1889.] 



On the Cavendish Experiment. 



257 



The tmit deflection is that which would be produced if each large 

 ball acted only on the small ball near it, and if the small balls 

 occupied the positions a"b". 



If the position which is chosen for each attracting mass is nearer 

 the plane of the beam than the transverse plane, that is, if the 

 azimuth of the large masses is less than 45°, the best length of the 

 beam will be more than half that which would bring the ends 

 opposite the attracting masses. 



Tt might be urged against this argument that a difficulty would 

 arise in finding a torsion fibre that would give to a very short beam 

 loaded with balls that it will safely carry a period as great as five or 

 ten minutes, and until quartz fibres existed there would have been a 

 difficulty in using a beam much less than a foot long, but it is now 

 possible to hang a thing only half an inch long and weighing from 

 20 to 30 grains by a fibre not more than a foot in length, so as to 

 have a period of five minutes. If the moment of inertia of the 

 heaviest beam of a certain length that a fibre will safely carry is so 

 small that the period is too rapid, then the defect can be remedied by 

 reducing the weight, for then a finer fibre can be used, and since the 

 torsion varies approximately as the square of the strength (not 

 exactly because fine fibres carry heavier weights in proportion), the 

 torsion will be reduced in a higher ratio, and so by making the 

 suspended parts light enough, any slowness that may be required may 

 be provided. 



Practically, it is not convenient to use fibres much less than one 

 ten-thousandth of an inch in diameter, and these have a torsion ten 

 thousand times less than that of ordinary spun glass. A fibre one five- 

 thousandth of an inch in diameter will carry a little over 30 grains. 



Since with such small apparatus as I am now using it is easy to 

 provide attracting masses which are very large in proportion to the 

 length of the beam, while with large apparatus comparatively small 

 masses must be made use of owing to the impossibility of' dealing 

 with balls of lead of great size, it is clear that much greater deflec- 

 tions can be produced with small than with large apparatus. For 

 instance, to get the same effect in the same time from an instrument 

 with a 6-foot beam that I get from one in which the beam is five- 

 eighths of an inch long, and the attracting balls are 2 inches in 

 diameter, it would be necessary to provide and deal with a pair of 

 balls each 25 feet in diameter and weighing 730 tons instead of about 

 If lb. apiece. There is the further advantage in small apparatus 

 that if for any reason the greatest possible effect is desired, attracting 

 balls of gold would not be entirely unattainable, while such small 

 masses as two piles of sovereigns could be used where qualitative 

 effects only were to be shown. Owing to its strongly magnetic 

 qualities, platinum is unsuited for experiments of this kind. 



u 2 



