( 450 ) 



Fig. 4. 

 Ap 



>C rapid principal 



oscillation 



rapid pendulum L 

 interm. princip. osc. 

 slow pendulum ^i 



reduced system 



^ slo 



w prmcip. osc. 



Thej correspond to the slow and the 

 rapid principal oscillation differing considera- 

 bly in general in length of penduhim from /' 

 and /j') and therefore by reason of (15) 

 giving rise to oscillations of the frame which 

 are of the same order of magnitude as those 

 of the pendulums. 



So unless special measures are taken with 

 respect to the decrease of the friction of the 

 frame, these oscillations will have to stop, 

 the more so as they are not sustained by 

 the action of the motive works. 



So the only oscillation which will be able 

 to continue for some time is the intermediate 

 principal one whose length of pendulum is lying 

 between /j and ^ ; entirel}^ in accordance with 

 the observations of Huygens ^) and also with 

 those of EiiLicoTT described in note (4) p. 438 

 when for the latter we overlook for a moment 

 the observed periodic transference of energy. 



C. Discussion of the case that l^ and 4 differ but very tittle and 

 that at the same time c^ and c, are small numbers. 



13. The remarkable thing in this case is that now the remaining 

 quadratic equation (19) is also satisfied by a root differing but little 

 from l^. So there are now two roots of the original cubic equation 

 situated in the vicinity of 4, one found just now and expressed by (18) 

 and the other which is likewise easily found by approximation and 

 represented by the expression 



L — 



I'— I, 



(20) 



This root is, at first approximation, independent of A = l^ — Z, ; 

 so when the lengths of the pendulums approach each other suffi- 

 ciently, it is, though small, yet many times larger than A. These 



1) See the graphic representation of Fig. 4. 



2) See however note (3) p. 452 ; from which is evident that the case which 

 really presented itself in Huygens' experiments is probably not the one discussed 

 here, but the more compUcated case C. 



