( 734 ) 



f*^-f- 



Fig. 9. 



R(f-\-A^xp.^ to the right lying in 

 the meridian plane of </) remains in 

 Sr invariable. Thus "in space" that 

 meridian plane rotates about the 

 vector R(p-}- A^\]\, by which the 

 "cone in space" is known, and 

 likewise proves to be a cone of 

 revolution. Analogous for Si . Fig. 9 

 shows the two cones of rotation 

 in S,: The outer cone is the 

 moving one. 



2nd Three of the squares of inertia are equal and unequal to the 

 fourth. We take the axis of the unequal one as X^ axis in S^. Then 

 A^ = A^ = Az = A; a^ =^ a^^ a^ = a; b^ = h^ = b^ = b; and the 

 equations {h) pass into 



b 



xp 



V (p . If? 



therefore ip and if? are both perpendicular to tp and to if', whilst r/)-l-if?=zO, 

 so y -}- i|? is constant and <f and if? are each for itself constant in absolute 

 value, so that they both rotate about their sum ("in space" that 

 vector of the sum has in general quite a different position for >SV 

 than for Si) by which the two "cones in the solid" are determined. 

 "Invariable rotating" of S^ we have here wherever (p and if', 



regardless of their value, coincide. To find 

 the "cone in space" for S,-, we notice the 

 invariability in >S',. of R<p -f- ^4 if?. "In space" 

 ./) rotates about R f> -\- ^4 if?, for the angle 

 ^f v^ between those two vectors remains constant. 

 In Sl rotates analogously "in space" if' about 

 R\p-\-A'f. Fig. 10 represents the tvv^o cones 

 of rotations in S,- (Here too the outer cone 

 is the moving one). 

 We remind the readers once more, that where we bring (p and if', 

 as far as their positions in the solid are concerned, into relationship 

 with each other, we must of course in our mind make the positions 

 to the right and the left that is of the systems of coordinates OXr 

 Yr Zr and OXi Yi Zi to coincide with each other, so that but one 

 system of coordinates OXYZ is left (for instance for the equations 



FiR. 10. 



