C. S. Peirce — Oscillation of l'r miniums. 255 



150 diameters, and is usually placed at a distance of about 

 fifteen feet. The observations are made by placing the wire of 

 this telescope successively in coincidence with the different 

 lines of the graduated arc, and accurately noting the moment 

 at which the point of the pendulum is just bisected by the 

 wire at the extremity of its swing. It would thus be quite 

 impossible to overlook a variation of the amplitude amounting 

 to one ten-thousandth of the radius, while that of the pendu- 

 lum was, say one-thirtieth of the radius. 



The motion of a pendulum upon a flexible support has two 

 harmonic constituents. One of these has nearly the natural 

 period of the pendulum, the other nearly the natural period 

 of the oscillation of the support. If the amplitude of the sec- 

 ond motion is sensible, an irregularity of the arc of oscillation, 

 often of a plainly periodic character, will necessarily result. 

 The ratio of the amplitude of the second harmonic motion to 

 that of the first depends upon the manner in which the pendu- 

 lum is started; and upon a very flexible stand it is easy to 

 stmt the pendulum in such a way as to produce a considerable 

 variation in the amplitude. But theory shows that if the 

 pendulum be started by pushing it to one side by a force ap- 

 plied at the center of oscillation and then letting it go, the 

 second harmonic constituent vanishes. Now, this is the man- 

 ner in which I always endeavor to start a pendulum. That, in 

 point of fact, the second harmonic constituent is insensible is 

 shown by the fact that it hardly shows itself even in the oscil- 

 lation of the support, where it is relatively many times larger 

 than in that of the pendulum. The equations showing this 

 are given in my paper appended to the report of the Stuttgart 

 meeting of the International Geodetic Association. 



Mr. Sherman deduces the consequences which would nsuli 

 from the motion of the support having a different period from 

 that of the pendulum. But for the considerable number of 

 supports that I have examined in this respect, the mean period 

 of the oscillation of support and pendulum have been the 

 same. This is proved by the fact that, however long the ex- 

 periment is continued, the oscillations of the one and of the 

 other appear to be synchronous. There may, it is true, be a 

 portion of the motion of the stand which is not synchronous 

 with the main part of the motion of the pendulum ; but this 

 circumstance will have no appreciable effect on the period of 

 the pendulum, if the latter is properly started. 



Of the periodic phenomena observed by Mr. Sherman, I can 

 propose no explanation, because I am unacquainted with the 

 details of his experiments. But similar phenomena might re- 

 sult from a faulty mode of starting a pendulum upon a very 

 flexible support. 



