NO. 16.J QUALITATIVE RESULTS. 63 



easily be imagined. Owing to the photographs being taken obliquely from 

 below — as also on account of the refraction in the water — their breadth 

 is seen 4*1 times reduced in proportion to their length. In order to see the 

 length and breadth of the waves in their true proportions, the figure should 

 consequently be seen sideways, so that its length becomes 4*1 times shorter; 

 this is attained, when the quadrangle below Fig. 1 looks like a square. 

 All details in the figure, except the waves, are, of course, then seen quite 

 erroneously. 



The boat, a model of the Fram (scale 1 : 200) is, in the figures PI. XIII, 

 entirely hidden in the opaque fresh-water, and we only see the diverging train 

 of waves, the head of which indicates the position of the boat. The photograph 

 is reproduced on such a scale, that the boat's length in the figure, is 36 mm., 

 or just the same as in the figures PI. XV— XVII. If this be noted, it can 

 be understood, on Fig. 3, PI. XIII, that the fresh-water is pressed down under 

 the bow of the vessel, there forming a little hollow in the salt water, whilst 

 at the stern the boundary is raised, so that the keel becomes visible in the 

 clear salt-water. The disturbances thus described, spread as diverging and 

 transverse waves very similar to the well-known wave-systems following a 

 steam-launch in smooth water (see for instance Fig. 3, PI. XII). The diverging 

 waves are very clearly seen in the figures, PI. XIII; the transverse waves, on 

 the other hand, do not appear very distinctly. This is evidently due to the 

 light having come from the side of the tank, so that the transverse waves 

 have no shadows. I have observed steam-launches from a hill athwart, and 

 their waves have then had a striking resemblance with those in the figures 

 on PI. XIII; unfortunately I have never had an opportunity of taking a pho- 

 tograph of such an instance. In Figs. 2 and 3, PI. XIII, the section of the 

 boundary becomes visible along the glass walls of the tank, as a sinuous 

 curve evidently indicating the transverse waves, as well as an oblique section 

 of the diverging waves (somewhat exaggerated through their reflection against 

 the walls). The velocity of the boat is smallest in Fig. 1 and greatest in Fig. 3. 

 The towing forces were in the three cases 0"25 gr., 0"50 gr., and 0-75 gr., re- 

 spectively; and the maximum resistance, calculated according to the rules given 

 below, should be 1 gr. One sees that the transverse waves increase very much 

 in length and height as the velocity of the boat is increased. 



