572 



NATURE 



[Sept. 26, 1878 



greatest velocity. Passing this point, it goes slower and 

 slower till it again comes momentarily to rest, and then 

 begins its backward motion, and repeats again the same 

 changes in velocity. 



It is now necessary that the student should gain clear 

 ideas of the nature of this pendulous motion. It is the 

 cause of sound. It exists throughout all the air in which 

 a sound may be perceived, and, by the changes in the 

 number, extent of swing, and combinations of these pen- 

 dular motions, all the changes of pitch, of intensity, and 

 of quality of sound are produced. Therefore the know- 

 ledge which we now desire to give the reader lies at the 

 very foundation of a correct understanding of the subject 

 of this book. 



An experiment is the key to this knowledge. It is the 

 experiment with 



The Conical Pendubivt 



An ordinary pendulum changes its speed during its 

 swings right and left exactly as a ball appears to change 

 its speed when this ball revolves with a uniform speed in 

 a circle, and we look at it along a line of sight which is in 

 the plane of the circle. 



Experiment d^~'L^\. one take the ball and wire to the 

 farther end of the room, and by a slight circular motion 

 of the end of the wire he must cause the ball to revolve 

 in a circle. Soon the ball gets into a uniform speed 

 around the circle, and then it forms what is called a 

 conical pendulum ; a kind of pendulum sometimes used 

 in clocks. Now stoop down till your eye is on a level 

 with the ball. This you will know by the ball appearing 



etzrf to 



Fig. 2. 



to move from side to side in a straight line. Study this 

 motion carefully. It reproduces exactly the motion of an 

 ordinary pendulum of the same length as that of the 

 conical pendulum. From this it follows that the greatest 

 speed reached during the swing of an ordinary pendulum 

 just equals the uniform speed of the conical pendulum. 

 That the apparent motion you are observing is really that 

 of an ordinary pendulum you will soon prove for yourself 

 to your entire satisfaction ; and here let me say that one 

 principle or fundamental fact seen in an experiment and 

 patiently reflected on is worth a chapter of verbal descrip- 

 tions of the same experiment. 



Suppose that the ball goes round the circle of Fig. 2 

 in two seconds ; then, as the circumference is divided into 

 sixteen equal parts, the ball moves from i to 2, or from 2 to 

 3, or from 3 to 4, and so on in one-eighth of a second. But 

 to the observer who looks at this motion in the direction 

 of the plane of the paper the ball appears to go from i to 

 2, from 2 to 3, from 3 to 4, &c., on a line A B, while it 

 really goes from i to 2, from 2 to 3, from 3 to 4, &c., in 

 the circle. The ball when at i is passing directly across 

 the line of sight, and, therefore, appears with its greatest 

 velocity ; but when it is in the circle at 5 it is going away 

 from the observer, and when at 13 it is coming toward him, 

 and, therefore, although the ball is really moving with its 

 regular speed when at 5 and 13, yet it appears when at 

 these points momentarily at rest. From a comparison of 

 the similarly numbered positions of the ball in the circle 



and on the line A B, it is evident that the ball appears to 

 go from A to B and from B back to A in the time it takes 

 to go from 13 round the whole circle to 13 again. That 

 is the ball appears to vibrate from A to B in the time of 

 one second, in which time it really has gone just half 

 round the circle. A comparison of the unequal lengths 

 13 to 12, 12 to II, II to 10, See, on the line A B, over 

 which the ball goes in equal times, gives the student a 

 clear idea of the varying velocity of a swinging pendulum. 

 Fig. 3 represents an upright frame of wood standing 

 on a platform, and supporting a weight that hangs by a 

 cord. A A is a flat board about 2 feet (61 centimetres) 

 long and 14 inches (35-5 centimetres) wide. BB are 

 two uprights so high that the distance from the under 

 side of the cross-beam c to the platform A A is exactly 

 41^^ inches (i metre and 45 millimetres). The cross- 

 beam C is 18 inches (457 centimetres) long. At D is a 

 wooden post standing upright on the platform. Get a 

 lead disk, or bob, 3^^ inches (8 centimetres) in diameter, 

 and I inch (16 millimetres) thick. In the centre of this 

 is a hole i inch (25 millimetres) in diameter. This disk may 

 easily be cast in sand from a wooden pattern. At the 

 tinner's we may have made a little tin cone ij\ inch (30 



millimetres) wide at top, and 2 J inches (57 millimetres) 

 deep, and drawn to a fine point. Carefully file off the 

 point till a hole is made in the tip of the cone of about 

 Yff inch in diameter. Place the tin cone in the hole in the 

 lead disk, and keep it in place by stuffing wax around it. 

 A glass funnel, as shown in the figure, may be used 

 instead of the tin cone. With an awl drill three small 

 holes through the upper edge of the bob at equal distances 

 from each other. To mount the pendulum, we need 

 about 9 feet (271*5 centimetres) of fine strong cord, like 

 trout-line. Take three more pieces of this cord, each 10 

 inches (25 "4 centimetres) long, and draw one through, 

 each of the holes in the lead-bob and knot it there, and 

 then draw them together and knot them evenly together 

 above the bob, as shown in the figure. On the cross-bar, 

 at the top of the frame, is a wooden peg shaped like the 

 keys used in a violin. This is inserted in a hole in the 

 bar— at F in the figure. Having done this, fasten one end 

 of the piece of trout-line to the three cords of the bob, 

 and pass the other end upward through the hole marked 

 E ; then pass it through the hole in the key F ; turn the 

 key round several times ; then pass the cord through the 



