265] 



EMANANTS AND PITCH INVARIANTS. 



277 



If three screws, a, @, y, are all parallel to the same plane, and if 9 be a 

 screw normal to that plane, then we must have 



dR dR 



dR 

 dfr 

 dR 



dR 



264. Conditions that Three Screws shall be parallel to a 

 Plane. 



^ * 



Since a screw of a three-system can be drawn parallel to any direction, 

 it will be possible to make any three of the quantities 6 l , ... 6 6 equal to zero. 

 Hence, we have as the condition that the three screws, a, /3, 7 shall be 

 all parallel to a plane the evanescence of all the determinants of the type 



dR 

 dR 



dR 



d 7l &amp;gt; 



dR 



dR 



dR 



dR 



dR 



dR 



265. Screws on the same Axis. 



The locus of the screws d perpendicular to a is represented by the 

 equation 



If we assume that the screws of reference are co-reciprocal, then the 

 equation just written can only denote all the screws reciprocal to the one 

 screw whose co-ordinates are 



Pi di &quot; PS da 6 



It is manifest that all the screws perpendicular to a given line cannot be 

 reciprocal to a single screw unless the pitch of that screw be infinite, other 

 wise the condition 



(p a +p e ) cos (f&amp;gt; d sin &amp;lt; = 



could not be fulfilled. We therefore see that the co-ordinates just written 

 can only denote those of a screw of infinite pitch parallel to a. 



