TRANSMISSION OF INFORMATION 549 



be the same at a time t/k that it was at time t in the original system. 

 If the same change is made in the damping constant and frequency 

 of each one of the modes of free vibration, their resultant, or the wave 

 set up by any one symbol, will also be so changed that any particular 

 value occurs at time t/k instead of /. Suppose also that the interval 

 r between selections be changed to r/k. Then any two symbols 

 originally separated by a time /i will be separated by ti/k. The 

 value of the interfering wave at the time h/k when the disturbed 

 symbol occurs will be the same as it was at the corresponding time h 

 when it occurred in the original system. Hence the contribution of 

 this wave to the intersymbol interference is unchanged. Since this 

 relation holds for all of the interfering symbols, the total intersymbol 

 interference remains unchanged, and so the number of possible symbols 

 that may be distinguished is unaltered. The rate of making selections 

 is changed in the ratio k, and hence the maximum rate of communica- 

 tion is changed in the same ratio as the damping constants and natural 

 frequencies. 



Now let us consider what physical changes must be made in the 

 system to bring about the assumed changes in the damping constants 

 and natural frequencies of the various modes. Take the simple case 

 of an inductance, capacity and resistance connected in series. Here 

 we have the well-known relations 



LC \2L 



(23) 



If R remains fixed and L is changed to L/k, a becomes ka. If, in 

 addition, C is changed to C/k, co becomes koj. What we have done 

 is to leave the energy-dissipating element, R, unchanged and change 

 both the energy-storing elements, L and C, in the inverse ratio in 

 which the rate of communication is changed. For more complicated 

 systems the expressions for a and co are correspondingly complicated. 

 In every case, however, it will be found that if all of the dissipating 

 and storing elements are treated as in the simple case just considered 

 all of the damping constants and natural frequencies will be similarly 

 altered. Where mechanical systems are concerned we are to substitute 

 for electrical resistances their mechanical equivalents, and for induc- 

 tances and capacities, inertias and compliances. This generalization 

 that a proportionate change in all of the energy-storing elements of 

 the system with no accompanying change in the dissipating elements 



