58 THE EXPANSION OR CONTRACTION OF DIMENSIONS 



The particulars of the three types are given in the following table : 



The varying ratios of length and breadth and draught are shown on the respective 

 curves. 



The curves of sectional areas of the parent forms are shown on Plate 8, and 

 represent the three different types of varying length and constant displacement. 

 In presenting the results of the experiments it has been deemed advisable to give 

 them in the form of wave-making resistance per ton of displacement, in terms of 

 speed-length ratio. For any particular case the surface friction is readily calcu- 

 lated, and although when total resistance is considered the results may appear dif- 

 ferent from those due to wave resistance only, it is the latter which is usually the 

 unknown quantity. The fact that the residuary resistance is obtained by subtract- 

 ing the frictional from the total resistance, together with possible minor experi- 

 mental errors, would probably account for certain inconsistences which appeared 

 in the final results. In general, however, within the limits of economical speed for 

 each type, or before the region of the first "hump" in the resistance curve, the re- 

 sults were fairly consistent, and the following curves represent the average varia- 

 tion in each case. Beyond the above speeds the variation in resistance did not 

 seem to follow any simple law but varied somewhat with the speed. 



The curves shown in Plate 9 represent in general the variation of residuary 

 resistance per ton of displacement with respect to breadth. They are the results 

 for the medium draught (b) for each type, but the same characteristics were found 

 to hold for the other draughts at which the models were tried. 



Within the limits of the variation of breadth shown, the residuary resistance 

 appears to vary as about the 1.65 to the 1.7 power of the breadth, or the residuary 

 resistance per ton of displacement as about the .65 to .70 power of the breadth, if 

 the lines are simply expanded or contracted and the displacement allowed to vary 

 accordingly. 



The eflfect of variation of draught due to expanding or contracting the dimen- 

 sion in this direction, did not appear to be quite as consistent as in the previous 

 case, but in general the average results are shown in Plate 10. They are for the forms 

 represented by the medium draught (b). Up to the limit of economical speed the 

 residuary resistance varies as about the .65 to .7 power of the draught. Above 

 these speeds the index gradually increases. The residuary resistance per ton of dis- 

 placement therefore varies inversely as about the .35 to the .3 power of the draught. 



