64 ROYAL SOCIETY OF CANADA 



maximum value of the coefficient is itself a maximum appears to be; in 

 the present case between 31-7 and 275, or about 30 feet per second. The 

 angle for this maximum appears to be about 40°. 



The same ffeneral result is arrived at from a consideration of the 

 data obtained for the vanes of elliptical and parabolic section ; but in 

 those cases it is still more ditRcult with the data obtained to approximate 

 to a numerical result. The maximum efficiency, however, probably oc- 

 curs at a smaller angle of deflection and reaches a higher value for the 

 elli])tical. tmd higher still for the pai*abolic section. 



There is a ])henomenon Avhich is always more or less noticeable with 

 these vanes which will be bi'iefly described. The path of the water flow- 

 ing OÛ' the vane is never tangential to the curve of the vane at the point 

 where it leaves it, but is always slightly more inclined to the axis of 

 revolution of the surface. This effect may be traced to the turning 

 moment, acting on the freely moving stream, brought about by the fric- 

 tion owing to the different velocities of different parts of the stream as it 

 leaves the vane. The particles which have been nearest the surface of 

 the vane have their velocity considerably reduced by friction on that 

 surface : the outer layers of water have only been moving over other 

 "water, and conseqitently their velocity is less reduced. The effect on a 

 stream of the friction of a faster stream on one side and a slower one on 

 the other will be to deflect the direction of motion of the sti-eam away 

 from the faster-flowing stream ; and this is the effect observed in the 

 present case. 



These ex})orimcnts mci-ely touch upon the subject of the efficiency of 

 vanes. By varying the relative sizes of the vane and jet, a great variety 

 of results would be obtainable, many of which would more nearly repre- 

 sent cases met with in practice than those given here. Further investi- 

 gation will probably throw some light on some of the peculiarities notice- 

 able in the present results ; and it is hoped that the experience and data 

 gained in these results maj^ be of use in any further research in the same 

 subj»;ct. 



