48 THE LINEAR COMPRESSIBILITY OF COPPER AND IRON, 



much the rod has been shortened by the application of a given amount of 

 increased pressure. 



To make sure that the apparatus had undergone no accidental change 

 during the trial, the pressure was relieved, the bolt C was afterwards with- 

 drawn until the platinum point again just touched the surface of the mer- 

 cury, and the initial operations were repeated, giving usually a very satis- 

 factory agreement with their first indication. 



In this manner the absolute linear compressibilities of iron and copper 

 were determined. 



To the observed linear contraction of the metal rod in this apparatus 

 three small corrections must be applied in order to obtain the true value. 

 These corrections are for first, the contraction of the platinum needle; 

 secondly, the error due to the millimeter thickness of glass in which the 

 metal rods rested for insulation ; and thirdly, the contraction under press- 

 ure of the globule of mercury. All three of these corrections are nega- 

 tive, diminishing the value for the compressibility. 



Of these corrections, the first and second may be most simply applied by 

 adding a correction to the actual length of the metal rod. As platinum is 

 about half as compressible as iron,* the platinum needle was equivalent 

 to about 5 mm. of iron ; and as glass is about six times as compressible as 

 iron, the millimeter of glass was equivalent to 6 mm. of iron. Thus the 

 iron rod, with the platinum above and the glass below, behaved as if it 

 were 2.68 meters long, instead of 2.67 meters. With copper the percent- 

 age correction is slightly less, but not enough to affect the significant 

 figures given. Because these corrections of only about 0.4 per cent in all 

 are beyond the limit of accuracy of the measurements, they might have 

 been neglected altogether. 



The third correction is more serious and less easy to apply. Its 

 magnitude may be computed as follows : The drop of mercury weighed 

 0.23 gram and therefore had a volume of 16.6 c. mm. As the diameter 

 of the cup in which it was contained was 3 mm., or its area 7.1 sq. mm., 

 the mercury must have been nearly 3 mm. deep, allowing for the curva- 

 ture of the meniscus. The globule of mercury must have changed 

 0.0000037 X 400 X 16.6 = 0.0246 c. mm. under pressure. This decrease 

 spread over a cup 7 sq. mm. in area would have caused a fall of 0.0035 mm. 

 But, on the other hand, the contraction of the cup holding the mercury 

 would have caused this liquid to rise 0.0003 mm. if the mercury itself had 

 not changed in volume. The difference between these values, 0.0032 mm., 

 may be taken safely as the probable fall of the mercury under pressure in 

 the iron cup, and 0.0031 mm. as the probable fall in the copper cup. It 

 was assumed that the shape of the meniscus did not change appreciably, 



*See Richards and Stull, this publication, pp. 61-62. 



