Frederick Guthrie on Stationary Liquid Waves. 387 



fragmentary orbits. This has, of course, its counterpart in vi- 

 brating elastic rods. The mathematical interpretation of the 

 experimental fact is very valuable. I do not suppose that such 

 interpretation can be complete until account is taken of the co- 

 hesion and viscosity of liquids, to which, on the other hand, 

 such experiments may supply a new weapon of attack. The 

 other kinds of wave-systems, the rate of which Lord Rayleigh 

 predicts mathematically, and which in rectangular troughs were 

 described, but not investigated with regard to their period, in the 

 elaborate work of the brothers Weber, I had already examined 

 in regard to their period both in circular and rectangular troughs. 

 In this respect it is safe to predict that eveiy system of vibra- 

 tion of a square or round Chladni plate may be reproduced in a 

 square or round vessel of water, and that the time-ratio will be 

 preserved. Further, in water-wave systems we can have mono- 

 nodal vibration, which for automatic motion is inadmissible in 

 vibrating plates. With the exception of those above studied, 

 the more complex systems appear short-lived. 



34. That the wave-motion of the binodal circular system is 

 not only isochronous with the radius pendulum, but also coin- 

 cides with pendular motion throughout the whole course of 

 both, appears from the fact that the two sustain one another 

 when in direct integral mechanical connexion. Fig. 8 shows 

 such an arrangement. A tuning-fork, B, having the plane of 



Fig. 8. 



its prongs horizontal, is fastened to a heavy stand, A. Resting 

 on the fork is a knife-edge, C. To C is attached a vertical 

 screw-rod, E, carrying a nut (invisible in the figure) which sup- 

 ports the heavy weight D, consisting of a series of leaden disks. 

 Also fastened to C is a cardboard sector, F. The circular edge 

 of F is split, and into the, crack is pasted a paper gutte. A silk 

 thread, G, is fastened to F, and carries a little paraffin disk, H. 

 The pendulum-length is altered by the nut E until the disk H 



2C2 



