Intelligence and Miscellaneous Articles. 79 



I proceed to explain this hypothesis. Suppose that we wish to 

 set a pendulum, in motion, but are required to fulfil the two 

 following conditions : — first, we are obliged to hold the cord of 

 the pendulum (point of suspension) in our hand, and this hand is 

 also to be the motive power, to start and keep the pendulum in 

 motion ; second, we are only to be allowed a lateral movement of 

 the hand of one inch each way, making in all two inches. 



Now the amount of motion or amplitude of a pendulum is 

 estimated by the angle the cord or rod makes with the vertical ; 

 and clearly, if the point of suspension moves laterally, it thereby 

 creates an angle. If, further, the point of suspension has a re- 

 ciprocal motion in accord with the possible time of the pendulum, 

 then, by the principle of the summation of impulses, the motion of 

 the entire pendulum will be gradually augmented up to a limit 

 determined by well-known mechanical theorems. But if amplitude 

 is expressed by angular magnitude, then, if the initial angle be in- 

 creased, the total motion must be acquired in less time and be 

 greater. From which it follows that, retaining the conditions 

 above stated, if we operated on a pendulum ten inches long, we 

 should set it in its maximum motion in less time and with less ex- 

 penditure of force than if we operated on a pendulum fifty inches 

 long. Experience confirms this. 



A fork vibrates after the manner of a pendulum, and may be 

 looked upon as an inverted pendulum ; but whereas, the length of 

 a pendulum determines its vibrating period, the length and thickness 

 together determine the period of a fork. Again, the period of a 

 fork varies directly as the thickness, but inversely as the square of 

 the length ; hence a small alteration of length will make a large 

 difference in its period ; or, conversely, a large alteration of period 

 does not imply a large difference in length. 



From measurements made with an electro-chemical registering 

 apparatus, which I designed for this and similar investigations, I 

 find that when a fork of the usual dimensions (between Ut 3 and 

 Ut 4 ) is in vibration, its stem or handle alternately rises and falls 

 in accord with the period of the fork, through a distance of about 

 •y 1 ^ inch. When a fork on its case is influenced by a distant fork, 

 the case gives the stem this up-and-down motion, which is con- 

 veyed to the prongs, and sets them in vibration, after the manner 

 of the hand starting a pendulum, as specified above. 



This motion of -£$ inch may be looked upon as a constant, and 

 corresponds to the two-inch motion of the hand in the illustration. 

 If we decrease the length of the fork without altering the constant, 

 we thereby allow of a greater initial angle, the result of which we 

 have already noted ; it is the same as shortening the pendulum- 

 cord. This much understood, we are in a position to explain the 

 deportment of the bell-metal forks cited. The velocity of sound 

 in bell-metal is much less than in steel ; hence, retaining similar 

 thicknesses in both cases, an Ut 3 fork in bell-metal would be shorter 

 than an Ut 3 fork in steel, the ratio of the length of the steel to 

 that of the bell-metal ranging as 90 : 75. Therefore, though we 



