92 PROCEEDINGS OF THE AMERICAN ACADEMY. 



whence, 



AF = p (--^^ dp= -b log p+C. 



This equation cannot be expected to hold for low pressures. The 

 constants may be determined as follows. From the curves for W 

 above 5000 kgm. we find that an approximate value for h is 0.1. If 

 furthermore we assume as a fair average of all twelve liquids that 

 AF = —0.25 when p =5000, the equation becomes, 



AF = -0.1 log.p + 0.6017. 



The equation evidently cannot hold for infinite pressures, because it 

 demands that AF decrease indefinitely, and it is physically impossible 

 that AF should become less than —1. But the pressure at which this 

 would happen according to the above formula is 9,060,000 kgm. This 

 is so very far beyond the range of these experiments, that it would 

 probably be safe to apply a similar equation as an approximate expres- 

 sion for any experimental pressures above 5000 kgm. 



The mathematical analysis gives us, furthermore, information as 

 to the ultimate behavior of the work of compression. F'or the actual 

 work must eventually be less than that given by the above formula, 

 which corresponds to a smaller change of volume. It must be, there- 

 fore, that at higher pressures the curvature reverses, and the curve 

 becomes convex upwards. Methyl and amyl alcohol show the begin- 

 ning of this effect, but in view of the extreme remoteness of the vanish- 

 ing of the volume predicted above, it may well be that this slight 

 change of curvature is merely one of the many local variations. 



The maximum amount of work stored up at 12000 kgm. is nearly 

 the same for all twelve liquids; much more nearly equal than the 

 initial differences in the compressibilities would lead us to- expect. 

 The variations in the maximum are about 25%, whereas there are 

 initial variations in the compressiljility of 100%. If we admit water 

 to our family of curves, as we may because the final work of com- 

 pression is over 9 kgm. m., the variation in the initial compressibility 

 may be 400%. Initial differences of compressibility have little effect 

 on the work at the maximum pressure, because of the comparatively 

 small amount of work done at low pressures. 



The total amount of mechanical work stored up in a liquid is quite 

 considerable. P^or example the work of compression of ether at 12000 

 kgm. would suffice to raise it through about 45000 ft., or to give it a 

 velocity of 1700 ft. sec. 



