Elastic Solids to Metrology. 537 



in grammes weight per sq. cm., we shall obtain fairly 

 representative results. 



The supposed change in^? is 13*6 x 76, or 1034, in grammes 

 wt. per sq. cm., and we get the following approximate 

 results : 



8v/v= -o>/p = 58 x 10- 8 in (i.), = 103 x 10" 8 in (ii.), 



= 517xl0- 8 in(iii.). 



As a second example, consider what would be the difference 

 in the volume of one of the international standard kilograms 

 of platinum iridium, if, instead of being supported on its base 

 in air, it were suspended from the top. The form is approxi- 

 mately a right circular cylinder of height equal to the 

 diameter, and the specific gravity is approximately 21*55 ; 

 thus the height must be approximately 3" 90 cm. The value 

 of E is given by Benoit* as probably about 19*7xl0 8 in 

 grammes wt. per sq. cm., and if we suppose ^ = 1/3 we have 

 & = E. The difference in question is thus according to (8) 

 and (9), neglecting the weight of the air displaced, 



or 



egiectmg tne weignt or tne air displaced, 

 &; = W(f+?)/3£=10 3 x3-9-H(59xI0 8 ), 

 Sv = 66 X 10 -8 c.c. approx., 

 3d = —31 x 10~ 8 annrox. 



Sp= —31 x 10~ 8 approx. 



If :the kilogram were in water the difference would be 

 about 5 per cent, less than the above. If the kilogram were 

 transferred from air at atmospheric pressure into a vacuum, 

 the increment in volume would amount to about 24 x 10~ 6 cc 



In the original work on the prototype kilograms by Marekf 

 volumes are recorded to 1 X 10~ 5 c.c, so that in absolute 

 strictness a standard pressure ought to be assigned at which 

 a kilogram has its normal volume. Apparently, however, the 

 last figure in Marek's results is treated as ornamental, the 

 probable error affecting the previous significant figure. In 

 Benoit's later work on the subject, while the observational 

 volumes of the kilos are sometimes recorded to 1 x 10~ 5 c.c, 

 the final statement of the accepted results gives two figures less. 

 We may thus conclude that for the highest degree of accuracy 

 aimed at up to now, the laying down of a standard atmospheric 

 pressure, or of a precise type of support, is unnecessary whether 

 the kilo be in air or at a moderate depth in a liquid. If, 

 however, a kilo were used at a great depth in a heavy liquid, 

 or under a high gaseous pressure, the compressibility would 



* Trav. et M6m. Bureau International des Poids et Mesures, tome vii. 

 u Rapport " by Benoit, p. 27. [Benoit's value is given in connexion with 

 the meter prototypes, which seem made of the same alloy as the kilo- 

 grams.] 



f Trav. et M6m. du Bureau International, tome iii. 



