23_32. FORCES WHICH ACT IN ONE PLANE UPON A PARTICLE, OR UPON THE SAME POINT OF A RIGID BODY. 23, 24. Forces acting in the same line on a point PLANE CHAPTER III. 3968. FORCES WHICH ACT IN ONE PLANE BUT NOT UPON THE SAME POINT OF A RIGID BODY. ........ 39–57. The Theory of Couples..... . 58–63. Parallel forces in a plane 64-68. Non-parallel forces in a plane ...... 19 29 31 CHAPTER IV. 69_98. FORCES NOT IN ONE PLANE WHICH AOT UPON DIFFERENT POINTS OF A RIGID BODY. 71–77. Parallel forces not in a plane 78–80. Resultant of three couples 81–95. Any forces acting on a rigid body 96. Equilibrium of three forces acting on a rigid body 98—101. Conditions of equilibrium of any forces made general 36 41 42 53 54 THE CENTRE OF PARALLEL FORCES, AND THE CENTRE OF GRAVITY. 121–125. The Centre of Parallel Forces. 126–142. The Centre of Gravity. 143-157. Position of Centre of Gravity of rectilinear and regular 158–173. General Properties of the Centre of Gravity... 174–183. Application of Integral Calculus in finding the Centre of 174, 175. ' Centre of Grávity of a curve line. a surface of any form......... ...... 181. - ......... CHAPTER VII. 186—230. MECHANICAL INSTRUMENTS 189–194. The Lever 195–207. The Pulley ....... 208–211.· The Wheel and Axle........... 212–214. The Inclined Plane 215. The Screw 216. The Wedge 217. General Property of Machines 218. White's Pulley 219. Hunter's Screw 220. Compound Wheel and Axle 221. The Genou. 223—225. Toothed Wheels..... 226. The Endless Screw 227. The Common Balance 228. The Steelyard 229. The Danish Balance 230. Roberval's Balance 120 123 125 131 132 133 136 137 138 139 140 141 143 147 ..... 150 151 249. Roofs and Bridges........ 250–267. The Catenary....... 164 165 CHAPTER XI. PROBLEMS APPENDIX.. MISCELLANEOUS PROBLEMS.. 178 .... 214 .... 221 S TA TICS. INTRODUCTION. DEFINITIONS AND PRELIMINARY NOTIONS. 1. In the Science of MECHANICS of which STATICS forms a part, matter is considered as essentially possessing extension, figure and impenetrability. The least conceivable portion of matter is called a particle. 2. We conceive of matter that it can exist either in a state of rest, or motion. If then matter, once at rest, pass into a state of motion, the change, not being essential to the existence or nature of matter, is of necessity ascribed to some agent, which, as to its nature, is essentially independent of the matter influenced. Whether this agent reside in the matter influenced, or in external objects, or in both, are questions which can only be answered after experimental investigation. This agent is called force; and . it will be perceived from this statement, that a force is judged of entirely by the effects which it produces : and hence, if in the same circumstances two forces produce equal effects, we infer that the forces are equal. . 3. It is assumed, that the effect of two equal forces acting in concert, is double the effect of one of them; three, treble; and so on. The reason of its being necessary to make this an assumption is, that in our ignorance of the nature of force, are compelled to judge of it by the change which it produces in the state of rest or motion of matter; and it is obvious, that we can no more judge that one such change B we |
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