DESCRIPTION OF PLATES. 



PLATE III. 



Fig. 31. The centre of inertia of the bodies A, B, C, D, may be determined, 

 either by finding E the centre of inertia of A and B, and supposing a body equal to 

 their sum to be placed in it, then determining F from E and C ; and G, the point 

 required, from F and D ; or by finding first H and I from A, C, B, D, taken in pairs, 

 and dividing H I in due proportion in the same point G. P. 41. 



Fig. 32. The point A being the centre of inertia of the bodies B, C, D, E, the 

 products obtained by multiplying B by B F, C by C G, D by D H, and E by E I, 

 are equal, when added together, to the product of the masses of all the bodies by the 

 distance A K ; all the lines drawn to the plane F I being parallel. P. 42. 



Fig. 33. The weights ABC will remain at rest when they are in the same pro- 

 portion to each other as the respective sides of the triangle D E F ; D F being parallel 

 to E G. P. 47. 



Fig. 34. The bodies A, B, remain in equilibrium when their centre of inertia C 

 is immediately below the point of suspension D. P. 47. 



Fig. 35. The system of bodies A, B, C, is at rest when the centre of inertia D is 

 immediately below the point of suspension E. P. 47. 



Fig. 36. The bodies A, B, remain at rest when the centre of inertia C is imme- 

 diately above the point of support D. P. 47. 



Fig. 37. The bodies A, B, remain at rest when the centre of inertia C coincides 

 with the fulcrum, or point of support. P. 47. 



Fig. 38. The irregular body A B remains at rest when the centre of inertia C is 

 immediately below the point of suspension D. P. 47. 



Fig. 39. A being the centre of gravity of the board B, C, the point of suspension 

 being D, E, or F, the position of the vertical line will be D A, E A, or F A. P. 47. 



Fig. 40. The equilibrium of the vessel A is stable, that of the vessel B tottering ; 

 the path of the centre of gravity having its concavity upwards in the first, and down- 

 wards in the second. P. 48. 



Fig. 41. Paths of the centre of gravity of an oval. P. 48. 



Fig. 42. Paths of the centre of gravity of a body resting on a sphere. P. 48. 



Fig. 43. A, the path of the centre of gravity of a body standing on a flat basis ; 

 B, the tottering equilibrium of the same body inclined. P. 48. 



Fig. 44. The effects of a certain inclination of a waggon, loaded with light and 

 heavy materials, are represented at A and B respectively. P. 48. 



Fig. 45. The suspension of a weight from a rod projecting over a table. P. 49. 



Fig. 46. A shows the path of the centre of gravity of a loaded cylinder on an 

 inclined plane, B that of the centre of gravity of a double cone moving towards the 

 more elevated end of a triangular surface. C is an elevation of the double cone. 

 P. 49. 



Fig. 47. A B is a lever of the first kind, the forces acting on different sides of the 

 fulcrum C ; D E of the second kind, the forces being applied at D and F, on the 

 same side of E. P. 50. 



Fig. 48. A force applied at A may be held in equilibrium by a triple force, applied 

 in the direction B C, either at B or at C, or in a direction perpendicular to the arm 

 C D at E, D E and D B being each one third of A D. P. 51. 



Fig. 49. A force, acting at A on the lever A B, has a great mechanical advantage 

 in turning the lever C D ; but when the levers are in the position BE, D F, the force 

 acts with a similar disadvantage. P. 51. 



Fig. 50. The diameter of the cylinder A being three times as great as that of B, 

 the weight C, or an equivalent force applied to the winch D, will support a triple 

 weight at E. P. 51. 



