a 2 a , 9 , da -^ - 



■^ + n*a + ->p-,-=E cos kt, 



o26 Oft a Simple Resonance Experiment. 



representation of Tait, making use of the properties of the 

 logarithmic spiral of Descartes, 



If we now apply the alternating field 7i = Hcos^, the 

 equation becomes 



d s u „ da 



which is satisfied by a solution of the form 



a = F sin (Jd+ </>), called a forced vibration. 



Its superposition upon the free damped vibration of the 

 system gives the general integral, and the classical study of 

 the case leads to the conclusion that resonance occurs, the 

 power of the external vibrating force being maximum at 

 that moment when the frequency constant k is equal to the 

 value of ki, i. e. the value of the frequency constant of 

 the free vibration when no friction is present. 



If we refer to figs. 2 and 3 we now see the reason why 

 the resonance curves shift to the right when the frequency 

 of the alternating current increases; for when /the frequency 

 of the current flowing through becomes larger, we must 

 increase also f\ and consequently I in order to obtain 

 resonance. 



The curves for the high values of the frequency are flatter 

 than those for the lower frequencies, and curve No. 3 shows 

 even two maximum values, the first corresponding to the 

 oscillations in which one of the poles of the needle points 

 towards the N pole of the solenoid, and the second those in 

 which the other pole of the needle points towards the same 

 pole of the solenoid. 



5. The value of the current I giving the resonance 

 phenomena can be checked very accurately. 



For that purpose we notice that our experimental arrange- 

 ment is a synchronous monophase motor with variable 

 reluctance and reduced to its theoretical simplicity. We 

 suppose the current I shut off. The theory of that kind of 

 alternate motors was given by Blondel, and I applied 

 BlondePs theory to explain in a more adequate manner 

 than is usually done the process of starting the ordinary 

 synchronous motor *. The peculiar qualities of that kind of 

 motors are well known ; the very simple experimental arrange- 

 ment we have before us gives us an opportunity of verifying 

 some of them in a very easy way. First we observe that 

 the rotor (the needle) being at rest, there is no starting 



* Revue Electrique, Paris, 1912. 



