324 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



D; 



B 



]m 



T^ 



At 



C 



D 



D, 



The compressibility of the steel replacing the water also evidently 

 enters as a correction factor. This compressibility is relatively slight, 

 and it has been previously determined over a range of 10,000 kgm. 

 The value of the compressibility of the steel also changes with the 

 temperature, but this change has also been shown by direct experi- 

 ment to be slight, so slight that it can 

 be neglected. In the present work the 

 value was assumed to be constant, in- 

 dependent of temperature and pressure, 

 having the value 58 X 10"^ per kgm. 

 per sq. cm. 



There is also a correction to be 

 applied for the compressibility of the 

 kerosene, if the amount does not happen 

 to be the same in the two sets of ex- 

 periments, and it was seldom that the 

 amount was exactly the same. The 

 variation was very small, however, and 

 the correction is easy to apply if the 

 compressibility of the kerosene itself 

 is known. This was determined with 

 sufficient accuracy for the purpose by 

 an independent set of experiments, 

 exactly the same in principle as those 

 for determining the compressibility of water. The results of these in- 

 dependent experiments are given at the end of the paper. 



The following formulas were used in making the corrections, and 

 include all the corrections mentioned qualitatively above. Figure 1 

 shows the position of the piston at different times in the course of 

 the experiment. The left hand part of the diagram (denoted by the 

 suffix 1) is for the cylinder when it is filled with kerosene and bessemer 

 steel only, and the right hand part (denoted by the suffix 2) is for the 

 cylinder when it contains water, kerosene, and bessemer steel. A and 

 C are the positions of the piston at the arbitrary zero of pressure in 

 these two sets of experiments (this arbitrary zero was usually taken 

 in the neighborhood of 2000 kgm. and will be denoted by p), and B 

 and D indicate the position at some higher pressure, the same in 

 the two sets, which will be denoted by p'. We now write down 

 the expressions for the total volume of the cylinder beneath the 

 piston. 



Figure 1. Diagram showing 

 the position of the piston. To 

 go with the computations for 

 the corrections to be applied to 

 the compressibihty. 



