760 



PLATE III. 



Fig. SI. The centre of inertia of the bodies A,B, 

 C,D, may be determinet) either by finding E the cen- 

 tre of inertia of A and B, and supposing a body equal 

 to their sura 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 HI in due proportion in th? 

 same point G. P. 54. 



Fig. 32. The point A being the centre of inertia of 

 the bodies B, C, D, E, the products obtained by multi- 

 plying B by B F, C by C G, D by D H, and E by E I, 

 »re equal, when added together, to the product of the 

 masses of all the bodies by the distance A K; all ihe 

 lines drawn to the plane F I being parallel. P. 55. 



Fig. 33. The weights ABC will remain at rest 

 when they are in the same proportion to each other 

 as the respective sides of the triangle D EF; D Fbeing 

 parallel to EG. P. 61. 



Fig. 34. The bodies A, B, remain in equilibrium 

 when their centre of inertia C is immediately below the 

 point of suspension D. P. 61. 



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. 61. 



Fig. 36. The bodies A,B, remain at rest when the 

 centre of inertia C is immediately above tlie point of 

 support D. P. 61. 



Fig. 37. The bodies A, B, remain at rest when the 

 centre of inertia C coincides with the fulcrum or point 

 of support. P. 61. 



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. 61. 



Fig. 39. A being the centre of gravity of the board 

 B,C, the point ofsuspension being D,E, or F, the posi- 

 tion of the vertical line will be D A, E A, or F A. P. 62. 



Fig. iO. The equilibrium of the vessel A is stable j 



tiiat of the vessel B tottering, the path of the centre of 

 gravity having its concavity, upwards in the first, and 

 downwards in the second. P. 62. 



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

 P. 62. 



Fig. 42. Paths of the centre of gravity of a body 

 resting on a sphere. P. 62. 



Fig 4S. A, the path of the centre of gravity of k 

 body standing on a flat basis; B, the tottering equili- 

 brium of the same body inclined. P. 63. 



Fig. 44. The effects of a certa'm inclination of a 

 waggon, loaded with light and heavy materials, are re- 

 presented at A and B respectively. P. 63. 



Fig. 45. The suspension of a weight^om-aTp^ pro- 

 jecting over a table. P. 64. >' ,•,,,, ,,: p ,pf , : 



Fig. 46. A shows the path of the centre of gravity 

 of a loaded cylinder on an inclined plaije, 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 tone. P. 64. 



Fig. 47. A B is a lever of the first kind, tlie forces 

 acting on different sides of the fulcrum C; D E of tlie 

 second kind, the forces being applied at D and F, on 

 the same side of E. P. 65. 



Fig. 48. A force applied at A may be held in equi- 

 librium by a triple force, applied in die 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. 67. 



Fig. 49. A force, acting at A on the lever A B, h^i 

 a great mechanical advantage in turning the lever C D ; 

 but when the levers are in the position B E, D F, the 

 force. acts witli a similar disadvantage. P. 67. 



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 £. P. 6T. 



