NO. 15.] EXPERIMENTAL ERRORS AND CORRECTIONS. 89 



force was consequently 0'8— 01 = 0'7 gr. As each interval of time is T09 seconds, the 



acceleration was 3 / 4"36 = 0688 cm./sec. 2 = 0-00070 g. The virtual inertia of the boat is 



consequently - 7/00007 = 1000 gr„ which is 125 per cent of the boat's own weight. 



Several such estimations gave between 110 and 130 per cent. I have used the mean, and 



assumed the virtual inertia of each boat-model to be 120 per cent of its own weight. 1 



In the case of the large .PVa)»-inodel (weight 800 gr.) an acceleration of 1 cm./sec. 



1*20X800 

 in one interval of time then corresponds to a force = . „,.;;„,,■ = 0'90 gr. In this wav, 



P09X981 



the values in the 8th column of the tables, are calculated. From the corrected resistances 

 given in the 9th column, the resistance-curves in the case of homogeneous water (Figs. 1—3, 

 PI. X), are calculated according to the formula 



resistance = C, + C 2 [velocity] 2 ; 

 the constant term being necessary owing to the friction against the steering string. This 

 formula is in good agreement with all measurements at velocities below 15 cm. per second. 

 For higher velocities the differences between calculated and observed resistance, are greater 

 (up to 0'2 gr.), but this is of less importance because the range of velocities at which 

 dead-water resistance was measured, lies below 15 cm. per second. The curves for the small 

 JVam-models (Figs. 8 and 9, PI. VI) are not calculated, but are drawn evenly through 

 the separate points determined experimentally. 



When the boat was moving in dead-water, its velocity periodically in- 

 creased and diminished (see pp. 67 seq.). In this case the only possible 

 way of applying the results, was to take the mean about which the velocity 

 seemed to oscillate, and assume the resistance at this velocity to be equal to 

 the towing force. These mean velocities are given in the 10th column of the 

 tables, and are represented on the diagrams PL VII — VIII, by a short hori- 

 zontal line on the left hand side of each diagram (see for instance diagrams 

 77 — 81, PL VII). When the towing-force was not near the maximum resi- 

 stance, the velocity-oscillations were quite regular, and the mean velocity could 

 then be determined very accurately. When, however, the towing-force was a 

 little below the maximum resistance only an uncertain determination, or no 

 determination at all, could be made of the velocity (see for instance, diagrams 

 81 and 82, PL VII. The upper left hand corner of the resistance-curves, could 

 therefore be drawn only approximately. See further the explanation of the 

 tables, p. 76. 



To avoid the inconvient velocity-oscillations, I attempted to start the boat 

 with a smaller force and then, when it had reached its greatest velocity, to 

 increase the towing-force approximately so as to keep this velocity uniform. 



1 This is the same ratio which is given by Fronde for full-sized ships. See p. 489 in 

 White 1. c. p. 33, where this quantity — 120 per cent of a ship's weight — is called 

 her "virtual weight". 



12 



