Mathematical and Physical Papers. 233 



true harmonic motion, and the slowest hitherto observed by the au- 

 thor of this paper. It would require a pendulum many hundred 

 feet long to secure this rate of vibration. There is still another 

 oscillatory movement to be observed in our pendulum, and this is 

 a vertical oscillation, an up-and-down movement, due to the longi- 

 tudinal elasticity of the wire. This movement is much more 

 frequent than the former and has no influence on the Foucault 

 experiment. 



It will be seen from inspection of the graphs that the minor 

 axis of the elliptical oscillation is very small, not more than one- 

 tenth of an inch in a swing of four feet, and the air currents are 

 probably responsible for most of this. The time is so recent since 

 the installation of the apparatus that but few experiments have 

 as yet been made, but they encourage us to expect results as good 

 as any hitherto obtained by other observers. 



There is a thought, too, that this pendulum may record seismic 

 motions, which will certainly be of interest. 



The pendulum is where any visitor to the state-house can see it, 

 and there is a certain impressiveness in the sweep of the heavy 

 weight to and fro so steadily. When starting with long vibrations, 

 and watched for some time, close observers will notice that the 

 period of oscillation is sensibly shorter as the arc becomes less. 

 The old Florentine, Galileo, was mistaken in thinking the swinging 

 chandelier performed its vibrations in equal times, whether through 

 long or short swings, but he was near enough right to instal the 

 pendulum as our most perfect measurer of time. Starting with an 

 arc of ten feet, this pendulum will continue to swing as much as 

 fourteen hours when it does no work in tracing the smoked glass. 

 After a few hours its path cuts across its first direction with an angle 

 that shows the time of a complete rotation at this latitude to be 

 more than forty hours. The cuts herewith given exhibit the devia- 

 tion at different intervals, but experiment has not been made suf- 

 ficiently as yet to secure accurate numerical results. These may 

 be given in a future paper. 



It was intended to exhibit the tracings of this pendulum by half- 

 tone engravings taken from the smoked-glass blue-prints, but they 

 will not do for making printing plates, and time has not been al- 

 lowed for securing them in other ways. For the finest results these 

 experiments must be made when the air is still, because the wind 

 gives a tremulous motion to the state-house roof which disturbs 

 the pendulum. 



