( 453 ) 



Savart on the contrary lias effected with the aid of liis X'^'^^Pö^^ 

 spring at whose ends ahnost equal pendulums were attached both 

 principal oscillations ^). 



But besides these two principal oscillations which deviate in their 

 periods of oscillation, and moreover by the circumstance that the pendu- 

 lums will move in a parallel mode for one and in an antiparallel 

 mode for another, there is still a third manner of motion which 

 must be able to continue indefinitely. 



16. To prove this let us again start from an arbitrary compound 

 oscillation w = A''wt' -|- ^A^i + ^S-^a ; then unless the friction in the 

 frame be extremely slight the oscillation K'si' w^ill soon disappear. 

 When however in the I'emaining motion K^ is much smaller than K^, 

 it is clear that as the intermediate principal oscillation is then the chief 

 one for the motion of the two pendulums, the motive works 

 of both clocks will regulate themselves according to it, so that they 

 will not be able to contribute to the sustenance of the principal 

 oscillation K^:^,^ which will thus likewise have to die away, so that 

 finally only a pure oscillation Ki^i will be left, for which both 

 clocks will follow the rate of the intermediate principal oscillation. 



If on the contrary after the disappearance of the slow principal 

 oscillation K^ is much smaller than K^, it will have to be the inter- 

 mediate principal oscillation, which dies away, whilst the rate of the 

 clocks will finally regulate itself entirely according to the rapid oue. 



But in the intermediate case, when the proportion of K^ to K, lies 

 within certain limits, also a manner of motion will be able to 

 appear under favourable circumstances where both principal oscillations 

 are sustained for indefinite time, whilst each of them will govern 

 the behaviour of one of the two clocks; for from the equations (15) 

 it is easy to deduce that in general the proportion between the 

 amplitudes x^ and se, is different for both principal oscillations *). 

 Then the values of K^ and /Cj and so also their proportion will in the 

 long run be entirely governed by the power of the motive works, 



1) I.e. note (4) page 439. Savart had however I' <li=^U; therefore with him 

 it is the slow principal oscillation which plays the part given here in the supposition 

 V> ly> I2 to the rapid one. 



2) By substitution of the value (18) for A we find for the intermediate principal 

 oscillation x^ : xo = Ci— 2 ^^C^) : Co— 2 ^o("0; whilst the substitution of (20) furnishes 

 for the rapid principal oscillation 



Ki : y-2 = 



^ + I'-L 



— 1 (w) 



?1 



I'-L 





so for very small values of a we have for this one xi : xo = |i('") : ^o(»'y. 



