ÖZ7' ^,^ „ ÖC7' dU' 



I'X= - ^TT =—AX , Fy =- ^^ =-BV , Fz=- ^jj =-C2, etc. 

 o A dl óZ 



We may tlieretbre attribute these components to attractive forces 

 of the spaces A^=0, Y=:0, Z= 0, . . . (principal diametral spaces), 

 which are perpendicular to these spaces and proportional to the 

 "principal weights" A, B, C', . . . 



For a point on the principal axis of X holds 



Fx=-AX , ^V = , Fz = 0, etc. 



Consequently the principal weight A may be determined by dividing 

 the force at a point of the principal axis of A' by the distance A' 

 of that point to the principal diametral space A^ = 0. To determine 

 the weight of another direction I, only those points are required, at 

 which the direction of the force coincides with the direction I, i. e. 

 the points the normals of which to the hyperellipsoids ii have the 

 direction I. When dividing the amount of the force existing at such 

 a point Q by the distance of the tangent space of Q to the centre 

 P, the quotient found is equal to the weight of the given direction. 



So, in order to determine the weight q^ of the direction of the 

 original ^r'-axis (or of the .«-axisj, we only have to turn back to the 

 coordinate system x,y,z',..., relatively to which the equipotential 

 spaces have the equation 



For a point Q {x , y' , z', . . .) at which the normal to the equipotential 

 space, passing through Q, is parallel to the .^'-axis (or to the .2?-axis), 

 we have 



or 



hence 



or 



or 



[piai^] x' 4- [piai(ii\ y' + [pi«iyi] z' -\- . . . — g^.v', 

 [pi^iai] x' + [pi^i^^ y' 4- Ipi ^,y,] c' + . . . = 0, 

 [/>;y.«.] x' + [piji^i^ y' + [p,Yi^ ^' + . . . = 0, 



1 y' ^' 



[pi«r]— + \piai^i] — ;- + [piaiyi] — ;- + . . . — 1 = 0, 



gx gxx gxx 



gx gxx gxx 



