DE. PLUCKEE ON FtJNDAItlENTAL VIEWS EEGAEDr^G MECHANICS. 371 



3. Both the intensity (P) and the moment (R) of a rotatory force depend only upon 

 the position of the origin ; they do not depend upon the direction of the axes of coordi- 

 nates. Indeed^ and^ denoting the distance of the planes {t, u, v), (t/, u', vf), by means 

 of which a rotatory force {fu'i^, tuv) is determined, from the origin, and u the angle 

 between the planes, we have 



Again, the intensity (P) being given according to (10), the moment of the rotatory 

 force (R) remains the same when the axis of rotation gets into any other position, as 

 long as S, the distance of the axis from the origin, does not change, and in particular 

 when the axis of rotation turns round the axis of the moment. 



4. The six coordinates of an ordinary force {afi/z, xyz) remain the same when, the 

 mutual distance of the two points {x'y'^) and {x:, y, z) not being altered, the point (a/, y, z*) 

 acted upon moves along the direction of the force. So do the six coordinates of a rota- 

 tory force (<'^«V, tuv) when, P remaining the same, the plane (^, ?/, ?/) acted upon rotates 

 round the axis of rotation. A repulsive or attractive force may act on each point of 

 its direction, a rotatory force on each plane passing through its axis. Let 



t'x-\-vJy+v'z—l=s'=Q, 

 tX +UI/ -{-vz —l=s=0, 



be the equations of the planes (t!, u', v') and {t, u, v) by which a rotatory force is deter- 

 mined. In denoting by ^' and p any two arbitrary constants, the following equations, 



s-ys'=0, 



s'—(/jS =0, 



represent any two new planes passing through the axis of rotation. Let (^'„, ?/„, vj,) and 

 (to, «„, Vo) be the corresponding symbols of the new planes. The first of the two 

 planes, depending upon the constant fjb', may be regarded as any plane acted upon by the 

 rotatory force, and accordingly the second plane, depending upon the constant [ji,, may be 

 determined so that the intensity of the rotatory force, and therefore its moment, shall 

 not be changed. In this supposition 



indicating planes acted upon parallel to OX, OY, OZ ; let G, H, I be the points in 

 which the corresponding second plane meets the same axes. If any other plane passing 



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