CONTENTS. xi 



CHAPTER XI. 



THE DYNAMICS OF A RIGID BODY WHICH HAS FREEDOM OF THE 

 THIRD ORDER. 



SECT. PAGE. 



107. Introduction, . ....... .: ...;:>. . ' . . 116 



108. Screw Complex of the Third Order, . ' < , ",' > . . 117 



109. The Reciprocal Scre\v Complex, . . ... ,., . . .118 



HO. Distribution of the Screws, . . '--.'' ib. 



in. The Pitch Quadric, ..... , . . .119 



1 1 2. Screws through a Given Point, 122 



113. Screws of the Complex parallel to a Plane, 125 



114. Determination of the Cylindroid, . * . . . . .126 



115. Miscellaneous Remarks, ... ... . . .128 



1 1 6. Virtual Co-efficients, , . . ,.,- , v . f , , , .-, . . . . . 130 



117. Four Screws of the Screw Complex, . . . . . ib. 



118. Equilibrium of Four Forces applied to a Rigid Body, . . . 131 



119. The Ellipsoid of Inertia, ./.,.,.., . . . 1. . 133 



1 20. The Principal Screws of Inertia, ... . . . . . 134 



121. Lemma, . 1 <'#' '. '-"'"'', .... 135 



122. Relation between the Impulsive Screw and the Instantaneous Screw, ib. 



123. Kinetic Energy acquired by an Impulse, " . . ... . . 136 



124. Reaction of the Constraints, 138 



125. Impulsive Screw is Indeterminate, . /. ib. 



126. Ellipsoid of the Potential, . .. ,;! .-. ,* '* ... - ... . 139 



127. The Principal Screws of the Potential, . . . . ' . .140 



128. Wrench evoked by Displacement, . . . . . . . ib. 



129. Harmonic Screws, . .141 



130. Oscillations of a Rigid Body about a Fixed Point, . . .142 



CHAPTER XII. 



THE DYNAMICS OF A RIGID BODY WHICH HAS FREEDOM OF THE 

 FOURTH ORDER. 



131. Screw Complex of the Fourth Order, 146 



132. Screws Parallel to a Given Line, ib. 



133. Screws in a Plane, ib. 



134. Property of the Pitches of Six Co-reciprocals, . . . . 147 



135. Another Proof, 149 



136. Property of the Pitches of n Co-reciprocals, 149 



137. Special Screw of the Complex, 150 



138. Particular Case, ib. 



139. Statics, ib. 



