THE BLACK BOX 6/8 



through a spring -S to a heavy wheel M, which is rigidly connected 

 to the output shaft O. O's degree of rotation is shown on the dial 

 V, which is its output. The wheel dips into a trough with liquid F, 

 which applies a frictional force to the wheel, proportional to the 

 wheel's velocity. If now, starting from given conditions, the input 

 u is taken through some sequence of values, so will the output v 

 pass through some determinate sequence of values, the particular 

 sequence depending on v's initial value, on v's rate of change at 

 that moment, and on the sequence used for the input at u. 



Fig. 6/8/1 



The lower system is electrical. Its input is a potentiometer, or 

 other device, 7, that emits the voltage shown on the scale .y. In 

 series are an inductance L, a resistance R, and a capacitance C. 

 P is a current meter (such as is used in domestic supplies) recording 

 the sum of the currents that have passed through it. The sum is 

 shown on the scale y, which is its output. 



If now the values of L, R and C are adjusted to match the stiffness 

 of the spring, inertia of the wheel, and friction at F (though not 

 respectively), then the two systems can show a remarkable functional 

 identity. Let them both start from rest. Apply any input-sequence 

 of values at u, however long and arbitrary, and get an output- 

 sequence at V, of equal length: if the same sequence of values is 

 given at x, the output at y will be identical, along its whole length, 

 with that at v. Try another input sequence to u and record what 

 appears at v : the same input given to x will result in an output at 



95 



