258 



Prof. C. V. Boys. 



[June 20, 



By far the greatest advantage that is met with in small appa- 

 ratus 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 espe- 

 cially 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 con- 

 venient 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 advantage 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 beam, 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* position for the attracting masses, because, in showing 

 the experiment to an audience, the largest effect should be obtained 

 that the instrument is capable of producing ; while in exact measures 

 of the constant of gravitation this position has the further advantage 

 that the only measurement which there is any difficulty in making, 

 viz., the angle between the line joining the large masses and the line 

 joining the small, which may be called the azimuth of the instrument, 

 becomes of little consequence under these circumstances. In the 

 ordinary arrangement the slightest uncertainty in this angle will 

 produce a relatively large uncertainty in the result. I have already 

 stated that if an angle of 45° is chosen, the distance between the 

 centres of the large balls should be 2v^2 times the length of the beam, 

 and the converse of course is true. As it would not be possible at this 

 distance to employ attracting balls with a diameter much more than 

 one and a half times the length of the beam, and as balls much 

 larger than this are just as easily made and used, it will be well to 

 find out what will be the position for maximum deflection when the 

 centres of the attracting balls are any distance apart. 



In the case already considered the problem gives rise to equations 

 of too high an order to be readily solved, and so in the particular case 

 referred to the result was obtained by arithmetical means. If the 



