ANOMALOUS BEHAVIOUE OF DELICATE BALANCES, ETC. 



391 



From the above data two series of values for the RP. were calculated : Series I. 

 being derived from groups of three, and Series II. from groups of five, observations. 

 We here state, more precisely, how the different and successive values for the R.P., 

 given under (a) and (/3) in Table I., were deduced. 



After releasing the beam, two complete vibrations were allowed to take place 

 before commencing the observations. Some 30 to 40 readings of the extreme 

 positions of the pointer then followed, and the data were utilised thus : Observations 

 1, 2, and 3 were taken and the first value for the RP. given under (a) calculated ; 

 the second value was calculated from observations 3, 4, and 5 ; the third value from 

 observations 5, 6, and 7 ; and so on. Similarly, the values enumerated under (/?) 

 were deduced from the groups 2, 3, and 4 ; 4, 5, and 6 ; 6, 7, and 8, &c. ; the final 

 values for the R.Ps. being those obtained by taking the means of (i) and (&) ; 

 (<z 2 ) and (&) ; ( 3 ) and (&,) ; &c. 



The mean values given in Column 8 result from the application of the same method 

 to overlapping groups of five observations. Plotting the successive values of the 

 R.P. along the Y-axis, and the corresponding times along the X-axis, we obtain the 

 curves shown in Fig. I. 



109 



s 

 toe 

 s 



107 



s 



/OS 



s 



101 



s 



104 



s 



103 



S 



102 



Fi, 9 L 



I 



I. 



Complete l/ibracions - 



10 /2 



is is 



22 2+ so s& 30 32 j# j$ sa -to 



The more sinuous and dotted line curve is obtained by making use of the R.Ps. 

 calculated from groups of three observations of the pointer ; the other curve is a 

 representation of the values derived from calculations based upon groups of five. 



The type of curve here presented is quite unlike that which we should expect to 

 obtain. It will be observed that, although the general trend of the two curves is 

 identical, the first named supplies greater detail. Towards the end of the experiment. 

 however, the two almost coalesce, and, just before the conclusion of the observations, 

 the RP. becomes almost constant, and approaches an ideal value which is represented 

 by the curve OX. The portion ob was derived by extrapolating. 



