( 729 ) 



equiangular to the left, (from which ensues as a matter of fact 

 that also 



OXr, OYr\ ^^ /OXi, OYi 



are equiangular to the right). 



The systems OXr Yr Zy and OXi Yi Zi execute the motions of 

 aSV and S[ which are to be considered. 



Let us farther call ^Wj , ^tOj , ^co^ , jcu^ , ^w^ , jtu,, the components of 



the velocities of rotation according to the system OX^ X^ X^ X^ ; 



and f/ 1 , f/s , ^3 the components of the velocities of rotation of Sr 



according to OXy, OY,, OZ,, likewise t|^i , if.% , tf^j the components 



of the velocities of rotation of Si according to OXi, OYj, OZi. Then 



we know the components of velocity of rotation to the right 



OX,-^OX, ^. OYr-^OZr 



i (/Ü, + itoj according to ^^ _^ ^^ or accordmg to ^^ _^^p^ 



and analogues, and likewise the components of velocity of rotation 



OX^-^OX, 

 to the left I {^oj^ — jtoj according to or according to 



OX^ — ^ C/Aj 



The Euler equations of motion "in the solid" (giving the opposite 

 of the apparent motion of the surrounding space) follow more simply 

 than according to Frahm out of the vector formula 



fluxion of moment of motion = moment of force — rota- 

 tion X moment of motion 



which is easy to understand for a three dimensional space as well 

 as for a four dimensional one, 



(and where the sign X indicates the vector product) 



F'or, ^'in the space" the fluxion of the moment of motion = moment 

 of force; but of this for the position in solid has ali-eady been 

 marked the fluxion wanted to keep the position constant in the solid, 

 i. e. the fluxion which corresponds to the rotation of the moment- 

 \'ector about the rotationvector and this is =: rotation X moment 

 of motion. 



Let us call the squares of inertia ^m.v^^ etc. Pj etc. and let us put 



