158 New Experiments on the Mean Density of the Earth. 



with a probable error of 0*0312. 



The smaller result obtained with the bismuth sphere can 

 decide nothing in the present uncertainty ; the result with the 

 much more strongly magnetic iron sphere is, on the contrary, 

 divergent enough to render it probable that a disturbing influ- 

 ence was exercised here ; it may be conjectured that the mag- 

 netism of the iron sphere acted repulsively upon the diamagnetic 

 mass of lead ; hence, diminished the deflection of the arm due to 

 gravitation, and gave too great a value. 



It is at all events evident from this, that, in the principal 

 experiments, where the sphere made use of was much more 

 feebly diamagnetic than the sphere of bismuth, no sensible action 

 of the kind spoken of could have been exerted. 



Cavendish himself found, and the experiments of Baily and 

 myself completely corroborate his observation, that it is not prac- 

 ticable to determine the time of oscillation of the torsion-balance, 

 once for all, and then simply to ascertain the deflection. caused 

 by the approximated mass, inasmuch as on account of the change- 

 ableness of the force of torsion of the suspending wire spoken of 

 above, correct results can only be obtained when the time of 

 oscillation and the deflection are determined simultaneously. 

 This is also the reason why experiments made by me at the sug- 

 gestion of Professor Forbes, and which consisted in deducing the 

 mean density of the earth from the observed times of vibration, 

 first, when the attraction of the mass was permitted, as hereto- 

 fore, to act at right angles to the direction of the arm, and 

 secondly, parallel to this direction, led to no useful result. In 

 the present arrangement of my apparatus, this might be readily 

 accomplished by placing two masses of lead diametrically oppo- 

 site to each other ; these, however, being so situate, that in one 

 instance the line joining their centres should be normal to the 

 direction of the arm, and afterwards parallel to this direction. 

 In this way the arm of the torsion-balance would not be at all 

 deflected ; but its time of oscillation would in the former case 

 be increased, and in the latter diminished, and from the ratio 

 of both it would be easy to deduce the result sought for. With 



