AND THE EFFECT UPON RESISTANCE. 59 



If length alone is varied, breadth and draught being kept constant, we have 

 simply a combination of the foregoing: for if all dimensions were varied propor- 

 tionately the residuary resistance per ton of displacement would be constant at 

 constant speed-length ratios. Increasing, say, the length only is therefore equiva- 

 lent to reducing both breadth and draught of the parent form simultaneously. 



As a check upon this, each of the forms was expanded or contracted longi- 

 tudinally, and the results are shown for the medium draught (b) in Plate ii. If the 

 length be increased, say, n times, breadth and draught remaining constant, we 

 obtain a similar form to that of the parent type in which the breadth and draught 

 have each been reduced n times; and therefore if the residuary resistance per ton of 

 displacement at corresponding speeds varies as the .7 power of the beam and in- 

 versely as the .3 power of the draught, the combined result would be that this fac- 

 tor will vary as «-'h- »' or -— . In other words, the residuary resistance per ton 



n 



at constant speed-length ratio will vary approximately inversely as the (length)''. 

 An examination of the above curves, Plate 11, will show that this is practically 

 the case. 



As the three original parent forms were made of the same displacement but of 

 different lengths, the effect of influence of length for this particular series could be 

 readily obtained. The curves, Plate 12, show the results for the three different 

 draughts at which the models were tried. They represent constant speed curves 

 for varying lengths with constant beam, draught and displacement, and illustrate 

 the well-known influence of length as affecting residuary resistance. The total resist- 

 ance curves would not, of course, show such a marked difference, as the longer 

 form, though finer, would have a greater friction than the shorter and fuller form. 



SHALLOW-DRAUGHT TYPES. 



In connection with some experiments upon certain types of river steamers, 

 such as those of the Mississippi stern-wheel type, occasion was had to determine the 

 effect of variation of breadth only. These are rather extreme types where the 

 ratio of length to draught was from 40 to 50 and the ratio of breadth to draught 

 varied from about 8 to 12. Two different types were tried, the stern in both cases 

 being that usually adopted for the stern-wheel vessel, and the bows either ship- 

 shape or "scow" form. 



In these cases the wave-making resistance at corresponding speeds, within the 

 limits of speed at which these vessels would normally be run, appears to vary as 

 about the .75 power of the beam, or per ton of displacement inversely as the .25 

 power of the beam. 



As the models of the above contained a large percentage of parallel middle 

 body, this part, which represents a practically rectangular form, was also tried 

 at different breadths. The ratio of breadth to draught was the same as for the 

 previous forms, but in this case the residuary resistance appeared to vary directly 



