[From the Cambridge and Dublin Mathematical Journal, Vol. ix.] 



V. On a particular case of the descent of a heavy body in a resisting 



medium. 



EVERY one must have observed that when a slip of paper falls through 

 the air, its motion, though undecided and wavering at first, sometimes becomes 

 regular. Its general path is not in the vertical direction, but inclined to it 

 at an angle which remains nearly constant, and its fluttering appearance will 

 be found to be due to a rapid rotation round a horizontal axis. The direction 

 of deviation from the vertical depends on the direction of rotation. 



If the positive directions of an axis be toward the right hand and upwards, 

 and the positive angular direction opposite to the direction of motion of the 

 hands of a watch, then, if the rotation is in the positive direction, the hori- 

 zontal part of the mean motion will be positive. 



These effects are commonly attributed to some accidental peculiarity in the 

 form of the paper, but a few experiments with a rectangular slip of paper 

 (about two inches long and one broad), will shew that the direction of rotation 

 is determined, not by the irregularities of the paper, but by the initial circum- 

 stances of projection, and that the symmetry of the form of the paper greatly 

 increases the distinctness of the phenomena. We may therefore assume that 

 if the form of the body were accurately that of a plane rectangle, the same 

 effects would be produced. 



The following investigation is intended as a general explanation of the true 

 cause of the phenomenon. 



I suppose the resistance of the air caused by the motion of the plane to 

 be in the direction of the normal and to vary as the square of the velocity 

 estimated in that direction. 



Now though this may be taken as a sufficiently near approximation to the 

 magnitude of the resisting force on the plane taken as a whole, the pressure 



152 



