f ' 



404 



Rev. C. S^. L0ia7i on the Pe»iiuliim Experiment 



-• 



all affected by the direction of thejjibrations in respect to the 

 points of the coghpass. •iv^ 



Messrs. Diifoit* and Wartmann, However, at Gtfeteya, found the 



rate to be less irt their experiment^|{y^heu the vibrations were in 

 the direction of the meridian tha^i .^fhen at right angles to it, as 

 may be seen froiifi the above tabli.'^^Hence Gen. Dufonr infers, 



that the formula A'=A sin. lae,^A = angulax motion of the 

 earthj and A' th^ motion around ffife vertical, 'orthat of the pen- 

 duhim plane,) il? ,not rigorously Applicable. ..M, Morren at Ren- 

 nes comes to a similar conclusion from his own experiments. 



But besides the*difficulty of conceiving any physical cause for 

 such a difference, the fact that other experimenters have not no- 

 ticed it, (although" their experiments appear to have been both 

 more extensive and conducted with at least equal care,) may lead 

 US to hesitate about adopting such a conclusion, especially when 

 the results of rigid mathematical investigations of the problem 

 reveal nothing of the kind, but give as an exact expression of the 

 the motion of the pendulum plane the simple formula just refer- 

 red to. The disturbing causes connected with such experiments 

 are too numerous, and too difficult to be avoided, to allow of any 

 such broad inference being drawn, except as the result of long 

 continued observations, made with reference to every variety of 

 circumstances. 



It has also been noticed by some observers, that the rate of 

 motion of the pendulum plane in a single trial, is not utn/ornij 

 but varies in the course of the experiment ; generally becoming 

 more rapid as the arc of vibration diminishes. In the experi- 

 ments at New Haven this acceleration of rate was noticed in a 

 majority of the experiments, though it w%s much more percepti- 

 ble in some cases than in others. 



Five experiments, in which the pend:|jutii was permitted to 

 vibrate till its plane had passed over 10^ ott the horizontal circle, 

 gave the times of passing over the first five and last five degrees 

 of the arc, as follows ; the pendulum being 71 feet in length, and 

 weighing 12 pounds. ^^ 



Time of 



first 50. 



Time of 

 •econd 50. 



Len^h of arc 



of oscillation 



at 00. 



1 



1 



m. B. 



X 



29 20 



2 



30 60 



3 



81 5 



4 



31 30 



6 



31 50 



Mean. 



30 55 



ni» 9. 



28 

 SO 



30 25 



31 30 



31 10 



30 13 





inches. 



40-5 

 40-6 



46 



44 



Lenf^h of arc 



of oBcillation 



at 50. 



inches. 



26 



25 



25-2 

 27-4 



Length of arc [ 

 of oscillation 

 at_lO^_ 



inches, 



18-5 



17'5 

 18-6 



i 



This varying rate of motion appeared to have no connection, 

 in the experiments at New Haven, with the ellipti^.motion.^ hich 

 the pendulum acquires ; for it was often most mei^ecl when the 





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