326 PROCEEDINGS OF THE AMERICAN ACADEMY. 



This enables us to solve the equations for the compressibility of the 

 water and the kerosene, giving, 



Ai'H,0 = {^0 (I>2 - -Di) (1 + ap') - SoMa (p - p') 



+ Avk (niik — m2k) + Avs ("Ms — '"•:«)} 



and for the kerosene, when the two runs are both made with kerosene, 

 as in determining the data for kerosene given at the end of the paper, 



Avk = {^0 (^2 - D,) (1 + ap') - SqAU {p - p') - Av, 



^2fc — ri%xk 



{m-is — wi,)} 



The considerations so far apply only to the measurement of com- 

 pressibility at constant temperature. The thermal dilatation is deter- 

 mined in the same way as the compressibility from the difference of 

 the thermal dilatation as given by two serts of experiments, one with 

 the water replaced by steel. The piston displacement is not the same 

 at corresponding pressures here, either, and a correction is to be 

 applied for the thermal dilatation of the part of the cylinder which is 

 exposed to pressure in the one experiment and not so exposed in the 

 other. But this portion of the cylinder to which the correction is 

 to be applied was seldom more than 1" in length, and the correction 

 for this amount of steel is negligible in comparison with the thermal 

 dilatation of the total quantity of water. There is also a correction 

 to be applied for the dilatation of the steel replacing the water, and 

 this correction is small but not negligible. It was assumed that the 

 dilatation of the steel remains independent of the pressure over the 

 pressure range used, and the value for ordinary mild* steels at atmos- 

 pheric pressure was employed. This value is 0.000039 for the cubic 

 expansion per degree Centigrade. 



The corrections to the measurements of the thermal dilatation are 

 not so serious or so important as those for the compressibility, since 

 the total effect is much smaller and most of the corrections become 

 negligible. The method of determining the thermal dilatation has 

 already been explained to be that of observing the change of pressure 

 brought about at constant volume by a known change of temperature. 

 From this the change of volume with temperature at constant pres- 

 sure can be immediately determined if the slope of the p-v curve at 



that point is known, for i -r- ) = — ( — ) ( ^ - ) • ' — - ) i^^ evi- 



\dTjp \dpJr\dTji \dpjr 



