DESCENT OF A HEAVY BODY IN A RESISTING MEDIUM. 117 



The part of the moment due to the obliquity of the motion will remain 

 nearly the same as before. 



We are now prepared to give a general explanation of the motion of the 

 slip of paper after it has become regular. 



Let the angular position of the paper be determined by the angle between 

 the normal to its surface and the axis of x, and let the angular motion be 

 such that the normal, at first coinciding with the axis of x, passes towards 

 that of y. 



The motion, speaking roughly, is one of descent, that is, in the negative 

 direction along the axis of y. 



The resolved part of the resistance in the vertical direction will always 

 act upwards, being greatest when the plane of the paper is horizontal, and 

 vanishing when it is vertical. 



When the motion has become regular, the effect of this force during a 

 whole revolution will be equal and opposite to that of gravity during the same 

 time. 



Since the resisting force increases while the normal is in its first and third 

 quadrants, and diminishes when it is in its second and fourth, the maxima of 

 velocity will occur when the normal is in its first and third quadrants, and 

 the minima when it is in the second and fourth. 



The resolved part of the resistance in the horizontal direction will act in 

 the positive direction along the axis of x in the first and third quadrants, and 

 in the negative direction during the second and fourth ; but since the resistance 

 increases with the velocity, the whole effect during the first and third quadrants 

 will be greater than the whole effect during the second and fourth. Hence 

 the horizontal part of the resistance will act on the whole in the positive 

 direction, and will therefore cause the general path of the body to incline in 

 that direction, that is, toward the righf. 



That part of the moment of the resistance about the centre of gravity 

 which depends on the angular velocity will vary in magnitude, but will always 

 act in the negative direction. The other part, which depends on the obliquity 

 of the plane of the paper to the direction of motion, will be positive in the 

 first and third quadrants and negative in the second and fourth ; but as its 

 magnitude increases with the velocity, the positive effect will be greater than 

 the negative. 



When the motion has become regular, the effect of this excess in the 



