Figure by means of the Pendulum. 457 



general intervals should be chosen which are not longer than 

 are necessary to secure the desired accuracy, and the swing 

 should be repeated in order to eliminate accidental errors. 



In the chronographic method, an error in the determination 

 of the interval between the first and last observation is simply 

 divided by the number of oscillations in the interval, and 

 therefore affects the result much more than by the coincidence 

 method. 



There have been many ways devised for noting these coinci- 

 dences. I shall first call attention to a few of the older 

 methods which leave nothing to be desired as to accuracy, but 

 which have been superseded by an elegant arrangement de- 

 vised by Professor Menclenhall and which, while giving all the 

 accuracy needed makes the observation both simple and easy. 

 First we had a piece of card-board fastened to the clock pen- 

 dulum. This card-board had on its surface a number of spots 

 which were seen to disappear at each coincidence of phase in 

 the motion. The time of disappearance and reappearance were 

 noted and the mean taken for the true coincidence. For in- 

 creased accuracy a number of spots were observed, and for 

 convenience in taking the time the spots were arranged in the 

 form of a curve, resembling a hyperbolic spiral, which would 

 give about equal times between successive disappearances for 

 all amplitudes of oscillation. This method was modified in the 

 case of the Peirce pendulums by placing a scale on the clock 

 pendulum and a small needle point on the gravity one. This 

 last procedure is in direct violation of the whole theory of 

 differential gravity measures, namely, that the pendulum must 

 undergo no change from one station to another. However, as 

 the mass added is exceedingly small, and besides is placed very 

 near the center of oscillation, where theoretically it would 

 have no influence whatever on the time of vibration, the 

 method is considered admissible. 



Both the preceding ways are applicable only to two moving 

 pendulums and suppose them to be of equal length. The 

 methods depend on sight alone. Coincidences have also been 

 observed by the eye and ear method, by comparing the beat 

 of an ordinary sounder used in telegraphing, with the transit 

 of a pendulum across the vertical thread of a telescope. This 

 avoids carrying a clock from station to station, a break circuit 

 chronometer furnishing the beat every second. The method 

 has not been very extensively employed, as it requires consid- 

 erable practice on the part of the observer. 



We now come to the last way, and which is believed to be 

 in many respects the best : and here we have to clo, not with 

 two pendulums, beating approximate seconds, but with a single 

 pendulum beating half seconds, whose coincidence must be 



