43(3 



Lord Rayleigb on the Resistance of Fluids. 



easily proved by experiment. For this purpose it is sufficient to 

 take a piece of thin brass plate shaped as in the figure (Plate V. 

 fig. 2), and mount it with its points bearing in two small in- 

 dentations in a U-shaped strip of thicker plate, easily made by 

 striking the strip with a conically pointed piece of steel driven 

 by the hammer. When this little apparatus is moved through 

 the water, the movable piece at once sets itself across the direc- 

 tion of motion. The same result may be observed when the ap- 

 paratus is exposed to the wind ; but in this case an unexpected 

 phenomenon often masks the stability of the transverse position. 

 It is found that when the plate is set rotating, the force of 

 the wind will maintain or accelerate the motion. This effect 

 might be supposed to be due to a want of symmetry, were it 

 not that the rotation occurs in either direction. It is evi- 

 dently connected with the disturbance of the fluid due to the 

 motion of rotation, and is not covered by the calculation lead- 

 ing to formula (4), which refers to the forces experienced 

 when the blade is at rest in any position. 



I am not aware of any experimental measurements with 

 which (4) could be compared ; but the result that the equili- 

 brium parallel to the stream is indifferent when the axis is 

 situated in the position defined by the ratio 11 : 5, is in agree- 

 ment with the construction of balanced rudders, of which the 

 front part is usually made of about one half the width of the 

 hinder part. 



The accompanying Table contains some numerical examples 

 of the general formulae. The first column gives the angle be- 

 tween the lamina and stream, the second the value of sin 2 a, 

 to which, on the old theory, the resistance should be propor- 

 tional ; the third column is derived from some experiments by 

 Vince on water, published in the ' Philosophical Transactions ' 

 for 1798. 









sin«(4-f7r) 



3 COS a 





a. 



90 



sin 2 a. 



Vince. 



4 + 7T sin « 



4 4 -f- it sin a. 





1-0000 



1000 



1-0000 



•0000 



•5000 



70 



•8830 



•974 



•8652 



•0369 



•2676 



50 



•5868 



•873 



•8537 



•0752 



•0981 



30 



•2500 



•663 



•6411 



•1166 



•0173 



20 



1170 



•458 



•4814 



•1389 



•0040 



10 



•0302 



•278 



•2728 



•1625 



•0004 



The quantity directly measured by Vince was the resolved part 

 of the resistance in the direction of the stream, from which the 

 tabulated number is derived by division by sin «. The fourth 

 column represents the law of resistance according to the for- 

 mula now proposed, a factor being introduced so as to make 



