116 EKMAN. ON DEAD-WATER. [norw. pol. exp. 



full-drawn curves apply to the case of a fresh-water layer af 5 cm. depth; 

 the specific gravity of the salt-water below, in each case (l'OlO — 1 - 160), is 

 given over each curve. The velocities of the boat-model, are plotted horizontally 

 in cm. per second, and the resistance to the boat, vertically in grammes. The 

 vertical distance between the lowest curve and one of the others, gives, for 

 the different velocities, the "dead-water resistance" in the case concerned. 



As might be expected, the effect of the fresh-water layer is, upon 

 the whole greater, the greater the specific gravity of the salt-water below. 

 The exact relationship is very simple. In Chap. II (p. 52) it was shown 

 theoretically that if the difference of specific gravity between the upper 

 and the lower water-layer be increased y times, the wave-making re- 

 sistance against a vessel in dead-water, mill increase in the same ratio, 

 if at the same time her velocity be ]ly times increased. It was also shown 

 that the same rule holds approximately true for the frictional resistance. It 

 will be shown below, that the "dead-water resistance" depends chiefly on 

 wave-making, and only to a smaller extent on friction ; and the above rule 

 should therefore hold very nearly true for the entire dead-water resistance. 

 The experiments are in complete agreement with this rule; as is best seen 

 if it be applied to different series of experiments in reducing them all to the 

 case of a difference of spec, gravity equal to 0"030, say. For instance, the 

 series of experiments Nos. 133—137, 138-145, 85V2— 97, 77—85, 146—153, 

 154—164 (see the tables pp. 80 — 82), were all made in a 5 cm. deep fresh- 

 water layer, but the spec, gravity of the salt-water below was l'OlO, 1"020, 

 1-030, 1-032, 1-070, 1160 respectively. If then, in the 1 st series the veloci- 

 ties be multiplied by V>3 and the corresponding dead-water resistances by 3, 

 in the 2 nrl series, by V.3/2 and 3/2 respectively, in the 4 th series by V3/3'2 

 and 3/3 - 2, and so on, and if resistance curves be drawn for each series of 

 reduced values, it will be found that they all coincide very nearly with 

 oneanotber, and the divergences themselves are chiefly of an experimental 

 character and not systematic. The maximum resistance does not differ in 

 any of the reduced curves by more than - 2 gr., from that found by direct 

 experiments with salt-water of specific gravity T030. The agreement is just 

 as good when the series 58—71 and 126 — 132 are compared (fresh-water layer 

 3 cm.: spec, gravity of the salt-water 1-030 and 1180). Considering that the 

 specific gravity in these experiments, varied by as much as from 101 to l'16and 



