Xll CONTENTS. 



PAGE 



152. Work done by a Twist 141 



153. Law of Distribution of v 142 



154. Conjugate Screws of Potential 142 



155. Determination of the Wrench evoked by a Twist 143 



156. Harmonic Screws 143 



157. Small Oscillations in general 144 



158. Conclusion . 144 



CHAPTER XIII. 

 THE GEOMETRY OF THE CYLINDROID. 



159. Another Investigation of the Cylindroid . 146 



160. Equation to Plane Section of Cylindroid 152 



161. Chord joining Two Screws of Equal Pitch 155 



162. Parabola . 157 



163. Chord joining Two Points 160 



164. Reciprocal Screws . . 181 



165. Application to the Plane Section 163 



166. The Central Section of the Cylindroid 166 



167. Section Parallel to the Nodal Line . 167 



168. Relation between Two Conjugate Screws of Inertia . . 168 



CHAPTER XIV. 

 FREEDOM OF THE THIRD ORDER. 



169. Introduction 170 



170. Screw System of the Third Order 170 



171. The Reciprocal Screw System 171 



172. Distribution of the Screws 171 



173. The Pitch Quadric 172 



174. The Family of Quadrics 173 



175. Construction of a Three-system from Three given Screws . . . . 175 



176. Screws through a Given Point 176 



177. Locus of the feet of perpendiculars on the generators . . . . 178 



178. Screws of the Three-System parallel to a Plane 179 



179. Determination of a Cylindroid 180 



180. Miscellaneous Remarks 182 



181. Virtual Coefficients 183 



182. Four Screws of the Screw System 184 



183. Geometrical Notes 184 



184. Cartesian Equation of the Three-System 184 



185. Equilibrium of Four Forces applied to a Rigid Body .... 186 



186. The Ellipsoid of Inertia 187 



187. The Principal Screws of Inertia 188 



188. Lemma . . . 189 



