Section 10. Discussion of Errors and Corrections. 37 



the mean coefficient of cubical expansion between 100 and 300 to be 

 0.00004:50 ; and this value was adopted for the corrections. The difference 

 between his steel and that used in the bomb can hardly be great enough 

 to cause an appreciable difference in the coefficient of expansion, since his 

 values for two steels as different as Bessemer steel with 0.15 per cent com- 

 bined carbon, and cast steel with 0.-45 per cent, differ by only 6 per cent ; 

 and an error of even 6 per cent in the coefficient of expansion would pro- 

 duce a maximum error, even at 306, of only 0.05 per cent in the specific 

 volume. 



(2) The quartz-crystal cup expands upon heating, thus diminishing the 

 volume of the bomb occupied by the solution. The correction for this, 

 even at 306, amounts to only 0.03 per cent. 



(3) The bomb expands owing to the pressure within. At 306, where 

 this correction is greatest, the vapor pressure plus the air pressure may 

 be estimated at 100 atmospheres. Assuming that the modulus of elasticity 

 of the steel is 17,372 kgm. per sq. mm., which is the value found by Pisato* 

 at 300, the volume correction due to this cause is -j- 0.025 per cent. This 

 is opposite in sign and essentially equal to the preceding correction ; they 

 therefore eliminate each other. 



(4) The volume of the tube 7\ is only 0.07 c.cm. or 0.06 per cent of the 

 whole volume of the bomb. It is therefore so small that no irregularities 

 in the extent to which it is filled with solution could much affect the result. 



(5) The volume of the bomb depends somewhat on the extent to which 

 the large nut is tightened up and the gold packing-ring compressed. Four 

 of the gold rings which had been used were chosen at random, and the 

 mean thickness of each was calculated from measurements made at eight 

 equidistant points with a micrometer caliper. The average deviation from 

 the mean thickness of these rings was such as to affect the volume of the 

 bomb by only 0.02 per cent. So this source of error can be unhesitatingly 

 disregarded, especially as each final specific-volume value is the mean of 

 the values obtained from several independent experiments. 



(G) The bomb is never completely filled with liquid, the vapor space 

 amounting, on an average, to about 1 c.cm. or 0.8 per cent of the total 

 volume of the bomb (about 124 c.cm.). A certain fraction of the water 

 is therefore vaporized, and the specific volume appears too small by a 

 corresponding amount. The specific volume of the vapor is not yet known 

 above 200. By extrapolation, however, from the values up to 200, the 

 specific volume of the vapor at 218 is found to be seventy-five times that 

 of the liquid. From this it follows that at 218 the correction is only 

 T5T ~1~ Ts, or about 0.01 per cent. Such a calculation is not possible at 

 the higher temperatures, 281 and 306 ; but that no considerable error 



*Nuovo Cimento (3), 4, 152 (1878). 



