TORSIONAL OSCILLATIONS OF WIEES. 



427 



Fig. 2 shows the result of taking n=l'02, 6 = 98, and choosing a for each experi- 

 ment, so as to make the points taken from observation in each experiment lie, 

 as far as possible, on a single curve. Ordinates {y) represent range of oscillation, 

 and abscissae represent number of oscillations (x) plus a. The diagram shows that 

 an improvement might be made by taking n larger, the product nb being still kept 

 equal to 100. The result is given in fig. 3, the value of n being T03, while that of 

 b is 97. It appears from that figure that an increase of b would introduce further 

 improvement. The result of making n=l'03 and 6=100 is shown in fig. 4. The 

 closeness with which the points lie on the curve is quite sufficient to justify the adoption 

 of the general equation 



y 1 ™ (x + a)= 100 



to represent the results of the whole series of experiments. As a rule, the points 

 which correspond to the first readings taken after the oscillations were started in 

 each experiment are those which lie furthest off the curve. If the first readings 

 were as accurate as the others we should have 



where y is the first reading. It is desirable to determine whether or not a slight 

 modification of this expression for a will apply when the actually observed values 

 of y are used. The data below show that this is the case. The first row gives the 

 observed values of y . The second gives the values of a, which were employed in 

 order to make the points agree well with the curve shown in fig. 4. The third row 

 gives the values of a, calculated by the above expression ; the fourth gives the values 

 of the differences between the observed and the calculated values of a ; and the fifth 

 gives the values of a, if we assume 1 "4 to be the true value of that difference, and 

 calculate a from the expression 



a= 1-4 + 100 y - lvs - 



The initial reading, 8'05, taken on the date 22.7.96, totally disagrees with the second, 

 third, and subsequent readings, and seems to have been a mistake. A value 7' 5 is 

 much more in accordance with the others. 



. 7-5 



16-5 



20-3 



26-2 



29 



30 



31-5 



32-5 



35-1 



45-2 



14-2 



7 



6 



5 



4-5 



4-4 



4 



4 



4 



3*8 



12-6 



5-6 



4-5 



3-7 



3-1 



3-0 



2-86 



2-77 



2-56 



2-36 



1-6 



1-4 



1-5 



1-3 



1-4 



1-4 



1-1 



1-2 



1-4 



1-4 



14-0 



7 



5-9 



5-1 



4-5 



4-4 



4-3 



4-2 



4-0 



3-8 



