CONTENTS. Xlll 



PAGE 



189. Relation between the Impulsive Screw and the Instantaneous Screw . 189 



190. Kinetic Energy acquired by an Impulse 189 



191. Reaction of the Constraints .......... 191 



192. Impulsive Screw is Indeterminate 191 



193. Quadric of the Potential 192 



194. The Principal Screws of the Potential . 192 



195. Wrench evoked by Displacement 193 



196. Harmonic Screws ............ 193 



197. Oscillations of a Rigid Body about a Fixed Point . . . . . . 194 



CHAPTER XV. 

 THE PLANE REPRESENTATION OF FREEDOM OF THE THIRD ORDER. 



198. A Fundamental Consideration 197 



199. The Plane Representation 198 



200. The Cylindroid 199 



201. The Screws of the Three-System 200 



202. Imaginary Screws .......... 201 



203. Relation of the Four Planes to the Quadrics 202 



204. The Pitch Conies 204 



205. The Angle between Two Screws 204 



206. Screws at Right Angles 206 



207. Reciprocal Screws 206 



208. The Principal Screws of the System 207 



209. Expression for the Pitch 208 



210. Intersecting Screws in a Three-System 212 



211. Application to Dynamics 214 



CHAPTER XVI. 

 FREEDOM OF THE FOURTH ORDER. 



212. Screw System of the Fourth Order 218 



213. Equilibrium with Freedom of the Fourth Order 219 



214. Screws of Stationary Pitch 221 



215. Applications of the Two-System . 224 



216. Application to the Three-System 226 



217. Principal Pitches of the Reciprocal Cylindroid 227 



218. Equations to the Screw in a Four-System 229 



219. Impulsive Screws and Instantaneous Screws . . . . . 229 



220. Principal Screws of Inertia in the Four-System . . . . . . 230 



221. Application of Euler s Theorem 231 



222. General Remarks 232 



223. Quadratic n-systems 233 



224. Properties of a Quadratic Two-System 234 



225. The Quadratic Systems of Higher Orders .... 235 



