372 Mr. C. Vernon Boys [June 8, 



An examination of the mobile system of the beam and suspended 

 gold balls, of which I exhibit a greatly enlarged and working model, 

 at once shows that all the parts are capable of independent movement 

 to an apparently perplexing degree- This in the theory of the 

 instrument I have treated provisionally as a rigid system, moving all 

 as one piece, which it certainly does not seem to be. For instance, 

 the lead balls, by their attraction of the gold balls, pull them out of 

 the perpendicular, so that their distance from the axis is greater than 

 that given by measurement by the optical compass. The error 

 amounts, in the case of the lower ball, when the lead is at its nearest 

 points to 1/10,000,000 inch, and I have not taken any notice of it. 

 When the beam is oscillating through so great an angle as 100,000 

 units" the centrifugal force only makes the gold ball move out four 

 times as much, and I have taken no notice of that. Again, when the 

 mirror is under acceleration by the fibre, the gold balls, hanging 

 5 and 11 inches below, do not follow absolutely; they must lag 

 behind, and so affect the period. Now in this case the gold 

 balls are suspended in a manner which is dynamically equivalent 

 to their being at the end of a pendulum 5j miles long, the shortest 

 equivalent pendulum that has ever been employed in work of this 

 kind ; but short as it is, I have not thought it worth while to be 

 perturbed by an uncertainty of a fow inches. There is one point 

 which in some of the experiments only has amounted to a quantity 

 which I do not like to ignore. It is due to the torsional mobility of 

 the separate fibres, about which each gold ball hangs, allowing them 

 in their rotation to slightly lag behind the mirror. As I did not see 

 how to allow for it, I applied to Prof. Greenhill, who immediately 

 told me what to do, and who, with Prof. Minchin, spent a day or two 

 in the country, covering many sheets of paper with logarithms, in 

 finding and solving for me the resulting cubic equation. The 

 correction on this account is 1/7850 on the stiffness of the torsion 

 fibre. 



There are four remaining corrections depending on the fact that 

 besides the gravitating spheres there are the ball-holders and 

 supporting wires and fibres, oil of which produce small but definite 

 disturbances in the gravitation. These are all calculated and allowed 

 for. They are : — 



Disturbances due to brass holders of lead balls 1/7320 



copper „ gold „ 1/265,000 



Attraction of lead balls for quartz fibres +1/200,000 



„ gold „ phosphor-bronze wires —1/115,000 



Then in experiment 9 gold cylinders were employed. Mr. Edser, 

 of the Eoyal College of Science, calculated for me the correction 

 to be applied if they were treated as spheres; this amounted to 

 1/3300. 



I have already mentioned that experiment 8 was made under more 

 than usually quiet conditions. Such extreme quiet is desirable, that 



