AS EXHIBITING THE ROTATION OP THE EARTH. 31 



These values show that the plane of pendulum revolution turns ahout an axis 

 parallel to the earth's with the relative angular velocity n; or, in other words, that 

 the plane preserves its parallelism to itself in space. 



If we had a succession of peniluhnns rigidly connected with each other, the dis- 

 turbing effect of gravity would be eliminated. Such a succession would be simply 

 a gyroscope, and the gyroscope, mounted in gimbals and set running in a meridian 

 plane, would exhibit the apparent rotation of its disk around an axis parallel to the 

 earth's axis equal and contrary to that cf the earth; wliich is simply saying that as 

 the earth revolves the plane of the disk maintains its parallelism to itself, and if we 

 suppose its axis directed at a star in the plane of the equator, it would follow that 

 star so long as the rotation of the disk is sustained.^ 



The pendulum experiment, in its ordinary form, exhibits not the whole rotation 

 of the earth, but only one component of it; the component which belongs to an 

 axis passing through the locality. It is perhaps quite as interesting and important, 

 as being the only experimental demonstration we can have of a principle difficult 

 of comprehension, but as fundamental to mechanics, since its enunciation by Euler, 

 as the corresponding one of the decomposition of linear velocities, viz., that of the 

 decomposition into distinct components, of rotary velocities. The plane of the pen- 

 dulum appears to turn relatively to the surface of the earth simply because the 

 earth turns just so much underneath it, the earth really revolving about the local 

 axis with a certain calculable component of velocity. The earth turns at the same 

 time with another component of velocity about another axis (the complementary one), 

 and the joint effect, or the resultant of the two components, is the rotation about 

 the polar axis. The second component, very great as we approach the equator, 

 where the first vanishes entirely, is not exhibited by the pendulum, and is only 

 detected by analysis as a slight disturbance. Convert the pendulum into tlie gyro- 

 scope, however, and this second component appears equally with the first. 



' OwinjT to the friction of the girabali?, there would be, practically, besides the motion above 

 described, a motion of tlie axis in the plane of the meridian, north or south, according to the direc- 

 tion of the disk rotation; this angular motion might be greater or less than the equatorial motion, 

 but would be, with a well-constructed apparatus, independent of it, at least for the brief time during 

 which a gyroscope experiment would last. 



