116 DESCENT OF A HEAVY BODY IN A RESISTING MEDIUM. 



on any given element of the surface will vary with its position so that the 

 resultant force will not generally pass through the centre of gravity. 



It is found by experiment that the position of the centre of pressure 

 depends on the tangential part of the motion, that it lies on that side of the 

 centre of gravity towards which the tangential motion of the plane is directed, 

 and that its distance from that point increases as the tangential velocity in- 

 creases. 



I am not aware of any mathematical investigation of this effect. The 

 explanation may be deduced from experiment. 



Place a body similar in shape to the slip of paper obliquely in a current 

 of some visible fluid. Call the edge where the fluid first meets the plane the 

 first edge, and the edge where it leaves the plane, the second edge, then we 

 may observe that 



(1) On the anterior side of the plane the velocity of the fluid increases 

 as it moves along the surface from the first to the second edge, and therefore 

 by a known law in hydrodynamics, the pressure must diminish from the first 

 to the second edge. 



(2) The motion of the fluid behind the plane is very unsteady> but may 

 be observed to consist of a series of eddies diminishing in rapidity as they 

 pass behind the plane from the first to the second edge, and therefore relieving 

 the posterior pressure most at the first edge. 



Both these causes tend to make the total resistance greatest at the first 

 edge, and therefore to bring the centre of pressure nearest to that edge. 



Hence the moment of the resistance about the centre of gravity will always 

 tend to turn the plane towards a position perpendicular to the direction of the 

 current, or, in the case of the slip of paper, to the path of the body itself. It 

 will be shewn that it is this moment that maintains the rotatory motion of 

 the falling paper. 



When the plane has a motion of rotation, the resistance will be modified 

 on account of the unequal velocities of different parts of the surface. The 

 magnitude of the whole resistance at any instant will not be sensibly altered 

 if the velocity of any point due to angular motion be small compared with that 

 due to the motion of the centre of gravity. But there will be an additional 

 moment of the resistance round the centre of gravity, which will always act in 

 the direction opposite to that of rotation, and will vary directly as the normal 

 and angular velocities together. 



