A Treatise on Statics: Containing the Theory of the Equilibrium of Forces; and Numerous Examples Illustrative of the General Principles of the Science |
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Page ix
... CATENARY , ROOFS , AND BRIDGES 245-248 . The Funicular Polygon . 249. Roofs and Bridges ........... 250-267 . The Catenary ......... 162 164 165 CHAPTER XI . PROBLEMS APPENDIX ......... MISCELLANEOUS PROBLEMS . 178 214 221 By the ...
... CATENARY , ROOFS , AND BRIDGES 245-248 . The Funicular Polygon . 249. Roofs and Bridges ........... 250-267 . The Catenary ......... 162 164 165 CHAPTER XI . PROBLEMS APPENDIX ......... MISCELLANEOUS PROBLEMS . 178 214 221 By the ...
Page 96
... catenary being a = 2 ( eā + e " ) , and my being the co - ordinates of the semi - arc ( s ) , shew that = x + ay 28 ax y = y-- S Ex . 4. The equation of a parabola being y2 = 4mx , shew that the distance of the centre of gravity of the ...
... catenary being a = 2 ( eā + e " ) , and my being the co - ordinates of the semi - arc ( s ) , shew that = x + ay 28 ax y = y-- S Ex . 4. The equation of a parabola being y2 = 4mx , shew that the distance of the centre of gravity of the ...
Page 161
... ( y − a ) 2 = 2 CaPx , by integration , which is the equation of a parabola . Hence BP , CQ are two semi - parabolas , whose vertices are B , C. M CHAPTER X. ON THE FUNICULAR POLYGON , ON THE CATENARY ELASTIC STRINGS . 161.
... ( y − a ) 2 = 2 CaPx , by integration , which is the equation of a parabola . Hence BP , CQ are two semi - parabolas , whose vertices are B , C. M CHAPTER X. ON THE FUNICULAR POLYGON , ON THE CATENARY ELASTIC STRINGS . 161.
Page 162
... CATENARY , ON ROOFS AND BRIDGES . ON THE FUNICULAR POLYGON . 245. ABCDEF ( fig . 76 ) is a cord , supposed devoid of weight , suspended from two points A , F in a horizontal line ; at the knots B , C , D , E ...... weights , W1 , W2 ...
... CATENARY , ON ROOFS AND BRIDGES . ON THE FUNICULAR POLYGON . 245. ABCDEF ( fig . 76 ) is a cord , supposed devoid of weight , suspended from two points A , F in a horizontal line ; at the knots B , C , D , E ...... weights , W1 , W2 ...
Page 165
... CATENARY . A Catenary is the curve assumed by a fine chain or flexible string when suspended from its extremities . 250. To investigate the equation of the catenary . Let AOF ( fig . 78 ) be the catenary ; A , F being the points from ...
... CATENARY . A Catenary is the curve assumed by a fine chain or flexible string when suspended from its extremities . 250. To investigate the equation of the catenary . Let AOF ( fig . 78 ) be the catenary ; A , F being the points from ...
Common terms and phrases
a₁ axle balance beam Cambridge catenary centre of gravity College components conditions of equilibrium consequently cos² curve cylinder density direction distance draw dx)² equal to zero equation equi exerts F₁ F₂ find the centre find the conditions find the position fixed axis fixed point forces acting forces F forces which act friction frustum fulcrum Hence horizontal plane inclined plane John Deighton length lever librium m₁ machine magnitude motion parallelogram particle passing perpendicular position of equilibrium pressure proportional pulley pyramid radius represent resolved respectively rest resultant couple right angles rigid body screw shew single force smooth string suppose surface suspended Taylor's theorem tension three forces transposed triangle Trinity College University of Cambridge virtual velocities wheel Wherefore ΣΖ ΣΥ ΣΧ
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