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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

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181.

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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
152

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249. Roofs and Bridges........

250–267. The Catenary.......

164

165

CHAPTER XI.

PROBLEMS

APPENDIX..

MISCELLANEOUS PROBLEMS..

178

.... 214

.... 221

By the same Author.

TREATISE ON DYNAMICS.

Third Edition.

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

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