416 Mr. H. Tomlinson on certain Sources of Error in 



namely, the rotation to and fro of the cylinders about their 

 axes, and that the rapid absorption of energy was owing to 

 the fact that the torsional vibration-period of the wire nearly 

 synchronized with the vibration-period of the cylinders about 

 their axes. I need hardly say that after this discovery I con- 

 sidered it necessary to re-try all my previous experiments with 

 improved arrangements. With more perfect apparatus, in 

 which the cylinders were clamped to the bar so as to be in- 

 capable of motion independently of the latter, I was glad to 

 find the main conclusions which I had previously drawn re- 

 specting internal friction confirmed. On one occasion, how- 

 ever, by what afterwards turned out to be the merest chance 

 in the world, the old phenomenon appeared with all its curious 

 concomitants, and beats were very plainly discernible between 

 two sets of vibrations which nearly synchronized. These two 

 sets of vibrations I set to work to disentangle in a manner 

 kindly suggested to me by Prof. G. G. Stokes, with whom I 

 had some correspondence on the subject. Suppose that in 

 one or more beat-intervals the slower vibration is dominant*, 

 and afterwards the quicker. If the amplitudes cross during 

 a beat-interval, that one is to be deemed dominant which is 

 dominant about the time of lull. Suppose there are m beat- 

 intervals in which the slower is dominant, followed by n in 

 which the quicker is dominant, and let N be the total number 

 of vibrations counted f . Then the number of vibrations of 

 the two component kinds will be : — 



For the slower, N — 2n, 

 For the quicker, N + 2m. 



In this way I managed without any difficulty to find that 

 one of the two vibration-periods was nearly a constant what- 

 ever the moment of inertia ; whilst the other, that due to the 

 torsional elasticity of the wire, increased as the square root of 

 the moment of inertia. At first I felt very strongly inclined 

 to believe that the former of the two vibration-periods per- 

 tained to some molecular state of the wire ; and I was espe- 

 cially deceived by the fact that always after rest the pheno- 

 menon became less marked, and, finally, almost vanished, 

 easily, however, to be reproduced in all its former intensity by 

 the slightest shock given to the wire, or by raising or lowering 

 the temperature slightly. The wire was of iron, and my pre- 

 vious experience of the effect of rest on the molecular dispo- 

 sition of this metal led me to draw the above-mentioned conclu- 

 sion. Had I not been thus deceived, I might more quickly 



* By dominant vibration is meant the vibration of greater amplitude, 

 f For accuracy, the counting should begin and end with a maximum. 



