NO. 15. | QUALITATIVE RESULTS. 69 



stance, there was not time enough, while the boat was going the whole length 

 of the tank, for the velocity to perform a complete oscillation; after having 

 attained a maximum of 10 cm. per second, the velocity steadily slackened 

 and dropped down to 3 cm. per second. In experiment 83, the towing force 

 was only O'l gr. more, and the velocity increased at first in very nearly the 

 same manner as in the former case. But now the towing-force is sufficient 

 to overcome even the maximum resistance, which corresponds to the top-point 

 on the resistance-curve (4) in Fig. 8, PI. VI, and in the present case takes 

 place at a velocity of about 10'5 cm. per second; and the velocity, after having 

 passed this value, is more and more rapidly accelerated. This is easily seen 

 by the curve bending upwards when it has passed the horizontal line 105. 



The changes or oscillations in velocity, were followed by peculiar changes 

 in the wave-motion, which clearly showed the cause of the former. When 

 the boat was unhooked and began to move, the boundary between the salt- 

 and the fresh-water was at first quite even. Gradually, quite small waves 

 arose, as in Fig. 1, PI. XIV, and the boat continued to be accelerated. After 

 a few seconds, the waves were greatly increased, the boat ceased to be ac- 

 celerated, and a "solitary wave" 1 became visible under its stem (Fig. % PI. XIV). 

 If the towing-force was smaller than the maximum-resistance, the boat was 

 then rapidly retarded and the solitary wave, moving steadily at the highest 

 speed which the boat had, went on in advance. When it had reached a 

 position ahead of the boat (about as in Fig. 3, PI. XIV), the velocity of the 

 latter was nearly a minimum ; the solitary wave steadily distanced it, and the 

 waves abaft came nearer, broke and disappeared. Then, the boat took a new 

 leap, the waves began to increase, and the whole phenomenon was repeated. 

 If the towing-force was greater than the maximum-resistance, the boat 

 overtook the solitary wave, so that it gradually dropped astern from the po- 

 sition in Fig. 2, PI. XIV. to that in Fig. 4, PI. XIV. After that, the boat 

 had her velocity rapidly accelerated, and simultaneously the height of the soli- 

 tary wave under her keel, was more and more diminished (Figs. 4, 5, 6, 

 PI. XIV). She was then rid of the "dead-water". 



A single permanent wave-crest moving along in the surface-layer (see Fig. 5, PL VI) 

 and quite similar to Scott Russell's solitary wave in shallow water, mentioned on 

 p. 39. Just as this latter, the solitary boundary-wave seems to move with about the 

 same velocity as long periodic waves. 



