290 Frederick Guthrie on Stationary Liquid Waves. 



By both theories the cause of the vertical motion is the 

 transference of water from the top of the one column to the top 

 of the other. This vertical motion is therefore as much a ne- 

 cessary consequence of the wind theory as it is of the gra- 

 vitation theory. 



XXXV. On Stationary Liquid Waves. 

 By Frederick Guthrie*. 



THE following numerical results of experiments may be of 

 use in the further study of wave-motion. They refer to 

 stationary waves mainly, and include those of circular and those 

 of rectangular troughs. The guiding idea was : — to deduce the 

 velocity of wave-progression under different conditions from the 

 frequency of recurrence of a given phase in the same place, in a 

 manner similar to that employed in the measurement of the velo- 

 city of a sound-wave through a solid by the pitch of the note 

 when a certain length of the solid vibrates longitudinally ; and, 

 by making use of reflection, to bring into a compact form for 

 study the effects of wave-progression. 



Circular Troughs. 



§ 1. The first condition of motion examined in circular troughs 

 is that which I shall call binodal. This motion can be easily set 

 up in a cylindrical trough of water if it be not much less than 

 9 inches in diameter, nor the water much less than 6 inches 

 deep. The bottom of an empty beaker glass serves well to ge- 

 nerate the waves, on account of its buoyancy. This is placed on 

 the centre of the water, and moved down and up at a rate de- 

 pendent upon the diameter of the vessel. The motion of the 

 water soon guides the hand, and, being judiciously humoured, 

 establishes itself and continues for many minutes with great 

 regularity. The number of times in one or more minutes that 

 the crest appears in the middle may be easily counted if the re- 

 flection of a window-sash is seen obliquely on the liquid surface. 



§ 2. Influence of amplitude. — Before examining the influence 

 of diameter (which with stationary waves amounts to an exami- 

 nation of the influence of wave-length), a brief examination of 

 the influence of Depth, Temperature, Density, and Amplitude 

 had to be undertaken, to determine at all events the margin of 

 variation admissible without vitiation of the result. The ampli- 

 tude was measured by standing a brass wire graduated in milli- 

 metres, and fastened to a leaden foot, in various parts of the 

 trough after the wave-system was established. 



§ 3. A cylindrical vessel, B, of tin plate had the mean dia- 

 meter 456 millims. (It was slightly elliptical, 455, 457 millims.) 



* Communicated by the Author, having been read to the Physical 

 Society on June 26, 1875. 



