274 Mr A. E. H. Love, On the Motion of a Solid [Oct. 29, 
and p’ is given by the equation 
(a, b, of 9, Pl, MyM SO) prt... Ue ale (7). 
The direction-cosines of OM, (a’), are proportional to 
al, +hm,+gn,, hl,+bm,+fn,, gl, +fm,+en,, 
and therefore the direction-cosines of the lne MO along which 
the translation takes place are 
—¢(aAr+hBu + 90*r)/apU, 
and two similar expressions in which 
UVr=€ [(aA°r+hBwt gO*v)y’ + (hAPrN+ GB + fOr) 
+ (gA°r + fB'u + cC0*v)"]/a*p*...(8). 
The velocity of translation V is given by 
php tee es ara 
€ pw p's" np” ar - 
where n° = e/E. 
Now q = cos MOP 
= [l, (al, +hm, + gn,) +m, (hl, + bm, + fn,) 
+n, (gl, +fm, + en,)]/U 
= — 6/p°U. 
Hence V=— : DP och Sued cwcoasdonlosalcueansidss Sassen eae eer (9). 
It follows that, if u,, v,, w, denote the components of V along 
the principal axes of the rotational ellipsoid, we shall have 
== (al, +hm, +gn,), 
with similar expressions for v, and w,, or 
€ : 
Mat [aA +hB up + 9 C*r] 
v, = == [RA bp FCF pl) pie eee (10), 
= = [gA°rA + f Bw + c0*r] 
in which only the parts in [ ] are functions of the time. 
The angular velocity (p, g, 7) is given by 
PPE Se Py a 
