40 NEW METHOD FOR DETERMINING COMPRESSIBILITY 



occur at a much higher pressure than the true pressure corresponding 

 to isothermal compression. Since the substance itself is the measuring 

 medium, it was thought possible that this instant self-heating effect 

 might afford a means of avoiding the lag which any form of thermom- 

 eter must involve, and thus give a truer measure of the adiabatic rise 

 of temperature on compression than any method involving a ther- 

 mometer. 



In the case of mercury (in jacket IV), contact was at first broken 

 upon rapid compression at 500 kg. /cm*, with a quantity of mercury 

 which finally gave a reading of 366 kg. /cm 1 , when the heat of com- 

 pression had been taken away. Thus the pressure of 500 atmos- 

 pheres caused a rise of temperature enough to cause an error of 134 

 atmospheres, which corresponds to an increase in the volume of the 

 mercury of 0.0040 milliliter, a value taken from the curve for this 

 jacket or easily calculated from the mercury-glass curve given on page 

 19. 1 



There were present 21.6 milliliters of mercury, hence the per- 

 centage expansion was 0.01S5. But a rise of i would cause an ex- 

 pansion of 0.0157 P er cent - ^ the glass were warmed also to the same 

 extent, or 0.0182 if the glass were stationary in temperature. Hence 

 the rise of temperature on compressing the mercury to 500 atmospheres 

 must have been somewhere between 1.2 and i.o, according to the 

 supposition adopted concerning the glass. The higher of these two 

 results is the more probable, and even this may be too low because of 

 the exceedingly rapid loss of heat from this system assumed to be in 

 an adiabatic condition. 



Another mode of stating this calculation may make the matter 

 clearer. The coefficients of cubic expansion and compressibility are 

 respectively represented by the ratios (dv/dt) and {8v/8p) t . If now 

 we make (8v) = (8v) t a proceeding actually carried out in the 

 above experiment the following equation is obtained by dividing one 

 by the other. 



St coeff. of compress. 



5p coeff. of expans. 



From this equation 



134 x 0.0000014 



3t = -^ 1 1.2, 



0.000157 



a result identical with that obtained before. In this case, of course, 

 since the actual change of pressure is the value used in the expression, 



1 The change of compressibility with temperature and pressure are neglected 

 in this calculation as being infinitesimals of the second order. 



