84 PROCEEDINGS OF THE AMERICAN' ACADEMY. 



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for example, would be that over the temperature range 40°-80°, 



The general l)ehavior of the compressibility that one is prepared to 

 expect from experiments at low pressures is a decrease with increasing 

 pressure, and an increase with increasing temperature. The familiar 

 conception of a liquid due to van der Waals is competent to explain 

 this. The difference between the free space open to the molecules 

 for their temperature vibrations and the total volume of the liquid is 

 equal to the volume of the molecules themselves, or else to a small 

 multiple of it. When pressure is increased, therefore, the free space 

 diminishes much more rapidly than the total volume. Now we may 

 suppose the pressure exerted by a liquid to be due in large measure to 

 the bombardment of the walls by the temperature agitation of the 

 molecules. The more frequent the collisions, the greater the pressure. 

 Now at constant temperature, the number of collisions is inversely as 

 the free space. At higher pressures, that is smaller volumes, a given 

 diminution of total volume implies a greater diminution of the free 

 volume than at low pressm-es, and therefore a greater increase of 

 pressure. So that at small volumes (high pressures) a given decrease 

 of volume carries with it a greater increase of pressure than at larger 

 volumes (lower pressures), or in other words, the compressibility 

 decreases with rising pressure. The increase of compressibility at 

 higher temperatures is to be explained in the same way. At higher 

 temperatures (constant pressure) the volume is greater and we expect 

 greater compressibility. This however, is not the only element 

 involved in the change of compressibility with temperature; there is 

 also a temperature effect as such. It was found in the paper on water 

 that, at equal volumes, the compressibility was always less at the higher 

 temperatures. The reason is evidently the more rapid agitation of 

 the molecules. At equal volumes, a given decrease in the total 

 volume, and so of the free volume, will produce the same proportional 

 increase in the number of impacts at high and low temperatures, but 

 at high temperatures each impact involves a greater change of mo- 

 mentum, with the result that at the higher temperatures a given de- 

 crease of volume produces a greater increase in pressure, which means 

 3, lower compressibility. 



A detailed examination of the curves shows that these expectations 

 are justified to a rather greater degree than was the case for the 

 thermal dilatation. The compressibility decreases with rising pres- 

 sure for all twelve liquids at 40°. A careful analysis of the difference 



