156 



NA TURE 



{Dec. 19, 1889 



Bailie are the use of mercury for the attracting masses 

 which can be drawn from one pair of vessels to the other 

 by the observer without his coming near the apparatus, 

 the use of a metal case connected with the earth to prevent 

 electrical disturbances, and the electrical registration of 

 the movements of the index on the scale, which they 

 placed 560 centimetres from the mirror. 



The great difficulty that has been met with has been 

 the perpetual shifting of the position of rest, due partly 

 to the imperfect elasticity or fatigue of the torsion wires, 

 but chiefly, as Cavendish proved experimentally, to the 

 enormous effects of air-currents set up by temperature 

 differences in the box, which, with large apparatus, it is 

 impossible to prevent. In every case the power of ob- 

 serving was in excess of the constancy of the effect 

 actually produced. The observations of Cornu are the 

 only ones which are comparable in accuracy with other 

 physical measurements, and these, as far as the few 

 figures given enable one to judge, show a very remarkable 

 agreement between values obtained for the same quantity 

 from time to time. 



Soon after I had made quartz fibres, and found their 

 value for producing a very small and constant torsion, I 

 thought that it might be possible to apply them to the 

 Cavendish apparatus with advantage. Prof. Tyndall, in 

 a letter to a neighbour, expressed the conviction that it 

 would be possible to make a much smaller apparatus in 

 which the torsion should be produced by a quartz fibre. 

 The result of an examination of the theory of the instru- 

 ment shows that very small apparatus ought practically 

 to work, but that in many particulars there is an advantage 

 in departing from the arrangement which has always 

 been employed, conclusions which experiment has fully 

 confirmed. 



As I have already stated, the sensibility of the appa- 

 ratus is, if the period of oscillation is always the same, 

 independent of its linear dimensions. Thus, if there are 

 two instruments in which all the dimensions of one are n 

 times the corresponding dimensions of the other, the 

 moment of inertia of the beam and its appendages will be 

 as tv' : I, and, therefore, the torsion also must be as «^ : i. 

 The attracting masses, both fixed and movable, will be as 

 «''^:i,and their distance apart as n:\. Therefore, the 

 attraction will be as n'^ltf- or «*: i, and this is acting on 

 an arm n times as long in the large instrument as in the 

 small ; therefore the moment will be as iv' : i ; that is, in 

 the same proportion as the torsion, and so the angle of 

 deflection is unchanged. 



If, however, the length of the beam only is changed, 

 and the attracting masses are moved until they are 

 opposite to, and a fixed distance from, the ends of the 

 beam, then the moment of inertia will be altered in the 

 ratio tt^ : 1, while the corresponding moment will only 

 change in the ratio of ;z : i ; and thus there is an ad- 

 vantage in reducing the length of the beam until one of 

 two things happens : either it is difficult to find a suffi- 

 ciently fine torsion thread that will safely carry the beam 

 and produce the required period — and this, I believe, has 

 up to the present time prevented the use of a beam less 

 than \ metre in length — or else, when the length becomes 

 nearly equal to the diameter of the attracting balls, they 

 then act with such an increasing effect on the opposite 

 suspended balls, so as to tend to deflect the beam in the 

 opposite direction, that the balance of effect begins to 

 fall short of that which would be due to the reduced 

 length if the opposite ball did not interfere. Let this 

 shortening process be continued until the line joining the 

 centres of the masses M M makes an angle of 45° with the 

 line 7n m ; then, without further moving the masses M M, 

 a still greater degree of sensibility can be obtained, pro- 

 vided the period remains unaltered, by reducing the 

 length of the beam 7n m to half its amount, so that the 

 distance between the centres of M M is 2 \/2 times the 

 new length m m, at which point a maximum is reached. 



It might be urged against this argument that a diffi- 

 culty 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 diffi- 

 culty in using a beam much less than a foot long, but 

 it is now possible to hang one only half an inch long 

 and weighing from twenty to thirty 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 10,000 times less than that of 

 ordinary spun glass. A fibre one five-thousandth of an 

 inch in diameter will carry a litde over thirty 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 deaUng with balls of lead 

 of great size, it is clear that much greater deflections 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 pound 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. 



By far the greatest advantage that is met with in small 

 apparatus is the perfect uniformity of temperature which 

 is easily obtained, whereas, with apparatus of large size, 

 this alone makes really accurate work next to impossible. 

 The construction to which this inquiry has led me, and 

 which will be described later, is especially suitable for 

 maintaining a uniform temperature in that part of the 

 instrument in which the beam and mirror are suspended. 



With such small beams as I am now using it is much 

 more convenient to replace the long thin box generally 

 employed to protect the beam from disturbance by a 

 vertical tube of circular section, in which the beam with 

 its mirror can revolve freely. This has the further ad- 

 vantage that, if the beam is hung centrally, the attraction 

 of the tube produces no effect, and the troublesome and 

 approximate calculations which have been necessary to 

 find the effect of the box are no longer required. The 

 attracting weights, which must be outside the tube, must 

 be made to take alternately positions on the two sides of 

 the beam, so as to deflect it first in one direction and 

 then in the other. For this purpose they are most 

 conveniently fastened to the inside of a larger metal tube, 

 which can be made to revolve on an axis coincident with 

 the axis of the smaller tube. There are obviously two 

 planes, one containing and one at right angles to the 

 laeam, in which the centres of the attracting balls will lie 

 when they produce no deflection. At some intermediate 

 position the deflection will be a maximum. Now, it is 

 , a matter of some importance to choose this maximum 



