160 Mr Hicks, On some Irregularities in the Values [May 26, 



why the mean density calculated from ivory and glass balls is 

 higher than the mean. 



All these effects would vary with the temperature, but the cor- 

 rections due to those variations although in the proper direction are 

 so small that they produce no effect to the fourth place of decimals. 

 It is difficult to conceive that the temperature- effects shown by the 

 table are due to convection currents in the torsion box, for the 

 closed box is itself within a case, within which the temperature was 

 found to vary extremely slightly during a day's experiments. It 

 is natural to look to changes in the geometrical dispositions of the 

 parts due to changes of temperature, as a source of the effects. 

 The expansion of the wood work would be so small as scarcely to 

 produce any perceptible change. The only metallic expansions 

 that occur to me as likely to produce alterations, are (a) in the 

 length of the suspension wires, (/3) the brass scale from which the 

 deviations were read, (7) the brass rod on which the microscopes 

 were mounted to measure the distance of the centres of the masses 

 and balls, (S) and the error introduced in measuring this distance 

 due to taking the differences between the surfaces and allowing for 

 the radii, which would vary with the temperature. It may be well 

 to notice each of these in order. 



(a) The centres of the attracting masses are on a level with the 

 centres of the balls ; consequently if these last be raised or lowered 

 slightly by a contraction or extension of the suspension, the effect 

 would be vanishingly small. The alteration in the attraction of 

 the supports would also be a negligeable part of the whole. 



(ft) With a rise of temperature the scale expands ; conse- 

 quently the reading for the deviation of the torsion rod in the two 

 positions of the masses will be too small. We therefore suppose 

 that the gravitational unit of force is smaller than it is, and thus 

 make the mean density of the earth larger. For this case therefore 

 the deduced mean densities would increase with the temperature — 

 in the opposite direction to what is actually the case. The cor- 

 rection to be applied for a temperature f F. above the mean would 

 be - 5-67 x -0000104* = - -0000591 



(7) The distances between the masses and balls were measured 

 by microscopes fixed to a brass bar, at a distance of 5 inches from 

 one another, which was roughly about the distance of the surface 

 of the attracting mass from the centre of a ball. The difference 

 from 5 in. of the actual distance was then measured by means of a 

 small pearl scale in the microscope. Hence a correction must be 

 introduced for the expansion of the brass bar. The reading will 

 make the distance too small by hit where a is the coefficient of 

 linear expansion for brass, and t is the difference between the 

 temperature of observation, and the temperature at which the 

 distance of the microscopes is exactly 5 inches. 



