412 BR. Spice—Sympathetic Resonance of Tuning Forks. 
intensity of resonance of Ut‘ forks is undoubtedly greater than 
the intensity of Ut* forks at six feet. 
A pair of forks were cast in a kind of bell-metal, and tuned 
to Ut*. On Keenig’s boxes the resonance was quite obvious at 
twenty feet, and at forty feet the responding fork drove a cork 
ball 8™™ diameter a distance of 10™™! This result was greater 
than that obtained with the steel Ut* forks of Koenig. In view 
of these facts, it seemed to me that a different explanation was 
required to clear up the difficulty ; and, after a careful experi 
mental examination of the question, I offer the following 
hypothesis : 
The intensity of sympathetic resonance of forks on their cases 
increases with the angular deviation or motion of the prongs. 
The question of number of vibrations per second has its 
proper value, but this value is small compared with the element 
above stated. : 
I proceed to explain this hypothesis. Suppose that we wish 
to set a pendulum in motion, but are required to fulfill 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 alloweda 
lateral movement of the hand of one inch each way, making i 
all two inches. : 
ow the amount of motion or amplitude of a pendulum 1s 
estimated by the angle the cord or rod makes with the vertical ; 
dulum, then, by the principle of the summation of diel gee 
the motion of the entire pendulum will be gradually augmen 
up to a limit determined by well-known mechanical theorems. 
in less time and be greater. From which it follows that, retar 
ing the conditions above stated, if we operated on a pandot . 
ten inches long, we should set it in its maximum motion 1) oss 
time and with less expenditure of force than if we opera en 
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 w pie length and 
Again: ‘6 
period of a fork varies directly as the thickness, but pune 
as the square of the length; hence a small alteration of re a 
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