536 Dr. C. Chree : Applications of 



meaning as before, 



8v=-{(W-W)$ r + Spv\l3k, ... (9) 

 Sv/v=-8plp=-{g(p-p>)? + Sp}l3k (90 



The direct effect of the pressure exerted by the surrounding 

 medium is the same in the two cases. 



We can eliminate the influence of the support on the 

 volume in three ways, by : 



i. Having the support at the level of the C.Gr. ; 

 ii. Selecting for the surrounding medium a liquid of the 



same density as the solid ; 

 iii. Taking the arithmetic mean of results from cases of 

 suspension and of support in which f' = f. 



§ 4. The results (8) and (9) have a special interest in 

 connection with determinations of specific gravity. The 

 ordinary method is to compare the weight of a body in air, 

 after making allowance for the w r eight of air it displaces, 

 with the loss of the apparent weight when it is weighed in 

 water. 



Now (8) and (9) call attention to the fact that the volume 

 of the solid and so the weight of the medium it displaces 

 depend both on the pressure of the surrounding medium and 

 on the method of suspension. For instance, when a solid is 

 weighed in water its volume, and so the volume of the water 

 displaced, is diminished if it is sunk more deeply in the 

 water, or if the atmospheric pressure on the surface of the 

 water is increased. Again if, as is usual, the body rests on 

 its base when weighed in the air, but is suspended by a wire 

 when weighed in water, there is a change in its volume 

 irrespective of any change in the pressure exerted by the 

 medium. 



We see from (8) and (9) that the influence of change of 

 pressure on a given volume is independent of its shape, 

 whereas the difference between the results in the suspended 

 and supported positions increases as the vertical dimension. 

 Ceteris paribus, the influence of pressure on total volume 

 varies as the third power of the linear dimensions, whereas 

 the influence of the mode of support varies as the fourth 

 power. The latter influence thus tends to become relatively 

 unimportant when the linear dimensions are very small. 



As numerical examples, consider the effect of transfer 

 from ordinary atmospheric pressure to a vacuum on the 

 volume of (i.) steel, (ii.) brass, (iii.) lead. The elasticity of 

 these materials has a pretty wide range, but if we assign to k 

 the respective values* (i.) 18 x 10 8 , (ii.) 10 X 10 8 , (iii.) 2 x 10 8 , 



* Cf. the tables in Lord Kelvin's article on Elasticity in the Enc. Brit., 



