( 445 ) 



^^jg- 2. 8. With respect to the manner of oscillating 



of the two suspended pendulums we shall 

 call it the antiparallel mode when the simul- 

 taneous greatest deviations are on different 

 sides as was the case in the observations of 

 HuYGENS, in the reverse case Ave shall call it 

 the parallel mode. 



It is easj to see then from (1 5) that the follow- 

 ing three possible combinations will always 

 appear, namely : for one of the three principal 

 oscillations the mode of oscillating of the pendu- 

 lums is the antiparallel one, for the two other 

 ones the parallel one, but in such a way 

 that for a definite greatest deviation of the 

 pendulums in a given sense the frame takes 

 for each of these two other principal oscilla- 

 tions an opposite extreme position ^). 



If thus for instance gj^'»' and ê^^"») have 

 equal signs as was certainly the case in the 

 mechanism used by Huygens (see fig. la) 

 and also in that of Ellicott, the antiparallel 

 mode of oscillation observed by Huygens 

 belongs to the intermediate principal one. 



rapid principal 



oscillation 



rapid pendulum l^ 



i C interm. principal 



oscillation 



slow pendulum l^ 



reduced system 



i 



slow principal 



oscillation 



9. P^or the application to the behaviour of two clocks connected 

 in the manner described we first consider l^ and 4 ^s very different 

 from each other, and that neither c^ nor c, is small. In that case 

 it is evident from the values of FQ^) and F{1^) differing greatly 

 from naught that neither of the principal lengths of pendulum nearly 

 corresponds to l^ or 4 ; however from (15) then ensues that the 

 oscillations of the frame are of the same order as those of the pen- 

 dulums at every possible mode of oscillating. 



Now it is of course not at all impossible that the principal oscillations 

 or certain combinations of them once set moving, might remain sustained 

 by the action of one or of both motive works under favourable 

 circumstances with sufficiently powerful works and when means have 



1) Dumas has : „dass, wenn .... die Auf hüngepunkte der Nebenpendel tiefer als 

 ,die Drehungsaxe des Hauptpendels liegen, alle Nebenpendel von kürzerer als der 

 ,zu erzielenden [principalen] Schwingungsdauer in gleichen Sinne mit dem Haupt- 

 , pendel Schwingen mussen, alle anderen im entgegengesetzen Sinne". Tliis too 

 follows immediately from the formulae (15) which, indeed, correspond essentially 

 to those of Dumas. 



