758 



PLATE I. 



Fig. 'I. The point A being supposed to move in a 

 right line to B, AB is the direction of its motion. P. 

 SI. 



Fig. 9. The lines A B, B C, C D, are the successive 

 directions of the point A, moving from A to D in the 

 figure A BCD. P. 21. 



Fig 3. The tangent A B is the direction of the mo- 

 tion of the point C, moving in the curve C D, when it 

 arrives at E. P. 21. 



Fig. 4. The square AB, moving on the hoard C D, 

 so that the points E, F, describe the parallel lines E G, 

 J E H, with eqOal velocities, the plane A E F B is in rec- 

 tilinear motion with respect to the surface C D. P. 24. 

 Fig. 5. The cycloid A B C, and the trochoid D E F 

 are the resuits of the rotatory motion of the points B 

 and E round the centre of the wheel, combined with 

 ^he progressive motion of the wheel along the base 

 AC. P. 24, 44. 



Fig. 6. A B is a fixed bar, C D an arm which slides 

 on it, ECF a thread passing round the pulley at C, 

 and either fixed to the pin on the slider F, or passed 

 over the pulley G, and fixed again at II. The arm 

 turns round the same axis that carries the pulley at 

 C, and may be fixed by means of the screw which is 

 cut on the axis, while two other screws keep it steady 

 , by pressing on the slider below it. The point I de- 

 scribes, by its compound motion, the oblique line KI. 

 P. 24. 



Fig. 7. The diagonal A B of the parallelogram C D 

 is the joint result of the motions, represented by its 

 sides AC, AD. P, 2a. 



Fig. 8. The line A B may be either simply drawn 

 in the direction A B, or it may be traced by the equal 

 motions AC and AD of the arm and its slider, or by 

 the unequal motions A E and A F. P. 25. 



Fig. 9. The body A, moving uniformly along the 

 line AB, first approaches to the point C, and then 

 recedes from it, as if repelled. P. 27. 



Fig. 10. When A Band AC approach each other, 

 and coincide, the diagonal AD becomes equal to their 

 snm. P. 30. 



Fig. 11. Atwood's machine. The boxes A, B, con- 

 taining equal weights, are connected by the thread 

 A C B, passing over the puUey C, which is supported ei- 

 ther on friction wheels, or by the points of screws, one 

 of which is seen at D. The box A is made to descend 

 either by a flat weight placed on it, or by the bar E, 

 which is intercepted by the ring F, and the box conti- 

 nues to descend till it strikes die stage G; the space 

 being measured on the scale H I, and the time by the 

 pendulum K, which may be kept in motion by a clock 

 scaperoent with a weight. The machine is levelled 

 by the screws L, M. P. 31. 



Fig. 12. The time of the descent of a falling bodjr 

 being represented by any portion A B of the base of a 

 triangle, the velocity will be proportional to B C, which 

 is equal to A B, and the space described during the 

 time D E, supposed infinitely short, will be propor- 

 tional to the area D E F G, which is expressed by the 

 product of BC and D E; consequently the whole area 

 A E F will represent the space described in the time 

 AE, and A HI the space described in the time AH; 

 but A II I is half of the square H K, and A E F of 

 E L : the space is therefore always as the square of tlie 

 time, and is equal to half the space which would be de- 

 scribed in the same time with the final velocity. P. 32. 



Fig. 13. The whirling table. The arms A B, C D, 

 are made to revolve on the axes E F, G II by the 

 string passing over the wheel I, the upper or under 

 pulley of either axis being employed at pleasure: the 

 stages K,L, with their weights, are placed at certain * 

 distances from the centre, by means of the racks or 

 teeth belovi them; they move along the arms by means 

 of friction wheels resting on wires, and they raise the 

 weights M,N, by rrieans of threads passing each over 

 two puUies. P. 35. 



Fig. 14. If a body revolving in a curve ABC, by 

 means of a force directed to D, describe the portions 

 A E, B F, C G in equal times, the areas A D E, B D F, 

 CDG, will be equal, and the velocities in A,B, and 

 G, will be inversely as the perpendiculars D H, D I, 

 andDK. P. 36. 



