A Treatise on the Theory of Screws

 XÜ CONTENTS. §§ page 152. Work done by a Twist.......................................141 153. Law of Distribution of v...................................142 a 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 Gylindroid. 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..........................................161 165. 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 Obder. 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