408 Rev. C. S. Lyman on the Pendulum Experiment 

 values of these quantities at the beginning and end of the exper- 



X 1 486000x24x0-2 ^^o^^o no on/ on// ?r 



inient,) then, m^——— ^^=0o-3443 = 0^ 20' 39''-5 per 



'^ ' (852)2 X 9-333 



hour- 



In this manner were computed the corrections for ellipticity 



given in the last coUimn but one of the table on page 405. It 

 will be seen from this table that the motion of the apses of the ^ 



ellipse as given by the forniulaj accounts for but a small part of 

 the difference between the observed rate of motion of the pen- 

 dulum plane and that which it would have were there no elHptic 

 motion. It must be remembered, however, that the formula does 

 not take into account the resistance of the air, and other fruitful 

 sources of disturbance. The agreement of the formula with the 

 differences in the rates of motion observed by Mr. Bunt is some- 

 what closer* 



The motion of the apses of the extremely narrow ellipse that 

 has been spoken of as arising from the earth's rotation, must 

 tendslightly to diminish the rate of motion of the pendulum plane, 

 since it takes place in the same direction as the motion of the 

 earth. This effect, however, will be entirely insensible,, since 



3 



J 



pendulum 

 it amounts to only a little more than S^'^of arc per hour, 



6. Conjiedion of the motion of the pendulum plane with the 

 earth^s rotation. — Many persons, even of education, find it diffi- 

 cult to understand how a vibrating pendulum, whose line of sus- 

 pension must constantly be directed to new points in space as the 

 earth revolves, can exhibit any thing like permanency in the po- 

 sition of its line of vibration with respect to the rotating motion 

 of the earth. It is true that the path of the pendulum ball, con- 

 sidered as in absolute space, is exceedingly complicated, being 

 compounded of its own oscillating movement, the motion of the 

 earth on its axis, and of the earth itself around the sun. But it 

 is not at all necessary to attend to this complication of motions 

 in the problem before us. 



In the first place let it be observed, that the direction of the 

 plane of vibration of a free pendulum is entirely independent of 

 any motion, whether of rotation or of translation, that the point 

 of suspension may have. Hold in the fingers a pendulum made 

 of a simple ball and string, and cause it to vibrate ; then twirling 

 the string between the fingers will only cause the ball to rotate 

 on its axis, without afiecting at all the direction of the vibrations ; 

 and walking forward, whether in a straight line or in a circle, will 

 in like manner, only shift the position of the entire pendulum, 

 which will continue to vibrate towards the same point of the 

 compass as at first. 



Again let it be noticed, that the direction of the force of grav- 

 ity being constant, that is, towards the center of the earth, the 



f. 



* 



