

DESCRIPTION OF PLATES. 



PLATE I. 



Fig. 1. The point A being supposed to move in a right line to B, A B is the direc- 

 tion of its motion. P. 15. 



Fig. 2. The lines AB, BC, CD, are the successive directions of the point A, 

 moving from A to D in the figure A B C D. P. 15. 



Fig. 3. The tangent A B is the direction of the motion of the point C, moving in 

 the curve C D, when it arrives at E. P. 15. 



Fig. 4. The square A B, moving on the board C D, so that the points E, F, de- 

 scribe the parallel lines EG, F H, with equal velocities, the plane A E F B is in rec- 

 tilinear motion with respect to the surface CD. P. 18. 



Fig. 5. The cycloid ABC, and the trochoid D E F are the results of the rotatory 

 motion of the points B and E round the centre of the wheel, combined with the pro- 

 gressive motion of the wheel along the base A C. P. 18, 34. 



Fig. 6. A B is a fixed bar, C D an arm which slides on it, E C F a thread pass- 

 ing 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 H. 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 describes, by its compound motion, the oblique line K I. P. 18. 



Fig. 7. The diagonal A B of the parallelogram C D is the joint result of the mo- 

 tions represented by its sides AC, AD. P. 19. 



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 A C and A D of the arm and its slider, or by the un- 

 equal motions A E and A F. P/19. 



Fig. 9. The body A, moving uniformly along the line A B, first approaches to 

 the point C, and then recedes from it, as if repelled. P. 21. 



Fig. 10. When A B and A C approach each other, and coincide, the diagonal A D 

 becomes equal to their sum. P. 23. 



Fig. 11. Atwood's machine. The boxes A, B, containing equal weights, are 

 connected by the thread A C B, passing over the pulley C, which is supported either 

 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 continues to descend till it strikes the 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 scapement with a weight. The machine is 

 levelled by the screws L, M. P. 23, 41. 



Fig. 12. The time of the descent of a falling body being represented by any por- 

 tion 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 proportional to the area D E F G, which is expressed by the product of 

 B C and D E ; consequently the whole area A E F will represent the space described 

 in the time A E, and A H I the space described in the time AH; but A H I is half 

 of the square H K, and A E F of EL: the space is therefore always as the square of 

 the time, and is equal to half the space which would be described in the same time 

 with the final velocity. P. 24. 



Fig. 13. The whirling table. The arms A B, C D, are made to revolve on the 

 axes E F, G H 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 below 

 them ; they move along the arms by means of friction wheels resting on wires, and 

 they raise the weights M, N, by means of threads passing each over two pullies. 

 P. 27. 



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, 

 C D G, will be equal, and the velocities in A, B, and G, will be inversely as the per- 

 pendiculars D H, D I, and D K. P. 28. 



b'2 



