APPENDIX I. l8l 



Two forces can be found on any pair of conjugate axes, 

 which are statically equivalent to two given forces on any 

 other given pair of conjugate axes. In presenting this paper 

 M. Chasles remarks that Mr. Sylvester's results lead to the 

 following construction : Conceive that a rigid body receives 

 any small displacement, then lines drawn tnrough any six 

 points of the body perpendicular to their trajectories are in 

 involution. M. Chasles takes occasion to mention also some 

 other properties of the conjugate axes. 



SYLVESTER (J. J.) Note sur V involution de six lignes dans Vcspacf. 

 Comptes Rendus; t. Hi., pp. 815-817 (April, 1861). 



The six lines are i, 2, 3, 4,5, 6. Let the line i be repre- 

 sented by the equations 



+ c& + d-u = o, 

 o-iX + fry + y<z -i- SiU = o, 



and let t,j represent the determinant 



y, 5, 



a j A 

 Form now the determinant A 8 



If A 6 = o, the lines are in involution. Considering only the 

 figures i, 2, 3, 4, 5, the determinant A a can be formed. If 



