4 



Hev. C. S. Lyman on the Pendulum Experiment. 



415 



The experiment of M. Bravais, with a conical pendulum, 

 (L'lnstitiit, No. 920, Aug. 20, 1851,) is extremely interesting, 

 and appeare to have been entirely successful. He concluded 

 from the nature of the case, that a free pendulum revolving in a 

 circle would perform its gyrations in less time when its motion 



coincided with the rotary motion of the earth, than when it was 

 contrary to it. 



To settle this by experiment, he adopted two distinct methods 



that of direct observation, and that of coincidences. 



In the first method he observed the time occupied by the same 

 pendulum in making from 900 to 1200 gyrations to the left, and 

 then the duration of the same number of revolutions to the right, 

 the pendulum being 33 feet 5^ inches in length. 



The observed times of rotation were as follows. 



Right to left. 



6^-39887 

 6 -39925 

 6-39815 

 6 -39959 

 6-40106 

 6-40116 



Mean diff. 



The difference by theory is 



Left to riglil. 



6^-39825 

 6 -39849 

 6 -39751 

 6 -39863 



6 -40032 

 6 -40044 



Diff. 



•00064 

 •00076 

 •00064 

 •00096 

 •00074 

 -00072 



€0074 

 000710 



The second method was even more precise. Two pendulums, 

 one slightly longer than the other, were suspended near each 

 other, in the plane of the meridian. One was set revolving to 

 the right, the other to the left simultaneously, and the passage of 

 the threads across the meridian was observed through a tele- 



'i 



scope 



Let 



-(--J .- .*.vwiv^ v'^/fciW w-AX^ ^-^^-w .-*..w v.." ^ 



n and W denote the number of oscillations of the respective pea- 

 duhims between two successive coincideucs, n'^n-{-\^ n^ being 



the shorter. 



pend 



volving in opposite directions respectively, and the recurrence of 

 the coincidences under the new circumstances, determines the 

 numbers N and N^=N+ 1. Let A^the latitude, T the length of 

 a sidereal day, / the time of a conical oscillation of the long pen- 

 dulum, separated from the effect of the earth's rotation, and f the 

 same for the short pendulum. Then we shall have by theory, 



sin i 



1 



1 



One trial gave 

 Another 



T t+vln^-n' N+N' 



207-86; N=217-82 

 «'=208-S6,-N'=218-82 



206-31 J N=215-96 

 w'=207-31;N'=216-96. 



n 



n 



