284 Experiments on the Vibration of Pendulums. 



Sliding up the isochronal piece still further, till the length of 

 the effective part of the spring was reduced to "50 inch, the fol- 

 lowing were the results : 



The lighter weight, 21b. 2oz. employed on experimenting with 

 the weaker springs, was found insutficient to keep the pendulum 

 in vibration with No. 5 ; 21b. lOoz. was found adequate to the 

 purpose, and it was therefore employed. 



In experimenting with this spring, the arcs of vibration were 

 not noted, as I found that both it and No. 4 were too strong for 

 the weight of the bob I was using, and to which the experiments 

 indicate that No. 3 was excellently adapted. 



The arc of vibration with the spring. No. 3, (viz. 2° 15') using 

 a weight of 41b. loz., required 191b. weight to produce it when 

 the pendulum was suspended by the silken threads. 



It appears then, from the preceding experiments on suspending 

 springs differing in length and strength, that there is one which, 

 with a given maintaining power, produces a greater arc of vibra- 

 tion than others, and gives the same arc to vibration with a smaller 

 maintaining power ; and, further, that with this same spring the 

 vibrations may, in point of time, be all considered as isochronous, 

 whether the arcs are large or small. And with the aid of the 

 isochronal piece, a spring of the proper length and thickess may 

 easily be selected in a very few trials. 



It may be noticed too, that unless the pendulum is first isoch- 

 ronized by some such method as that which has been pointed 

 out, anamalies may be imputed to imperfect compensation, which 

 have their origin in a very different source. 



In fine, it may be stated in conclusion, that if the pendulums 

 of astronomical clocks were furnished with what I have called an 

 isochronal piece, any person possessing a few springs of different 

 degrees of strength^ may with very little difficulty determine 

 what spring is best adapted to the weight of the pendulum, and 

 also what part of the spring may be most advantageously em- 

 ployed in action ; and I shall not think that the attention which 



