310 EEPOET— 1893. 



to produce a slight vertical swing of tlie miiTor attached to the end of the 

 pendulum. The position of equilibrium received no alteration -whatever. 

 After having placed the pendulum in the plane of the meridian, a 

 successful attempt was made to photograph its movements, the instru- 

 mental arrangement being very similar to that which is generally 

 employed in registering the variations of the magnetic elements. 



During the above observations, which only extended over a short 

 interval of time, a daily oscillation was the most important part of the 

 motions of the pendulum. I therefore employed the name of ' zero- 

 point ' for the mean position of the day, not expecting that at other 

 places the irregular movements of the zero-point would far exceed those 

 due to the daily period. The application of the word ' zero-point ' may thus 

 not appear very appropriate. I have, however, retained it during all the 

 further investigations in order to avoid confusion, and because the 

 character of the changes of the zero-point would not be better represented 

 if one were to speak of ' irregular ' or ' secular ' changes. 



In 1888 a grant from the Prussian Academy of Sciences allowed me 

 to undertake observations on a more extended scale. Two horizontal 

 pendulums, which have been in use up to the present time, were carefully 

 constructed by Messrs. Repsold, of Hamburg, whilst the necessary photo- 

 graphic apparatus was furnished by Mr. Wanschaff, of Berlin. In 1891 

 both instruments received small alterations, reference to which will be 

 made later on. 



Ohservations at Potsdam and Wilhehnshaven. — In November 1888 a 

 column was erected in a circular cellar situated below the east tower 

 of the Astrophysical Observatory at Potsdam. One of the pendulums 

 was placed in it with its plane in the meridian, and was at first observed 

 by the aid of a telescope from a distance of 4'7m. Different degrees of 

 sensitiveness were given to the instrument in oi'der to study the regularity 

 of the motions. It was found during these trials that the period of 

 oscillation of the pendulum is very dependent on the magnitude of the 

 amplitude, even when the latter is quite within the limits which in an 

 ordinary pendulum ensure the isochronism of the oscillations. Later experi- 

 ments at Strassburg, which Professor Becker was kind enough to make 

 for me by using a chronograph, showed that the formula 



T=To + C.«, 



in which C is a constant, represents the observed values of T in a 

 satisfactory way. The correction Ca is rather large when the period of 

 oscillation is great, and has to be taken account of if one wishes to 

 obtain an accurate value of Tq, which is the constant required for 

 reducing the observations. As it is impossible to make good observa- 

 tions of T when a is very small, a ought always to be observed at the 

 same time in order to be able to compute C and Tg. 



Further experiments were made to try the effect of weights deposited 

 in the neighbourhood of the column. Its foundation was about 90 cm. 

 below the floor of the cellar, and a ditch was left free round it. Notwith- 

 standing these precautions, a considerable tilting of the column of about 

 0""7 was caused, when a weight of 100 kilogrammes was moved from one 

 side of the ditch to the other. This tilting did not take place suddenly, 

 but required a considerable time, just as the soil did to recover its former 

 state after the pressure had been removed. 



When a person walked slowly round the space contained between the 



