﻿the Duplex HarmonograpTi. 495 



of the pendulums are under complete control. After having 

 roughly adjusted the frequencies by timing with a stop- 

 watch, the accurate timing is performed, under the guidance 

 of the simple harmonograms drawn by adjacent pairs. The 

 accuracy of the releases and the adjustment of the amplitudes 

 are similarly tested. The duplex harmonogram is then drawn 

 and can be identically repeated at pleasure. 



Friction. 



The beauty of many of the pictures drawn by previous 

 harmonographs is largely owing to the decrease of the am- 

 plitudes by friction and to slight defects in tuning. Our 

 pendulum-bobs were very heavy, and the friction of the 

 tracing-point was in some cases almost negligible. The 

 smallness of the friction is largely owing to the suspension 

 of the framed table, supporting the glass plate, from the 

 roof of the laboratory by a light thread. This device, though 

 theoretically inelegant, inasmuch as it introduces extra 

 restoring forces, has in practice no detrimental effect. 



DESCRIPTION OF THE DUPLEX HAEMONOGEAMS. 



The pictures were in the first place white line drawings 

 on the smoked background. The plates show the drawings 

 reversed, light for dark, prepared for the press by a photo- 

 graphic process in which the sensitive surface was facing 

 in the same direction as the original trace. Figures 7 

 to 18 are reproduced full size, the others being reduced as 

 seven to eight. 



Unequal Frequencies in Simple Batios ; 

 Friction Small. 



The frictional damping is not sufficient to separate the 

 successive paths of the tracing-point when the quantities 

 p, q, r, and s in equation (1) are as small whole numbers. 

 So that, unless friction is purposely introduced, the record 

 has to be stopped when the complete path has been traced 

 once. A few diagrams taken under the conditions that />. (/. 

 ?\ and s are as simple whole numbers and that friction is 

 small will be described first. 



