178 ANNUAL RECORD OF SCIENCE AND INDUSTRY. 



its bulb, iu which he placed the various bodies to be experi- 

 mented upon. His observations gave him the result that 

 the attraction of the earth was the same for all the bodies 

 upon which he experimented ; and his determination of 

 the length of the simple seconds pendulum at Konigsberg 

 is one of the most correct we possess. He, however, found 

 that when his cylinder was filled with water, the length of 

 the seconds pendulum as computed for that substance was 

 too great. The origin of this deviation Bessel attributed to 

 the fact that the inclosed fluid was by the swinging of the 

 pendulum set into vibrations of its own, whereby its mo- 

 ments of inertia in reference to the axis of vibration of the 

 pendulum was different from what it would have been in 

 the case of a uniform solid body. He accordingly found 

 that the experiments made with long pendulums filled with 

 water showed no such anomaly as in the case of shorter 

 pendulums. Professor O. E. Meyer, well known for his in- 

 vestigations into the friction of ^ases and fluids, having bust- 

 gested a somewhat different explanation, his student, Lubeck, 

 has made this matter the subject of an inaugural disserta- 

 tion, in which he considers the movement of the fluid con- 

 tained within a pendulum, whose bulb is, for simplicity's 

 sake, a hollow sphere instead of a hollow cylinder, Lubeck 

 shows that the fluid contained in the hollow sphere is not 

 set in motion by its rectilinear movement, but only by its 

 oscillations about the diameter at right angles to the plane 

 of the pendulum's vibration. This oscillation takes place 

 with velocities which are constant for each spherical surface 

 concentric with the hollow sphere, and any initial oscillatory 

 motion is, in a certain time, destroyed by the inner friction, 

 provided that it is originally of the same order as the veloc- 

 ity of the pendulum itself. After this time had elapsed, the 

 motion of the pendulum is quite periodical. The extent of 

 the arc through which the pendulum swings diminishes in a 

 geometrical ratio when the time increases in an arithmetical 

 ratio. The duration of the vibration of the pendulum is 

 greater than if the same pendulum contained within itself 

 a perfect fluid, instead of one having internal friction. The 

 duration of the vibrations is smaller than if the fluid should 

 be replaced by a perfectly solid body. When the length 

 of the pendulum becomes very great the inner friction of the 



