NO. 15.] 



EMPIRICAL LAWS OF RESISTANCE. 



119 



calculated in this way. Considering that the surface-disturbances must be measured some- 

 where in between the walls of the tank and the course of the vessel, these values agree 

 as well as could be expected, with the wave-heights shown by the photographs PI. XV— 

 XVI. 



The pressure-resultant against the boat-model, is calculated for its middle-body and for 

 its ends, separately. The calculation is made in the following way; the first line in the 

 table on the next page, gives the area of the midship-section of the boat model (below the 

 water-line), as well as those parts of it which lie above and below a level 3 cm. below 

 the water-surface, and the two lines following, give the means for the corresponding areas 

 at equal distances from the stem and the stern. From these areas, mean cross-sections 

 are calculated for the middle-body reckoned to 10 cm. from the ends, and for the rest of 

 the boat. The former numbers (A) and the latter (B), as well as the differences (A— B), 

 are given in the same table. 



If the water-pressure in one horizontal plane, be p t at the stem, p 2 10 cm. aft of 

 the stem, p, 10 cm. before the stern, and p 4 at the stern, then the sternward pressure- 

 resultant R will be given approximately by 



R = B (p, - p 5 + p 3 - Pi) + A (p 2 - p 3 ) 

 = B (p, - p 4 ) + (A - B) (p 2 - Pa ). W 



The values ofpt.po, p 3 , p 4 , have to be calculated from the surface-disturbances. As 

 was pointed out above, the moving forces are not concentrated only in the salt-water fresh- 

 water boundary, but are also distributed in the middle of the surface-layer; and the 

 formulae for the case of "long waves" (5 and 6, p. 44) therefore give better approximations 



1 The disturbance of surface-level was greater than could be measured with the level- 

 gauge. The dotted part of diagram 6, is therefore hypothetical. 



2 The diagram could not, in this experiment, be traced accurately enough, to permit of 

 a calculation of the pressure-resultant. 



