178 0. T. Sherman— A Pendulum Study. 



the time of swing, the limits of the integral will be irregular 

 with respect to the portion of -^- included, and we should 

 have a series of minor irregularities, themselves following some 

 law, superposed on the curve produced by the varying phase at 

 entrance. Again, since the value and relative period of -5-5- and 

 Y do not necessarily decrease in the same ratio with the con- 

 tinuance of the observation, the amplitude and period of the 

 disturbance should continually increase or decrease. All of 

 these are distinct from the traces of other errors of the pendu- 

 lum. This curve is a record of the variation of the time of 

 vibration produced by the motion of the plane of suspension, 

 and therefore a definition of the steadiness of the stand. We 

 deal, however, with means rather than the time of single vibra- 

 tion, and obtain a different defining curve for different limits 

 of the second integral. But from whatever number of vibra- 

 tions our means are derived we obtain the above peculiarities. 



