical aspect of the question, and shows that the wave-rate of 

 sequence which I had given for circular binodal waves corre- 

 sponds closely with the theoretical number deduced from the 

 hypothesis that in troughs of infinite depths the variation of the 

 diameter is the only thing which affects the wave-rate or period. 

 That the pendulum-, or, as I should prefer to call it, the Logan- 

 law, or law of magnification, should be so closely preserved 

 through the complex molecular movement which actually takes 

 place is of the greatest interest — the more so as the paths 

 of the particles are not increased by an increase of the trough, 

 but there is only a diminution of the eccentricity of their 



