24 THE TRUE VALUE OF a OF VAN DER WAALS' 



more nearly 6.8 than 7.5 even in isopentane quite close to, within 

 a fraction of a degree of, the critical. The reason for this is, I 

 presume, that dPjdT close to the critical temperature is always 

 too small since the Biot formula gives too high a value for P 

 here. The error appears twice, then, making tbc latent heat too 

 low, and P too high close to the critical, so that the calculated 

 ratio is always lower than 7.5 and lower than it ought to be. 



We have then to calculate the value of a the formula 

 a = 6.5 JP C V C 2 . The computations are given in col uni 3 of Table 2, 

 and I have also plotted the results in figure 1 , log a being there 

 plotted against the logarithm of the product of the molecular weight 

 by the number of valences. The values, with one or two excep- 

 tions, fall along a straight line, and it is clear that if this method 

 of computing a is correct, and I see no reason to doubt its 

 correctness, there is no question that a is dependent on the 

 product of the molecular weight by the number of valences. 



I do not know why a/V c 2 should always be equal to 6.5 P c . 

 That is I do not know what the significance of this constant of 

 proportion, 6.5, is. As it may help someone else to discover the 

 significance of this, I may mention one other fact I have disco- 

 vered, namely, that at about 0.94 T c in the saturated vapor PV 

 becomes exactly equal to ajV and at the same time the ratio of 

 [PV -\- ajV): RT becomes equal to 1.154, that is equal to 7.5 : 6.5, 

 or the ratio (P t . -j- ajV 2 ) ■. ajV 2 . At that point, also, Vj(V—b) 

 becomes equal to 1.154. This holds certainly in widely different 

 substances from C0 2 to the substances of Young. I do not yet 

 see the significance of these relations. We have then at 0.94 T t . the 

 following: 2 PV= 1.154 RT; and RTjPl'= 1.733. This factor, 

 1.733, corresponds to the critical coefficient S. 1.733 is the con- 

 stant (f Dieterici found in his equation: L — E= 1.733 RT, L?i e {djD) 

 in the case of substances where b c = V c j2. If S is 3.75 then SC' 

 should give us Kjl\. and 3.75 X 1-733 is 6.5. But I do not 

 understand the significance of these facts. 



In associating substances such as water and ethyl alcohol the 

 value of a calculated by this formula is always larger, and some- 

 times very much larger, than the value calculated from the mole- 

 cular weight and number of valences assuming these to be normal. 

 The cohesion of associating substances is, for some reason I do not 

 understand, greater than expectation from the theoretical number 

 of valences. These substances appear to have an additional cohesive 

 attraction. Perhaps this is of a chemical nature. 



