Lord Rayleigh on the Resistance of Fluids. 437 



the maximum value unity. The fifth column gives the distance 

 between the centre of pressure and the middle line of the blade, 

 expressed as a fraction of the total width. The sixth column 

 is the value of 



2(1 — 2 cos a + cos 3 a) + a sin a 

 4 + 7r sin a 



which is the distance from the anterior edge of the point where 

 the stream divides, and where accordingly the pressure attains 

 its greatest value. It will be seen that, as might be expected, 

 this distance becomes small at moderate obliquities. 



The result of Vince's experiments agrees with theory re- 

 markably well ; and the contrast with shr a is especially worthy 

 of note. The experiments were made with a whirling machine, 

 and appear to have been carefully conducted ; but they were 

 on too small a scale to be quite satisfactory. The subject 

 might now be resumed with advantage. 



From theory it would appear that any part of the region of 

 dead water behind the lamina might be filled up with solid 

 matter without in any way disturbing the motion or altering 

 the resistance : but in practice with actual fluids this state- 

 ment must not be taken without qualification. If the boundary 

 of the solid approach too nearly the natural position of the sur- 

 face of separation, the intervening fluid appears to be sucked 

 out until the lines of flow follow the surface of the obstacle. 

 This is the state of things aimed at, and approximately attained, 

 in well-designed ships, round which the water flows nearly 

 according to the electrical law. The resistance is then of an 

 entirely altered character, and depends only upon the friction 

 against the skin. 



It was observed by Sir William Thomson at Glasgow, that 

 motions involving a surface of separation are unstable. This 

 is no doubt the case, and is true even of a parallel jet moving 

 with uniform velocity. If from any cause a slight swelling 

 occurs at any point of the surface, an increase of pressure ensues 

 tending not to correct but to augment the irregularity. I had 

 occasion myself to refer to a case of this kind in a paper on 

 Waves, published in the ' Philosophical Magazine ' for April 

 1876. But it may be doubted whether the calculations of 

 resistance are materially affected by this circumstance, as the 

 pressures experienced must be nearly independent of what 

 happens at some distance in the rear of the obstacle, where the 

 instability would first begin to manifest itself. 



The formula? proposed in the present paper are also liable 

 to a certain amount of modification from friction which it 

 would be difficult to estimate beforehand, but which cannot be 



