246 Professor Edwin H. Barton [March 8, 



The questions which now naturally arise are {a) why this contrast ? 

 and ijb) can the gap be bridged ? The solution is simple. The 

 difference in appearance is only a matter of different ratios of periods 

 of the superposed viljrations. And this again is due to different 

 values of the coupJing, to borrow a term from electrical theory. We 

 have changed suddenly from a very loose to a very tight coupling. 

 AVe consequently passed at a bound from periods nearly equal (giving 

 a slow waxing and waning) to periods whose ratio exceeds 2 : 1 

 (involving the pause or twitch) ; for the theory shows that as the 

 coupling increases tlie ratio of the periods increases also. 



It is accordingly of interest to change the coupling gradually and 

 so bridge the gap between tbe two motions which seemed so unlike. 

 This was done by the cord and lath pendulum, in which the cord 

 pendulum is suspended from an adjustable stud on the lath pen- 

 dulum. AVhen the two suspensions are near together the value of 

 the coupling is almost equal to the fraction of the lath length at 

 which the cord is attached. When this fraction is unity, as in the 

 case of one pendulum hanging from the bob of the other, the 

 coupling has the value l/V^ or 58 per cent, nearly. (These simple 

 relations are for equal bobs and equal pendulum lengths.) 



III.— Electrical Vibrations, Forced axd Coupled. 



On passing along the second line of Table I., it was noted how 

 the various types of electrical vibrations may be obtained and the 

 striking analogy to them presented by the mechanical cases already 

 considered. 



Any electrical circuit containing a capacity and an inductance 

 may exhibit electrical vibrations. For the fundamental electrical 

 conditions are there present just as the mechanical ones w^ere in the 

 case of a simple pendulum. If the condenser is charged by a 

 suitable means, the quantity of electricity so displaced is urged to 

 flow l)ack again round the circuit by the electromotive force of the 

 charged condenser. If the resistance of the circuit is small enough 

 the electromagnetic inertia (measured by the inductance) ensures 

 that the current shall still flow after the condenser is discharged. 

 Thus its charge is reversed. So the vibrations continue till the 

 energy is dissipated by the resistance of the circuit. These are free 

 electrical vibrations. 



As an example of forced electrical viljrations we may think of a 

 circuit with capacity and small inductance (like that of a Fleming 

 cymometer), placed not too near to a circuit of similar frequency 

 but with much greater inductance. Then the cymometer will 

 res{)ond to the vil>rations of the other, i.e. it will execute forced 

 vibrations. These will not appreciably diminish the vibrations of 

 the main circuit. 



