718 Dr. B. van der Pol on Oscillation Hysteresis in a 



impossible at all, LH the impossible part for Mode II. On 

 closing the primary circuit only stable oscillations are 

 obtained, while the metastable states can only be realize! 

 when the system is first in a stable state and thereupon 

 slowly (compared with the damping coefficients) (or adia- 

 batically) brought to the metastable state. 



Some doubt, however, still exists whether it is exactly the 

 point of resonance which separates the regions where on 

 closing the primary circuit either a 2 or b 2 is finally 

 attained, as some dissymmetry still exists in the formula? 

 (E n #E T ). 



But a value for o> 2 2 very close to a*! 2 may easily be 

 obtained experimentally for which it is a mere matter of 

 chance whether a or b will finally be obtained. A simple 

 way of demonstrating this fact is by putting a big leaky 

 condenser in series with the grid of the triode circuit. It is 

 well known that with this arrangement the oscillations are 

 periodically quenched in an automatic way, so that regular 

 trains of vibrations are obtained. The group frequency may 

 e.g. be made of the order of one second. When next the 

 secondary circuit is coupled lo the primary we can, with a 

 heterodyne arrangement, produce an audible combination 

 tone corresponding to either the one or the other of the two 

 frequencies eoj and ' o> n . In general, each time only one of 

 these two combination tones is obtained, but with co 2 close to 

 or equal to ©^ the combination tone heard every second 

 jumps erratically between the two tones corresponding to 

 <Wj and w n respectively, and it is a mere matter of chance 

 which one of the two occurs. 



Finally, (9 a) yields for a) 1 = <B 2 



a 2== 3^ 0*1 -"««)> 

 4 I 



V= ^.( a i— a 2), 



4 / 



and thus shows that, as far as our approximations go, the 

 two amplitude carves intersect at the point of resonance. 

 But, moreover, these amplitudes at the resonance point are 

 independent of the coupling coefficient. Fig. 8, which gives 

 a set of observations of the mean square secondary current 

 (in a circuit like that of fig 1) as a function of co 2 2 for dif- 

 ferent coupling coefficients (increasing with the numbers 

 0, 1, 2, 3, 4, 5), is a confirmation of this theoretical result. 

 For very loose coupling (Carve 0) an ordinary resonance 

 curve is obtained, but for closer coupling (1, 2, 3, 4, 5) the 

 figure clearly shows that the intersection of the two branches 



