120 



EKMAN. ON DEAD-WATER. 



[NORW. POL. EXP. 



than the exact formulae for free waves. As far as the pressure in the salt-water is 

 concerned, only a rough approximation is necessary, because the corresponding terms in 

 the expression for the resistance, become very small. Equation (5) p. 44 is used, as 

 well for homogeneous water as for a surface-layer. In all the formulae, g (the accelera- 

 tion due to gravity) may be thrown out, if gramme be used in its frequent sense of force. 



1) Homogeneous mater. 



The values of B and (A - B) in (a) are to be taken from the first column in the 

 table above. If h l( ho, h 3 , h 4 , are the heights of the surface-level (in millimetres) at the 

 sections to which p,, p,, p 3 , p 4 refer, (h 2 -h 3 )/10 and (h l -h 1 )/10 may be substituted 

 for (p 2 -p 3 ) and (pi-p 4 ). and (a) becomes 



R = 1-6 (h, - h 4 ) 4- 1-8 (h„ - h 3 ) grammes (b). 



2) Fresh-water layer 5 cm. deep. 



The boat moves entirely in the fresh water. We have just as in the former case, 

 R = l-C(h 1 -h 1 ) + l-S(h 2 -h 3 ) (e). 



3) Fresh-water layer 3 cm. deep. 



The pressure of the fresh-water and of the salt-water, must be calculated separately, 

 according to formulae (5) and (6) p. 44. As the wave-length I is about 90 cm., Zml/l 

 may be put equal to 02. The values of B and (A - B) in the 2nd and 3rd columns of 

 the table above, are to be used. We then obtain 



R = (1-4 -0-2X0-2) (11,-114) + (1-3- 0-2X0-5) (h 2 -h a ) 

 = 1-36 (h , - hj + 1-2 (h, - h„) grammes (d). 



The differences of level (h, - hj and (h 2 - h 3 ) are found in the 10th and 11th columns 

 of the table p. 119; the pressure resultant calculated according to one of the formulae (b), 

 (c), or (d), is given in the 12lh column. 



The acceleration of the boat-model in the two first experiments, was inappreciable, 

 and the entire resistance was consequently equal to the towing-force. The numbers in 

 the 6th and 12th columns of the table p. 119, then show, that in homogeneous water, 

 about 45 per cent of the resistance was due to pressure, and only the other 55 per 

 cent to friction. Indeed a certain pressure is necessary to overcome the friction against 

 the water moving past the vessel astern; another part of the pressure-resultant is iden- 

 tical with the eddy-making resistance. 



It is therefore assumed that even in dead-water 45 per cent of the resistance not due 

 to wave-making, depends on the pressure alone and that the rest is due to frictional 

 resistance. The pressure resultant would then be equal to the wave-making resistance plus 



