1884.] of the Mean Density of the Earth. 159 



temperature that matter attracted itself more strongly than if we 

 made experiments at a low temperature ; consequently the mass of 

 the earth would not require to be so large in the first case as in 

 the second, to produce the same force on a gramme at its surface, 

 or its mean density would be less. 



In searching for some possible explanation of this temperature 

 effect, I have been led to notice a point in the theory of the experi- 

 ments which the then Astronomer Royal, Sir G. Airy, had not taken 

 notice of. The correction for this is more important than some 

 others which have been taken account of, introducing an alteration 

 in the third place of decimals, while the calculations are carried to 

 the fourth. In calculating the attraction of the masses, he has 

 neglected to consider that of the air displaced by the masses 

 attracting. The effect of this is to decrease the apparent attract- 

 ing masses by the masses of the air displaced. The correction to 

 be applied is easily determined. Let p be the density of the air, 

 o- of the large masses (lead in all the experiments), a of the 

 balls on the torsion rod, A the mean density of the earth as given 

 in the tables, and A x the corrected value of A. Then for this term 

 we may neglect roughly the effect of the support of the lead 

 masses, and the torsion rods. In this case 



at zero temperature, p = "00129, a = 11*4, whence 



•00129\ 



A, - A = - (-000113 + '9™®"j x 5-67, 



= - -00064 + 



(•00064 4.2*5) 



From this, the corrections to be applied in the case of the 

 different balls are found to be 



Pt, - -0010, Pb, --0013, Zn, - '0017, Brass, - '0015, 

 Glass, - -0031, Ivory, - -0045. 



In addition to this another correction ought to be applied, due 

 to the inertia of the air in which the balls move. For the balls 

 alone this would be determined, if there were no boundaries, by 

 supposing their masses increased by half that of the air displaced. 

 The effect of this would also be to make the true densities less 

 than those given by -0036/o-', on the supposition that the effect on 

 the rod itself would be much smaller in comparison. The effect of 

 the friction of the air would be eliminated by the method of ob- 

 serving the time of vibration. These corrections tend to explain 



