DESCRIPTION OF PLATES. vii 



PLATE V. 



Fig. 65. By means of the moveable inclined plane A B, of which the height A C 

 is one third of the horizontal length B C, the weight D, acting horizontally, sustains 

 a triple weight E, acting in a vertical direction. P. 55. 



Fig. 66. A B being one fourth of B C, the rope AB must exert a force of tension 

 equal to one fourth of the weight C, in order to support it, supposing the surfaces to 

 be without friction. But if the friction of the end of the beam A C were equal to 

 one fourth of the pressure, it would support the weight C without any other force, 

 whatever might be its magnitude. P. 55. 



Fig. 67. A B being half of B C, or one fourth of C D, the force extending the 

 rope C D each way is equal to the weight E. P. 55. 



Fig. 68. The thin wedge A B, of which the height is one fifth of the length, being 

 rolled round the cylinder C, makes the screw D, by means of which the weight E is 

 capable of supporting a weight five times as great as F. P. 55. 



Fig. 69. A is a screw, and B the nut belonging to it. P. 55. 



Fig. 70. The endless screw A B acts on the teeth of the wheel C D. P. 55. 



Fig. 71. The distance of the threads of the interior screw is four fifths of that of 

 the exterior or perforated screw, and this distance is one thirtieth of the circumference. 

 Hence the weight A is capable of sustaining a weight B 150 times as great as itself. 

 P. 56. 



Fig. 72. The apparatus for experiments on collision. Those balls which are not 

 employed may be left behind the graduated arc, as at A and B ; some of the strings 

 have balls of half the weight of the rest, others have a small dish C, on which 

 balls of clay, or of wax softened with one fourth its weight of oil, may be supported. 

 P. 58. 



Fig. 73. If the ball A strike the ball B in the oblique direction A C, the ball B 

 will be impelled in the direction C D perpendicular to the surface of contact ; and 

 the velocity E C being resolved into E F and F C, the part F C will continue un- 

 altered ; and if the balls are e x qual, the part E F will be destroyed, so that the ball 

 A will move after the stroke in the direction C G, excepting the effect of any accidental 

 disturbance which may be derived from the resistance of the surrounding bodies. If 

 we imagine a ball at C in contact with B, in the direction D B, we may aim a blow 

 at the centre of this ball, in order to drive the ball B to D ; and if B happen to be 

 situated any where in the semicircle D C G, the motion of A after the impulse will 

 be in the direction B G or G B, if there be no resistance. When the ball H is re- 

 flected by a fixed obstacle, as by the cushion of a billiard table, at I, its velocity K I 

 may be resolved into the parts K L, LI; the part K L continues, and may be repre- 

 sented by L M equal to K L, the part L I is converted into I L in a contrary direc- 

 tion, which when combined with L M makes IM, the angle LIM being equal to 

 L I K. We may find the proper direction for striking any ball by reflection if we 

 suppose a ball N in contact with the nearest point of the cushion, and making N O 

 equal to M N, aim at a ball supposed to be at O. In the same manner if we wish to 

 impel the ball P in the direction P Q by a stroke of the ball R after reflection at S, 

 we first place a ball at T behind P, and determine the direction R S by aiming at a 

 ball U, as if we wished to strike a ball at T with a direct impulse. But in the case 

 of a billiard ball, the rotation of the ball round its axis, which is not destroyed by 

 the collision, will cause the ball to move, on account of the friction of the table, in a 

 direction different from its first direction : thus the ball C will not go on to G, but 

 will strike the cushion between C and D ; and the ball H, after reflection at I, will 

 proceed in a direction a little nearer to N than I M ; so that the imaginary ball O 

 ought perhaps to be placed as far from the cushion itself as M, in order that the ball 

 may be struck after reflection. P. 62. 



Fig. 74. Mr. Smeaton's apparatus for experiments on rotatory motion. P. 64. 



Fig. 75. The moveable centre of suspension being fixed at the distance of 5 

 inches from one of the balls, and 7 from the other, the vibration is performed at the 

 same time as that of a pendulum 37 inches long. P. 65. 



Fig. 76. The three weights, supported on wheels, being drawn up the three in- 

 clined planes at the same time, by the action of three other equal weights, the 

 middle weight arrives first at the top, the length of its plane being twice the height. 

 P. 67. 





