KNOWLEDGE. 



January, 1911. 



they are frequently found wanting either in their of this kind, let us consider the curve shown in 



working or in their power of elucidating the problems Figure 4. Placing a centimetre scale along its 



in which they are emplo^•ed. A recent adaptation wa\'e crests, we can read off the distances of these 



of the old tuning-fork method of measuring time has crests from the starting point of the curve to the 



Figure 4. Waw Curve showing acceleration. 



revolutionized schools of dynamics. The tuning- 

 fork method will he best understood from a glance 

 at Figure 1, which shows an arrangement for allow- 

 ing a plate of glass to fall so as alwa\-s to be in 

 contact with a st\le attached to one prong of a 

 tuning-fork vibrating with known fre(]uenc^'. A 

 wavv-curve is traced on the glass by the vibrating 

 point, and the space fallen in a gi\'en time 

 can be determined by measuring the length of that 

 portion of the wavy curve which contains a number 

 of waves corresponding to the given time. Another 



Figure 5. Two trolleys for verifying the laws of momentum and impact. 



apparatus for measuring the \'elocitv of the rim of 

 a flywheel bv means of a tuning-fork is shown in 

 Figure 2. Now a tuning-fork is not ver\' eas\' to 

 manipulate, and it goes rather too fast for beginners. 

 Here it is that a great simplification has been 

 made b\- Mr. W. C. Fletcher, of the Board of 

 Education.* A strip of steel clamped at one end 

 carries a paint brush at the other end. A long trolle\' 

 carrying a strip of paper moves underneath this 

 paint brush in the direction of the steel rod's length. 

 Suppose the steel to vibrate ten times a second, then 

 the paint brush will trace a waw line on the paper, 

 and ten waves will re- 

 present the distance 

 travelled in one second. 

 The lengthsof the waves 

 give the velocities, and 

 the changes in the wave 

 lengths give the acceler- 

 ations. Figure 3 gives 

 an example of the way 

 in which Fletcher's 

 trolley may beeiTi- 

 ploved for measuring 

 the acceleration when 

 the trolley is allowed to 

 run down an incline. 

 One of the curve trac- 

 ings made by the paint brush is shown resting 

 by the side of the plane. As for the wav in 

 whicli tlic^ accelenition i:, determined from a curst' 



nearest half millimetre, thus 0"1. 0"35. 0"S. r45. 

 2-25. 3-2, 4-35, 5-65, Z"!, 87, 10-5, 12-4. 14-5, Ibvo. 

 From this, bv subtraction, we obtain the successive 

 wave-lengths,' viz.: (YId. (V45, 0-65, O'S, 0-95, MS, 

 l-j. 1-45" 1-6, 1-8, 1-9. 2-1, 2-25. It is obvious from 

 this that the wave length has been increasing fairly 

 uniformlv. the successive increments in wave-length 

 being again obtained bs- subtraction. Thus thev are 

 0-2, '0-2. 0-15. 0-15. 0-2. ()-15. 0-15. 0-15. 0-2," O'l, 

 0-2, 0-15. The average of all these is 0-167. 

 Now, since the wave-lengths correspond to periods 



of one-fifth second, it is 

 plain that the average 

 increase in the space 

 travelled in each one- 

 fifth second is increas- 

 ing at the rate of 0T67 

 centimetre in every one- 

 fifth second. Hence in 

 each second the in- 

 crease in the velocity is 

 5X0'167 centimetre 

 per one-fifth second, or 5x5xO"167 centimetres per 

 second. The acceleration is therefore 4' 17 centi- 

 metres per second per second. 



As an example of the way in which the ajiparatus 

 ma\' be employed we ma\' take the verification of 

 the law " .Acceleration is proportional to the 

 accelerating force." The \-ariable force is obtained 

 b\" var\-ing the slope of the plane. To avoid 

 ha\"ing to consider the force of friction, the 

 trolle\" is first connected b}' a string passing over a 

 pulle\', shown in the figure, to a scale pan of known 

 mass, and weights are added just enough to prevent 



FiGLKI. I 



.\n inertia bar ■ set ,.;n motion by a trolley. 



thejrolley from accelerating when it is given a start 

 down the plane. When the waves made by the 

 paint brush are of equal length the total force down 



'■'See School World, .May, 1904. 



