759 



PLATi; II. 



■ 1 i JL I. I 



Fig. 15. The ball A, revolving round the point B, 

 and being drawn towards it by means of the thread 

 BC, with a force variable at pleasure, its veldcity may 

 be observed to vary, abcording to itrdistancfe from the 

 point B. P. ST. 



Fig. 16. The curve A B C D E is an ellipsis; E and 

 G are its f6ci, A D its greater axis, and C E ite lesser 

 axis. P. ST. 



Fig. 17. The hol-izontal range, A B, Of a body pro- 

 jected at an elevation of 45", is greater than A C or 

 A D, the ranges of bodies projected with the same ve- 

 locity at a greater or less elevation. If the parallel 

 lines EF, G H, be always as the squares of A E, AG, 

 the curve A F H will be a parabola ; and such is the 

 path of a projectile. P. 39, 4o. 



Fig. 18. The path of a ball moviilg swiftly through 

 the atmosphere nearly resembles the curve A B. P. 

 89. 



Fig. IP. TheballA,having descended along the groove 

 A B, describes the parabola B C, passing through the 

 rings D, E. P. 40. 



Fig. 20. The cylinder A, loaded at the axis, de- 

 scends along an inclined plane more rapidly than the 

 cylinder B, loaded with an equal weight at the circum- 

 ference. P. 42. 



Fig. 21. The balls A, B,C descend along the planes 

 A D, B E, CF, of equal height, in times proportional 



and the balls B, E, deicendiug from any two points of 

 the curve, will meet at E, in the same time that the' 

 Ijall G falls from a point nearly j of A E above A. The 

 space described by the pendulum in descending is al- 

 ways proportional to the height H I, to which a body 

 setting out fiom E, and revolving uniformly in a circle, 

 will rise in the same time. The circle E I lies without 

 the cycloid C E D, and is somewhat less incUncd to 

 the horizon at equal distances from E. P. 44, 45. 



Fig. 25. The ball A, descending from B in the 

 curve B A, arrives at C before the ball D moving in a 

 right line on the plane B C. P. 46. 



Fig. 26. The balls A, B, C, being made to revolve 

 by means of the whirling table, they are always found 

 in the same horizontal plane. The joint connecting 

 them with the axis is represented at D, as seen from 

 above, r. 47. 



Fig. 27. The equal vibrations, represented by A B, 

 C D, compose, when united, the circular revolution 

 AEB: the unequal vibrations AB, FG, compose the 

 ellipsis AIIB; the place of the body being always as- 

 certained by combining the versed sines of two circu- 

 lar arcs increasing uniformly. P. 47. 



Fig. 28. The biUls A, B, as their revolution be- 

 comes more rapid, fly out, and the point C is depressed. 

 P. 48. 



Fig. 29. The mass of the body A being 1 and that 



to their lengths. The upper surfaces of the slips AD, of B 2, and AC being twice BC, C is the centre of iu- 



B E, C F, are slightly grooved. P. 43. 



Fig. 22. The balls A,B,C, descend in equal times 

 along the chords A D, B D, C D. P. 43. 



Fig. 23. The same ball, descending from equal 

 heights, at A, B, or C, by different paths, will rise to 

 the same height at D on the opposite side of E. P. 

 43. 



Fig. 24. Tlic thread A B, playing between the cy- 

 cloidal checks AC, AD, desciibes the cycloid C ED, 



ertia. P. 51. 



Fig. 30. The balls A and B are suspended by long 

 threads, which allow them to move in tlie arcs AC, 

 B D ; the ball A is perforated in a horizontal direc- 

 tion, and contains aspiral spring, which is confined by 

 the thread E, and being set at , liberty by burning 

 this thread, strikes the ball B, so as to cause each of the 

 balls to move through an arc, of which the chord is pro- 

 portional to the weight of the other ball, P. 52. 



