NO. 15.] 



EMPIRICAL LAWS OF RESISTANCE. 



127 



To get an idea of the degree to which the experimental results must be 

 corrected on account of the narrowness of the channel, we may compare two 

 series of experiments made in the large tank, one series with the small 

 Fram-model and one with the large model. The former series (experiments 

 284 — 288) was made in a 2 - 5 cm. thick fresh-water layer on the top of salt- 

 water of sp. gravity 1480, and the results are represented by Curve (2) ("wide 

 channel") in Fig. 9 PI. VI; Curve (1) in the same figure, gives the resistance 

 in homogeneous water according to experiments 278 — 280. The second series 

 (experiments 154 — 164) was made in a 5 cm. thick fresh-water layer on the 

 top of salt-water of specific gravity 1*160. We can in the way indicated 

 on p. 116, construct from the resistances in this case, the resistance-curve for 

 the case of salt-water of specific gravity 1480. And further, we may from this 

 curve according to the scheme on p. 125 construct the resistance-curve for the 

 case when all linear dimensions are diminished in the proportion 1 to Va. For 

 this purpose, the dead-water resistances are multiplied first by 18/16 and 

 then by (V2) 3 , that is by 9/64; and the velocities are multiplied by l/l8/16 

 and by l/j/2, i. e. by 3/4. The calculation is given in the table below, 

 just as in the table on p. 125. 



The values in the last column are obtained by adding to the numbers in 

 the 4th column the resistances in homogeneous water, found from Curve 1 



