46 REPORT — 1869. 



has already been pointed out, with the resistances derived from the surface- 

 friction. In fact, vre are thus brought to the scale of comparison which was 

 just now enunciated, that the entire resistances of a ship, and similar model, 

 are as the cubes of their respective dimensions, if their velocities are as the 

 square roots of their dimensions. 



In verification and illustration of the foregoing views, I tried, in the 

 autumn of 18G7, a large number of resistance-experiments with a pair of 

 models of contrasted forms, six feet long, by towh:g them simultaneously 

 from the ends of a pair of ten-foot scale-beams connected with self-recording 

 dynamometric apparatus, and mounted on booms projecting sideways from the 

 nose of a steam-launch, lent me for the purpose by Mr. Bidder. The water- 

 lines of the models arc shown in Plate I. fig. 1. One was of the wave-line 

 type, the other, having the same length, form of midship -section, and dis- 

 placement, had large rounded ends. I also tried similar experiments with a 

 pair of very nearly similar models of twice the dimensions and eiglit times the 

 displacement. I had already obtained a series of experimental results of the 

 same kind, but with less successful apparatus, from a similar pair of models, 

 three feet long. These data enabled me to compile for each model a dia- 

 gram of resistance iu terms of velocity. 



The three pairs of such diagrams, proper to the three pairs of models, were 

 laid down to scales corresponding to the dimensions of the models, according 

 to the system of comparison I have enunciated ; thus the velocity-scale for 

 the six-foot models is \/2 times, and that for the three-foot models twice 

 as open as that for the twelve-foot models ; and the resistance-scales for the 

 six-foot and three-foot are respectively 8 and 04 times as open as that for 

 the twelve-foot. According to my proposition, were the three sets of models 

 exactly similar the three sets of diagrams should be identical. 



Ileduced copies of these diagrams are shown in Plato I. figs. 2, 3, 4. 

 Their general agreement, especially as to the position occupied in the velo- 

 city-scale by the several saHent features of the curves and as to the relative 

 resistances of the contrasted forms, is very striking. It is true that on com- 

 paring the absolute resistances, the correspondence is not so close as it at 

 first sight appears. Thus the three-foot models exhibit throughout a 

 decided excess of resistance as compared with the six-foot ; but I think this 

 is probably attributable to their being small enough to be within the range 

 of viscosity. On comparing the diagrams of the twelve-foot and six-foot 

 models, however, we find that it is the larger model that has an excess of 

 resistance. This excess, which is slight, may be partly due to certain 

 minor differences of form which had been introduced iu the larger models. 

 It may also have partly arisen from the fact that the twelve-foot models, 

 owing to their greater dimensions, swam relatively nearer to the towing- 

 boat, a circumstance which may naturally have tended to enhance their 

 resistances. 



On the whole, I think that scries of diagrams supplies a very fair veri- 

 fication of the alleged scale of comparison. 



Besides thus throwing light on the question of comparison of the per- 

 formance of similar vessels of different dimensions, these experiments show 

 very clearly that strange forms may possess merits that are entirely un- 

 known and unexpected before experiment is made upon them ; for here we 

 find that an abnormal form (suggested simply by the appearance of water- 

 birds when swimming), if moving with a high though not excessive ve- 

 locity, experiences considerably less resistance than the wave-line form, the 

 accredited representative of the form of least resistance, particularly at high 



