no. 15.] EXPERIMENTAL ERRORS AND CORRECTIONS. 91 



since the velocity increased to a maximum and then diminished again. With 

 a towing force of 2'3 gr. (exp. 83), the velocity is accelerated more and more 

 slowly up to 10-5 cm. per second, and then the acceleration begins to in- 

 crease; which shows that the resistance was greatest at a speed of 105 cm. 

 per second and diminished again with further increasing velocity. The boat had 

 consequently got rid of the dead-water, and it is concluded that the maximum- 

 resistance is between 2-2 and 2 - 3 gr. For a more exact approximation, the 

 acceleration of the boat was taken into account in the following way. In 

 experiment 83 the velocity increased, when the acceleration was a minimum, 

 with about - 12 cm. /second per time-interval, which corresponds to an acce- 

 lerating force of 01 gr. The greatest resistance during the whole of this 

 experiment was consequently 2'3 — 01 = 2*2 gr. But it should obviously have 

 grown larger if the towing force had had any value between 2 - 2 and 2 - 3 gr. ; 

 and it should have attained its greatest possible value, if the minimum acce- 

 leration had been nil, i. e. if the towing-force had been equal to the "maximum- 

 resistance". The "maximum-resistance" is therefore assumed to be the mean of 

 the towing-force (2S gr.), and the greatest resistance during the experiment 

 (2.2 gr.), in this case 2.25 gr. This method, of approximation, has been 

 used in drawing all the resistance-curves ; and it seems to be confirmed when 

 applied to experiments with towing-forces exceeding the maximum-resistance 

 by different quantities. 



If, at the beginning of an experiment, there were even slight waves in 

 the boundary, they might have disturbed the results by increasing or decreas- 

 ing the resistance at the critical moment (compare foot-note, p. 73). Although 

 it was necessary to wait rather a long time in between two experiments, for 

 the wave-motion to subside, it is possible that small errors in the determi- 

 nation of the maximum resistance are introduced on this account. 



From experiment 82 we may on taking into account the retardation of 

 the boat, conclude, that the difference between the maximum resistance at steady 

 speed and the maximum resistance according to our definition, may be rather 

 considerable. When the velocity had dropped to 5 or 6 cm. /second, it 

 was retarded by 075 cm. /second in one time-interval, which indicates an excess 

 of resistance above the towing-force, of 075 X 0-90 = 0-67 gr. (see p. 89); the 

 resistance was consequently 2-2 + 0"67 = 2-87 gr. By subtracting the resist- 

 ance in homogeneous water (0-15 gr. at 5'5 cm. /second, see Fig. 1, PL X) we 



