138 Dr. Watson on the Determination of the 



produced by an erroneous value obtained for the period of the 

 cradle, which error can easily be made negligible, corresponds 

 to a mean error of "018 per cent, in the ratio of the moments 

 of inertia. 



To test the question as to whether the vibrations were 

 strictly isochronous, that is whether the period was independent 

 of the amplitude, a series of measurements were made with 

 different initial amplitudes, and the results are shown in the 

 following table : — 



Amplitude. 



Period. 



At commencement. At end. 



O / O i 



14 24 7 29 

 7 52 4 15 

 4 55 2 25 

 2 44 1 20 



3-6616 

 3-6613 

 3-6611 

 3-6611 



It would thus appear that with an initial amplitude less 

 than 5° the period is not, within the limits of the accuracy 

 of the observations, affected by the variation in the amplitude. 

 This point was also brought out because in many of the observa- 

 tions of period starting with an initial amplitude of between 

 4° and 5° one set of period observations were made, and then, 

 without altering the amplitude of the vibrations, another set 

 was made. The values obtained for the periods were, how- 

 ever, as often larger with the smaller amplitude as smaller. 

 As a further precaution the initial amplitude was in all cases 

 taken as about the same. 



When obtaining the expression for — - — — 2 above it has been 



assumed that the torsional rigidity of the suspension fibre is 

 the same whether the cradle is empty or loaded with one 

 of the bars. To test whether this assumption is allowable, a 

 set of measurements were made in which the period of the 

 cradle alone was measured. Then its period when loaded 

 with each of two bars separately, and finally when loaded 

 with the two bars*. The results obtained in the case of two 

 fibres are shown in the following table : — 



* The cradle used differed slightly from that shown in fig. 1, in that a 

 second pair of "V's were provided to allow of two bars being suspended 

 simultaneously. 



