372 DE, PLUCKER ON PUNDAMENTAL VIEWS EEGAEDIXG MECHANICS. 



through the axis of rotation and intersecting the axes of coordinates in the points Gr*, 

 H', I' is taken as the plane acted upon by the rotatory force, the corresponding second 

 plane intersects the same axes in three points G,, H,, I,, such that the three couples 



°^P°^"*'' O, G and G',G, 



O, H and H', H, 



O, I and r , I, 



constitute, on the three axes of coordinates, three systems of harmonic points. 



5. If any force be given, its intensity (P) is quite independent of the axes of rectan- 

 gular coordinates, which may be arbitrarily chosen, but its moment (R) depends upon 

 the choice of the origin. The point upon which the force acts, if free, is impelled along 

 a given line. If the point acted upon be attached to any fixed point, the translatory 

 movement is changed into a rotatory one. Any plane perpendicular to the direction of 

 the force revolves, if one of its points be fijced, round an axis, confined within the plane, 

 passing through the fixed point and perpendicular to the direction of the force. This 

 axis is the axis of the moment of the force with regard to the fixed point which in the 

 considerations of Part I. was the origin of coordinates. The cause producing the double 

 efiect is called force. This definition involves that the direction of the force and the 

 direction of the axis of its moment be perpendicular to each other. If there is a 

 moment, the axis of which is not perpendicular to the direction of the translatory move- 

 ment produced, the cause of it is no more a mere force : we called it a dyncmie. 



If any rotatory force be given, both the intensity of the force and the intensity of its 

 moment are independent of the direction of the axes of coordinates, only both depend 

 upon the position of the origin (3). A plane perpendicular to the axis of rotation 

 remains the same during the revolution. If there is another invariable plane, i. e. a 

 plane not able to turn round any axis confined within it, and therefore, this axis being 

 infinitely distant, not able to be displaced parallel to itself, the revolution is stopped 

 and transformed into a translatory movement of the plane acted upon. Indeed the 

 intersection of the two invariable planes becoming an invariable line, able only to move 

 along its own direction, the plane acted upon and all the planes connected with it are 

 displaced along the invariable line. The movement along this direction may be decom- 

 posed into three, along the axes of coordinates. The cause producing the double move- 

 ment is called rotatory force. If the condition that both axes (of rotation and of trans- 

 lation) are perpendicular to each other be not fulfilled, we shall call it a {rotatory) dyname. 

 If any point of the line, moveable only along its own direction, be fixed, it endures a 

 pressure along that line which is proportional to the translatoiy movement, and may be 

 likewise decomposed along the axes of coordinates. 



6. Let us, in order to confirm in the analytical way the general views of the last 

 number, consider a rotation the axis of which is confined in the plane XY, and within 

 this plane directed parallel to OX. Let us admit, too, that the plane acted upon, pass- 

 ing through the axis of rotation, is parallel to OZ. Under these conditions, the symbol 



