X.X11 TABLE OF CONTENTS. 



AST. PAC1I 



18. Perpendiculars let fall up-n components from intersection of outer 



polygon sides, are inversely as the components. 18 



1 9. Equilibrium polygon 19 



20. Case of a couple Conditions of equilibrium 20 



21. Properties of a couple 21 



J J. Force and equilibrium polygons for any number of forces 22 



23. Influence of a couple 24 



24. Order of forces in force polygon, a matter of indifference 25 



25. Pole upon the closing line Failing case for equilibrium 25 



26. Relation between two equilibrium polygons with different poles .... 26 



27. Mean polygon of equilibrium 27 



28. Line of pressures in an arch 28 



CHAPTER III. 



CENTRE OF GRAVITY. 



30. General method for determination of centre of gravity. 29 



31. Reduction of areas 30 



32. Reduction of triangle to equivalent rectangle of given base 81 



33. Reduction of trapezoid to equivalent rectangle 31 



34. Reduction of quadrilateral generally 81 



CHAPTER IY. 



MOMENT OP ROTATION OF FORCES IN THE SAME PLANE 

 IN GENERAL. 



35. Definition of moment of rotation 33 



36. Culmann's principle 33 



37. Application to equilibrium polygon 34 



CHAPTER Y. 

 MOMENT OF RUPTURE PARALLEL FORCES. 



38. Equilibrium polygon Ordinates to give the moments of rupture. ... 86 



39. Beam with two equal and opposite forces beyond the supports 38 



40. Beam with two equal and opposite forces between the supports 39 



41. Special cases of importance 41 



1st. Beam load Inclined to axis 41 



2d. Force parallel to axis 42 



8d. Forces in different planes 42 



4th. Combined twisting and bending moments 43 



5th. Application to crank and axle 44 



42. Loading continuous Load area 45 



43. Beam uniformly loaded 46 



44. Moment curve a parabola 46 



45. Beam continuously loaded and also subjected to action of concen- 



trated loads 48 



48. Influence of moving load. 50 



47. Load systems 53 



