358 Mr. C. Vernon Boys [June 8, 



sensibility, the greater angle of deflection produced by the attractions 

 when the period of oscillation is the same. This is more especially 

 the case in my apparatus where the two sides are at different levels. 

 But the question arises whether this reduction of linear dimensions 

 may not introduce irregularity and want of stability to such an 

 extent as to more than counterbalance the advantages to which I 

 have already referred. In spite of every endeavour that may be made 

 to keep the air quiet, to exclude draughts, to keep all the apparatus 

 at one temperature in a vault of constant temperature, infinitesimal 

 differences must exist ; one side of the apparatus must be hotter than 

 the other, though no thermometer could be made which would detect 

 the difference. In consequence of this difference of temperature the 

 air circulates, and so creates a draught which blows upon the mirror 

 and the suspended balls. I had erroneously come to the conclusion 

 that in apparatus geometrically similar these disturbances would 

 probably be in the proportion of the seventh power of the linear 

 dimensions, so that greatly increased stability would be obtained by 

 reducing the dimensions. However, I have discussed this matter with 

 Prof. Poynting, who has shown me that in reality the disturbances 

 would be proportional to the fifth power of the linear dimensions if, 

 as should be the case, the circulation of the air were so extremely 

 slow that the motion would be steady, whereas it would gradually 

 rise from this to the eighth power as the term involving the square 

 of the velocity increased in magnitude and the motion became 

 irregular. So long, therefore, as the apparatus is small enough to 

 prevent terms involving the square of the velocity from being appre- 

 ciable, the stability is the same whatever the size, but as soon as 

 the apparatus exceeds this, then the disadvantage of size very rapidly 

 becomes evident. In addition to this, the time needed to bring the 

 apparatus to a steady state is far greater with large apparatus. After 

 making the geometrical measures I leave my apparatus, small as it 

 is, three days, if possible, before observing deflections and periods. 



The diagram, Fig. 1, is a vertical section through the apparatus. 

 B and C represent an accurately turned brass box with a lid L, 

 which can be made to turn round insensibly by the action of the 

 wheels W W. The lid carries two tubular pillars P P, from the tops 

 of which the balls MM hang by phosphor bronze wires, being 

 definitely held in place by geometrical clamps on the heads of the 

 pillars. The lid also carries two supporting pillars R R. In the 

 centre tube the " beam mirror " N hangs by means of a quartz fibre 

 from an adjustable torsion head surmounted by a bell jar, and from 

 the ends of the mirror the two gold balls m m hang by separate quartz 

 fibres. Four rings of india-rubber are placed on the base to prevent 

 destruction of the apparatus in case the balls should drop by any 

 accident. Now it is evident that if the lid is turned from the 

 position in which it is shown, that is, with all four balls in one 

 plane, in which position the attractions do not tend to twist the 

 central torsion fibre at all, then these attractions will produce a 



