O. T. Sherman— A Pendulum Study. 177 



covered by the cross- wire of the telescope it bisected the knife 

 edge. The telescope was then directed to the mirror and 

 focused so that a division of the reflected scale was visible on 

 the cross-wire. The pendulum was then carefully set in 

 motion and allowed to come to rest. The position of the 

 reflected scale was first re-examined then the telescope re- 

 directed toward the thread. Although a hundred and twenty 

 observations were taken no change was detected. 



The only other explanation which has suggested itself is that 

 of small movements of the stand which are not synchronous 

 with the swing of the pendulum. In one set of observations 

 this resulted from the nature of the ground on which the stand 

 rested ; in another it varied with the varying tightness of the 

 joints from the dryness of the wood; in a third which has 

 lately been called to our attention it is apparently caused by 

 the vibration of the clock on the same wall. It has been 

 shown that the effect of the motion of the plane of suspension 

 due to the elasticity of the support increased the time of vibra- 

 tion by a constant. If, however, there are other causes for the 

 motion of this plane than the elasticity of the support, the vari- 

 ation of the time is represented by 



6f V 



here -— represents the variation of the velocity of the motion 

 the plane of suspension ; V, the velocity of the pendulum 

 ie to its instantaneous position. Of this differentia] ~ ==X 



±A 



bbe sa 



me period the integi 



•al is evidently a 



— ^ has a period 





of the 



i arc or a constant. 



If, however, 



i, or 



series 



of periods, which i 



are different fro 



m that of "ft, 



the 



value 



of the integral will 



depend on the phase with which 



% 



enters 



; and since in the cc 



turseof the observation this phase 





again 



occur with the comn 



aencement of the period of --J-, 



the 



functh 



:>n representing th< 



i disturbance o 



f time of oscillai 



tion 



should be one possessing 



maxima and mil 



lima disposed acc( 



>rd- 



ingto 



some law. Since the phase of -|£ 



at entrance reacts 



:on 



Am. Jour. Sci.— Third Series 



, Vol. XXIV, No. 1 



11.— September, 1882. 





