NO. 16.] QUALITATIVE RESULTS. 65 



a very clear idea of the shape of the waves. From the boat's stern a couple 

 of diverging, wing-shaped wave-hollows (elevations of the boundary) stretch out, 

 and where these waves strike the walls of the tank, the first stern-wave is 

 seen on the silhouette-photograph. After these waves, follows a couple of 

 diverging wave-crests (depressions of the boundary) which likewise strike the 

 wall. The waves following seem to approximate to the shape of transverse 

 waves. In Fig. 1, PI. XII, one may easily follow the profile of the waves 

 along the wall of the tank, and then recognize the shape of the silhouette 

 photographs (compare, for instance, Fig. 2, PI. XVI). In addition, the salt-water 

 in the middle of the channel is visible between the two first waves at the wall. 



The most important point which the photographs described above clearly 

 show, is that the waves largely increase in height when the velocity of the 

 boat increased towards the critical velocity, but when this is passed, and 

 the boat is free from the dead-water, the waves disappear ; quite in ac- 

 cordance with the reasons given in Chap. II, and with the analogous pheno- 

 mena discovered by Scott Russell. The waves which are seen at a distance 

 aft of the boat, in the bottom figure on PI. XV— XVII, might possibly be 

 explained as a section of diverging waves, but probably they are simply waves 

 remaining from an earlier moment when the boat was still moving at below 

 the critical velocity. 



Figs. 7 and 8, PI. XIV, illustrate the case in which the vessel moves 

 much faster than at the maximum wave- velocity ; in this case the difference 

 of specific gravity between the water-layers has no appreciable influence upon 

 the motion, which then takes place almost exactly as in homogenous water. 

 To show the motion of the water at different levels, these experiments were 

 made with three water-layers forming two boundaries 1 and 2 cm. below the 

 free surface; in the case of Fig. 7 as in the experiment, the middle water-layer 

 is black and - the others are clear, and vice versa in Fig. 8. The difference 

 of spec, gravity between each two of the water-layers is about 00005 only, 

 and the maximum wave-velocity is less than l - 4 cm. per second. The velocity 

 of the boat-model, is about 5 cm. per second in Fig. 7 and about 7 cm. per 

 second in Fig. 8. (In the latter case spirals of black water were seen in the 

 middle layer, arising from vortices). 



It was mentioned in Chap. II (p. 42) that in consequence of the wave- 

 motion in the boundary, there must arise very low waves in the surface of 



