NO. 15.J 



EMPIRICAL LAWS OF RESISTANCE. 



125 



(experiments 11 — 17 and 72 — 76). The small model was drawn in the small 

 tank, and the large one in the large tank, in fresh-water layers of 2 and 

 4 cm. depth respectively. The dimensions of the boat-models are then in the 

 same ratio as the depths of the surface-layers; but the width of the tank 

 was, by comparison, a little greater in the latter case. The spec, gravity of 

 the salt-water was in both cases, P030. The results of the experiments with 

 the small model are represented graphically by Curve (4) in Fig. 8 PI. 

 VI. From the results of the experiments with the large model we shall by 

 Froude's rule calculate the resistance against the small model and after- 

 wards compare with the directly observed values. The calculation is inserted 

 here as an example. 



Experiment 72 shows a resistance to the large model, of 1*5 gr., at a 

 velocity of 6'5 cm./second. These figures are found in the first and second 

 columns in the table below (first line). 



The resistance in homogeneous water at the same velocity, is according 

 to Fig. 1 PI. X, 0-18 gr.; the difference 15— 0-18 = P32 is the dead-water 



resistance and is given in the third column. 



Now 



HP = 0165; 



6j5 



V2 



= 4-6. 



The dead-water resistance experienced by the small model at a velo- 

 city of 4 - 6 cm./second, should then according to Froude's rule, be 0165 gr. 

 These figures are given in the 4th and 5th columns. According to Curve (1) 

 in Fig. 8 PI. VI the resistance in homogeneous water, at the last-mentioned 

 velocity, is 0-032 gr. This added to 0-165 gives the total resistance against 

 the small model, and the rounded result 0-20 gr., is found in the 6th column. 

 The other figures in the table are calculated in the same way. 



