117119.] STABILITY OF MOTION. 135 



with a similar equation for r, and 



^tfw A (A- C} 2 

 C -tf + A B~ J &amp;lt;&quot; = &amp;lt;&amp;gt; 



with a similar equation for q. The motion is therefore stable only 

 if A be greater than either B or C. It appears from Art. Ill that 

 the only direction of stable motion of an ellipsoid is that of its 

 least axis. For practical illustrations of this result see Thomson 

 and Tait, Art. 33G. 



119. If in (24) we write T= & + & , and separate the terms 

 due to f& and respectively, we obtain expressions for the forces 

 exerted on the moving solid by the pressure of the surrounding 

 fluid ; viz. we have for the total component (, say,) of the fluid 

 pressure parallel to x 



_ _ d_ 



& & do dw 



and for the moment (U) of the same pressures about x, 



d 



% = - ~+w-j -- v -j -- \- r j -- q -j- . 

 dt dp dv aw dq 2 ar 



The forms of these expressions being known, it is not difficult to 

 verify them by direct calculation from the formula (18). We should 

 thus obtain an independent though somewhat tedious proof of the 

 general equations of motion (24). 



If the body be constrained to move with a uniform velocity of 

 translation, the components of which, relatively to the axes of 

 Art. 113, are v, v, iv, we have K, |J, ? = 0, so that the effect of 

 the fluid pressure is represented by a couple whose components 

 are 



The coefficients A, B, C in the expression for 2T differ from those 

 in the expression for 2^ only by the addition of the mass of the 

 solid, so that it is immaterial in (21) which set of coefficients we 

 understand by these symbols. 



If we draw in the ellipsoid 



Cz* = const ............. .......(46), 



