﻿the Duplex Harmonograpli. 

 Index of Diagrams 19 to 35. 



499 



No. 

 19 



Frequency 

 Ratio. 



Initial 

 Amplitudes. 



Class, 

 direct or 

 retrograde. 



Nature 



of 

 Roulette. 



Remarks. 



A&B 



C &D 



A&B 



C&D 



1 



3 



a 



a 



direct 



epitrochoid 





20 



1 



3 



a 



a 



retrograde 



hypotrochoid 





21 

 22 



1 



1 



3 

 3 



a 

 a, 



a/3 

 a/3 



direct 

 retrograde 



epicycloid 

 hypocycloid 



Well-known caustic 

 by reflexion. 

 Astroid. 



23 



1 



2 



a 



a 



direct 



epitrochoid 



Trisectrix. 



24 



1 



2 



a 



a 



retrograde 



hypotrochoid 





25 



1 



2 



a 



a/2 



direct 



epicycloid 



Carclioide. 



26 



1 



2 



a 



a/2 



retrograde 



hypocycloid 





27 

 and 



28 



}• 



i?+A 



a 



a 



retrograde 



hypotrochoid 



Path of electrou 

 vibrating in magnetic 

 field. 



29 

 30 



P 

 V 





a 



a 



a 



(D fixed) 



a 



not an 



epicyclic. 



direct 



not a 



roulette. 



epitrochoid 



31 



V 



P+A 



a(p+h)/p 



a 



retrograde. 



hypocycloid 





32 



33 



34 

 35 



2 

 2 

 2 



1 

 1 

 1 



A&B 



fixed 



a/3 



a/3 



a/3 

 (B fixed). 



a 



a 



a 



(D fixed) 



a 



not an 



epicyclic. 



direct 



not an 

 epicylic. 

 not an 

 epicyclic. 



not a 



roulette. 



family of 



epitrochoids 



not a 



roulette. 



not a 

 roulette. 



Involute of a circle. 



Limagou of Pascal... 

 cardioide... trisectrix. 



of the pen relatively to the table is thus compounded of two 

 uniform circular motions in the same direction. The trace 

 will be a direct epicyclic, the two motions beino- sometimes 

 spoken of as " concurrent/' If the pendulum C releases D 

 the trace is a retrograde epicyclic due to the combination 

 of "countercurrent" circular motions. The direct epicyclics 

 are all epi-trochoids or epi-cycloids, while the retrograde 

 epicyclics are hypo-trochoids or hypo-cycloids. 



Frequencies in simple ratio. 



In figure 19 all the amplitudes are equal. The frequency 

 of the pendulums C and D is three times that of pendulums 



2 K2 



