Lord Rayleigh on the Resistance of Fluids. 433 



cular to the plane of the lamina : and from this it would follow 

 that when a lamina is exposed to an oblique stream, the resist- 

 ance experienced would be that calculated from the same for- 

 mula as before, on the understanding that u now represents the 

 perpendicular component of the actual velocity of the stream. 

 Or if the actual velocity of the stream be Y, and a denote the 

 angle between the direction of the stream and the lamina, the 

 resistance would be per unit of area 



h P Y 2 sm 2 * (1) 



This force acts of course perpendicularly to the plane of the 

 lamina ; the component down the current is 



*pV S m 3 « (2) 



The argument by which this result is obtained, however, is 

 quite worthless ; and the law of the squares of the sines ex- 

 pressed in (1) is known to practical men to be very wide of 

 the mark, especially for small values of a. The resistance 

 at high obliquities is much greater than (1) would make it, 

 being more nearly in proportion to the first power of sin a 

 than to the square. 



As a proof that an edgeways motion of an elongated bodv 

 through water is not without influence on the force necessary 

 to move it with a given speed broadways, Mr. Froude says *, 

 " Thus when a vessel was working to windward, immediately 

 after she had tacked and before she had gathered headway, it 

 was plainly visible, and it was known to every sailor, that her 

 leeway was much more rapid than after she had begun to 

 gather headway. The more rapid her headway became, the 

 slower became the lee-drift, not merely relatively slower, but 

 absolutely slower." 



"Again, any one might obtain conclusive proof of the exist- 

 ence of this increase of pressure occasioned by the introduc- 

 tion of the edgeways component of motion, who would try the 

 following simple experiment. Let him stand in a boat moving 

 through the water, and, taking an oar in his hand, let him 

 dip the blade vertically into the water alongside the boat, pre- 

 senting its face normally to the line of the boat's motion, hold- 

 ing the plane steady in that position, and let him estimate the 

 pressure of the water on the blade by the muscular effort 

 required to overcome it. TYhen he has consciously appre- 

 ciated this, let him begin to sway the blade edgeways like a 

 pendulum, and he will at once experience a very sensible 

 increase of pressure. And if the edgeways sweep thus as- 



* Proceedings of the Society of CiYil Engineers, vol. xxxii., in a discus- 

 sion on a paper bv Sir F. Knowles on the Screw Propeller. 



Phil. Mag. S. 5. Vol. 2. No. 13. Dec. 1876. 2 F 



