THE TRUE VALUE OF a OF VAN DEK WAALS' 



I may say at the outset that the connection between the product 

 of the molecular weight by the number of valences and the value 

 of a was discovered empirically. I had no preconceived ideas on 

 the subject, and 1 tried a great many possibilities, among them the 

 very one adopted by van Laar, before T found what I believe to 

 be the true relationship. T was confronted at the start with the 

 difficulty of knowing what was the real value of a, a difficulty 

 which all have experienced who have studied the question. I felt 

 it necessary to find a method of computing a which should be 

 entirely independent of any assumption as to the value of the other 

 constant b, free in other words of any assumption of whether 

 b was constant, or varying with the volume. The method I 

 adopted was to compute a from the surface tension. This was 

 the method originally suggested by that great English physicist, 

 Thomas Young, in his classical paper on cohesion and capillarity. 

 He expressed in that paper the relation between cohesion and sur- 

 face tension. It is the formula: ,y = 7ù/3, where K is the cohesive 

 pressure, represented afterwards by van der Waals as a\V 2 , and 

 r is the radius of action of the cohesive attraction, s is the surface 

 tension energy per unit of surface. I took r to be a single mole- 

 cular diameter, as this is its most probable value, and 1 assumed 

 the law to hold at absolute zero, for the reason that it was more 

 convenient to go to the end, and it is apparent on the face of it 

 that the law can only hold at temperatures where the cohesion in 

 the vapor may be entirely disregarded. These assumptions are both 



Tliis is a fail- example of van Laar's method of criticism. This foot note plainly states 

 that Walden ami Swinne liai! v ted thai a of van der Waai. s' equation was 



dependent on tin' numher of valence: . and it implies accordingly that there was nothing 

 particularly novel in mj ■ tion. As a matter of tact Walden ami Swinne do not 



mention a of' van der \\ vals' equation in the place cited. They are dealing with the 

 specific cohesion, so called, which they expre s as is customary with the letter a 2 . They 

 say "<'^' J means (he specific cohesion a1 the normal boiling point." "The molar cohesion 



Ma^ 2 is for normal liquids at the boilin wesentlich additive ( Grosse, wenn 



audi mit konstitutivem Einschlag: das Analoge -i'i für die a rmalen Siedetemperaturen , 

 Tg. Beide I tfa^ 2 and 'i\. la ei „Valenzzahl" 2n proportional 



;. hier bedeutet £n die Summe der Valenzen der in den betreffenden Verbindungen 

 vorhandenen Elemente. (Eigentlich kann 'ormulierung nur fur die C, If, O und A' 



enthaltenden Stoffe aufrech.1 erhalten wi i // ist n gleich 1, hei <>- gleich2,oei 



N- gleich •'! mid lui C- gleich i)''. Tin to show that really Ma^ is propor- 



tional to the sum of the square roots of weights. The specific cohesion of 



which they speak and which tiny di not at all tin- factor a of van der Waals. 



It is, as a matter of fact, simply the height to whick a liquid rises in a capillar} tube 

 of 1 m.m. radius. All that they say aboul its relation to valence is that quoted, so far 

 as I could find. Moreover their paper was published in 1913. My first papers antedated 

 this, having been published in 1912 ami February 1913. 



