376 DE. PLtJCKEE ON FUIS'DAMENTAL VIEWS REGARDlXa MECHANICS. 



again the forces having their axes in the same plane, the following values are obtained 

 for the intensities and the moments of the three resulting new forces : 



in putting, for brevity. 



while the ratios 



In the general case the three resulting rotatory forces constitute, if compounded, a 

 (rotatory) dyname. In denoting the intensity of its force and moment by 11 and P, we 

 have 



(2^)^+(S«))=-f(S3)'=m 



(4)'+(4)"+(2?)=^'. 



2$ : S§) : S.3= cos I : cos [Jj : cos r, 

 S ^ : 2 — : 5) — = cos a : cos b : cos c 



p q r 



give the angles I, m, n and a, h, c, made by the axes of rotation and the axis of the mo- 

 ments with OX, OY, OZ. 

 If 



cos / COS a -\- cos m cos h + cos n cos c= 0, 



the resulting dyname degenerates into a mere rotatory force of given intensity and posi- 

 tion in space. 



In the case of equilibrium, 



23e=o, s.g)=o, S3=o, 



2 1=0, .S|=0, Sf=0. 

 If only the three last of these six equations equivalent to the following ones, 



5i=o, ^=0, «=o, 



are satisfied, ^, k, § become infinite ; accordingly the three axes of the rotatoiy forces 

 (10) are, within three planes of coordinates, at an infinite distance, and consequently the 

 corresponding rotatory movements are replaced by translatory ones, parallel to the planes 



