NO. 16.] EMPIRICAL LAWS OF RESISTANCE. 133 



layer is first to be divided by D and multiplied by 4 - 4. The corresponding 

 velocity given by curve (2), and the resistance given by the selected resistance- 

 curve, are noted. 



3) The last-mentioned quantity is the maximum dead-water resistance, 

 if the vessel has a weight of 800 tons, and if the difference of spec, gravity 

 between the surface-layer and the sea-water below, is 0"030. If these quan- 

 tities are w tons and d respectively, the resistance given by the selected 

 curve must be multiplied by w/800 and by d/003, i. e. by wd/24. 



4) In the case of a gradual transition from fresh surface-water into salt 

 sea-water, the diagrams in Fig. 2 PI. XI give an indication of the extent to 

 which the resistance found in (3), must be diminished on account of this 

 circumstance. 



5) Multiply the velocity found in (2), by iDjVi and by Vd/0'03; the 

 result is approximately the velocity corresponding to the above (1 — 4) calcu- 

 lated maximum dead-water resistance. Add to the latter the resistance to 

 the vessel in homogeneous water at this velocity; the sum then gives approxi- 

 mately the maximum resistance in the given water-layers. If the propelling 

 force of the vessel is greater, she will not under ordinary circumstances fall 

 into dead-water; and if she accidentally does so, she will be able to get free 

 again by stopping completely for a while, and by then going full speed ahead 

 again. If once in dead-water, and if this manoeuvre be not carried out, the 

 vessel might, however (as was mentioned on p. 110) be kept in the (lead- 

 water in spite of a considerably greater propelling force. 



Application of the experimental results to the case of the "Fram" 



at Taimur. 



The only case of dead-water from which we have definite and reliable 

 statements about the water-layers as well as of the vessel's speed and force 

 of propulsion, is that which happened to the Fram west off Taimur (see 

 Chap. I pp. 9 — 11). It is therefore of interest to see whether the experimental 

 results are in accordance with these statements or not. 



TJie force of propulsion of the ship, may be roughly calculated from 

 the indicated H. P. of her engine. From the "Alters mekaniske Verksted", 

 where the ship was built, I was informed that the engine with a speed of 

 6 knots (3*1 m. per second) developed 210 I. H. P. Of this work only a part 



