[satterly] new VIBRATION' EXPERIMENT 89 



case of rod), and we see that the period now depends onl\- on the 

 difference between A and B and not on their absokite \alues. 



The same formulae can be used for tubes having the same / and b 

 as long as b is small in comparison with /. 



Deductions 



(i) For balancing cylinders and rods of the same length {A—B)T~ 

 is a constant. 



{£) For balancing cylinders and rods having the same B and resting 

 on the same fixed cylinder the period is proportional to the length. 



Error Produced by Neglectixg the Radius Term ijn the 

 Numerator of the Formula for the Period 



For the cvlindcr 



V g{a-b) 



= 27r / 'i9 ( 1 + -^ ) approximately. 



_, / A 2/^ / 



1/ g{a-h) 



So that if è > — / the error will not exceed one per cent. 

 27 



Experiment 



The experiment has been tried with cylinders of glass, brass and 

 steel and with brass rods. Two brass saddles (see Figure) about 

 4 cms. high with a V-notch about 1>^ cms. wide were made and 

 screwed to the table about 3 to 4 inches apart to receive the fixed 

 cylinder. 



The balancing cylinders were then placed in position, set in 

 gentle vibration and timed with a stopwatch. Usually five or ten 

 vibrations were timed and the observations were repeated several 

 times to get a good mean. Individual readings are apt to vary 

 considerably due to roughness at the points of contact. This was 

 very noticeable with the brass cylinders vibrating on a brass cylinder. 

 The steel cylinders were found to be troublesome to keep on the 

 balance, perhaps because they arc so smooth. 



