7S2 



PLATE V. 



Fig. 65. Bjr means of the moveable inclined plane 

 AB, of which the height AC is one third of the hori- 

 zontal length BC, the weight D, acting horizontally, 

 sustains a triple weight E, acting iu a vertical direc- 

 tion. P. n. 



Fig. 66. A B being one fourth of B C, the rope 

 A B must exert a force of tension equal to one fourth 

 of the weight C, in orderto support it, supposing the 

 »urfacesj 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 with- 

 out any other force, whatever might be its magnitude" 

 P. T2. 



Fig. 67. AB being half of BC, or one fourth of 

 C D, the force extending the rope C D each way is 

 equal to the weight E. P. 72. 



Fig. 68. The thin wedge AB, of which the height 

 is one fifth of the length, being rolled round the cy- 

 linder 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. 72. 



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

 it. P. 72. 



Fig. 70. Tlie endless screw A B acts on the teeth 

 of the wheel CO. P. 72. 



Fig. 71. The listance of the threads of the inte- 

 rior screw is four fifths of that of the exterior or per- 

 forated screw, and this distance is one thirtieth of the 

 circumference. Hence the weight A is capable of 

 sustaining a %veight B 150 times as great as itsell". 

 P. 73. 



Fig. 72. The apparatus for experiments on collision. 

 Those balls which are not employed may be left be- 

 hind the graduated arc, as at A and B; some of tlie 

 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 he sup- 

 ported. P. 76. 



Fi;;. 73. If the ball A strike the ball B iu the 

 oblique direction A C, the ball B will be impelled iu 

 the direction C D perpendicular to the surface of con- 

 tact; and the velocity EC being resolved into EF 

 and FC, t!io part FC will continue unaltered; and if 

 the bulls are equal, the part EF will be destroyed, so 

 that the ball A will move after the stroke in the direc- 

 tion C G, excepting the effect of any accidental dis- 



4 



turbance which may be derived from the resistance ot 

 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 toD ; 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 reflected 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 partKLcontinues,and may be represented by 

 L M equal to K L, the part L I is converted into I L iu 

 a contrary direction, which when combined with LM 

 makes I M, the angle LI M being equal to LI K. We 

 may find the proper direction for striking any ball by 

 reflection if we suppose a ball N in contact with the near- 

 est point of the eushion, and making NO equal toMN, 

 aim at a ball supposed to be at O. In the same man- 

 ner if we wish to impel the ball P in the direction P Q 

 by a stroke of the ball 11 after reflection at S, we first 

 place a ball at T behind P, and determine the direc- 

 tion RS 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 direc- 

 tion difterent from its first direction: thus the ball C 

 will not go on to G, but will strike the cushion be- 

 tween C and D ; and the ball H, after reflection at I, 

 will proceed in a direction a little nearer to N than 

 IM; 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. 82. 



Fig. 74. Mr. Stneaton's apparatusfor experiments on 

 rotatory motion. P. 84. 



Fig. 75. The moveable centre of suspension being 

 fixed at the distance of 5 inches from one of the balls, 

 and 7 from the otlier, the vibration is performed at the 

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

 85. 



Fig. 76. The three weights, supported on wheels, 

 being drawn up the three inclined 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. 88. 



