Intelligence and Miscellaneous Articles. 425 



rate of deviation exceeds the computed rate. This effect seems 

 paradoxical, and has led many to doubt the soundness of the theory, 

 as it seems to exceed the cause to which it is ascribed, or to exhibit 

 a motion in an opposite direction to that of the impulse. A little 

 attention to the circumstances will however remove this difficulty, 

 and show that the contradiction to theory is only apparent. 



If a pendulum is swung in a tub of water, drawn to the circum- 

 ference and let go with a considerable lateral impulse from west to 

 east, the resistance of the dense fluid causes it at each successive 

 vibration to fall visibly short of the height or distance from the centre 

 attained by it at the previous one, and the line of apsides sensibly 

 recedes, i. e. moves from east to west, and this retrogression con- 

 tinues until the whole fluid has acquired a rotatory motion). 



Now the resistance of the air must produce an effect similar in 

 kind, though not equal in degree, on a body moving in it, and this 

 retrograde motion of the apsides of the orbit arising from the gra- 

 dual loss of momentum, explains the excess of the actual deviation 

 over that expected from computation. The error arising from this 

 source will obviously be less the slower the loss of momentum, that 

 is, ccBteris paribus, the smaller the arc of vibration. 



A small arc is recommended by another consideration independent 

 of the resistance of the air or of friction, viz. that with a small arc 

 the motion of the line of apsides is slower, and the path of the pen-^ 

 dulum approaches nearer to a fixed orbit. I do not know whether 

 the motion of a body in the circumstances of Foucault's pendulum, 

 i. e. of a body performing a gyration approaching to a simple oscil- 

 lation, has been investigated ; and the investigation might prove diffi- 

 cult, as the path does not lie in one plane. But that the motion of 

 the line of apsides will be slower the smaller the arc, will appear from 

 considering generally that the periodic time of such a body must lie 

 between the time of two oscillations of the simple j)endulum, and the 

 time of one revolution of the conical pendulum moving at the same 

 height or distance from the centre from which the simple pendulum 

 is let go, and must therefore be always less than the time of two 

 oscillations of the simple pendulum. But the body will require the 

 full time of two simple oscillations to visit the opposite circumference 

 and return to its greatest height on the same side from which it set 

 dut, and will therefore have completed a revolution in its orbit be- 

 fore this height on the same side is attained, that is, the apsis of the 

 curve will be in advance of the point of starting, but the less so the 

 less the difference between the time of a gyration and that of two 

 simple oscillations, or ceteris paribus, the smaller the arc. 



To obviate as far as possible errors arising from the retrograde 

 motion of the apsides produced by the loss of momentum, and from 

 the direct motion produced by lateral impulse, a pendulum was em- 

 ployed, not of a spherical form, but of the shape of the pendulum of 

 a clock, and hung with its sharp edge horizontal. The height was 

 about 25 feet, the wire simply passing through a hole in a board, and 

 the weight 201bs. of lead. The arc of vibration was about four 

 inches on each side of the centre. For a period of 12 hours, v»^itbout 



