190 MOTION OF SOLIDS THROUGH A LIQUID. [CHAP. VI 



If we assume that v, w, q, r vary as e ?A *, and eliminate their ratios, we find 



O ......... (iv). 



The condition that the roots of this should be real is that 



should be positive. This is always satisfied when A&amp;gt;B, and can be satisfied 

 in any case by giving a sufficiently great value to p Q . 



This example illustrates the steadiness of flight which is given to an 

 elongated projectile by rifling. 



126. In the investigation of Art. 122 the term steady was 

 used to characterize modes of motion in which the instantaneous 

 screw preserved a constant relation to the moving solid. In the 

 case of a solid of revolution, however, we may conveniently use the 

 term in a somewhat wider sense, extending it to motions in which 

 the velocities of translation and rotation are constant in magnitude, 

 and make constant angles with the axis of symmetry and with 

 each other, although their relation to particles of the solid not on 

 the axis may continually vary. 



The conditions to be satisfied in this case are most easily obtained from 

 the equations of motion of Art. 121, which become, on substitution from 

 Art. 123 (3), 



...... (i). 



It appears that p is in any case constant, and that q 2 + r 2 will also be constant 



provided 



vfa=w/r, =k, say .................... . ............ (ii). 



This makes du/dt = 0, and 



cons t. 



It follows that k will also be constant; and it only remains to satisfy the 

 equations 



