798 



NA JURE 



[December i. 1923 



if all the ordinary causes of premature death were 

 eliminated, this would increase the average duratifjn 

 of life by not more than thirteen years. On the other 

 hand, he shows that the children of long-lived parents 

 have an expectation of life which is twenty years 

 greater than that of the average individual. 



It is evident, then, that if longevity is our goal it 

 is not medical science we must look to but eugenics, 

 and 1 doubt whether the question is one with which 

 we are concerned. The sorrow of the world is not 

 the eternal sleep that comes to every one at the end 

 of his allotted span of years, when man rests from his 

 lalxnirs. It is the pain, mental and physical, associated 

 with sickness and disability, or the cutting off of a 

 man by disease in the prime of life, when he should 

 have had many years of work before him. To us falls 

 the task of alleviating and preventing this sorrow. 

 In our childhood most of us learnt that suffering and 

 death came into the world through sin. Now, when 



as physicians we stand on the other side of good and 

 evil, we know that the sin for which nmn is continuously 

 [)aying the {jenalty is not necessarily failure to comply 

 with some one or other of the rough tril>al adjustments 

 to the environment, which we call morality, but is 

 always and in ever>' case ignorance or disregard of 

 the immutable working of the forces of Nature, which 

 is being continually revealed to us by scient '^ 

 vestigation. 



In spite of the marvellous increase in knowlcdj^c, 

 to some aspects of which I have directed your attention, 

 suffering is still widespread amongst us. Only by 

 following out the injunction of our great predecessor 

 — to search out and study the secrets of Nature by 

 way of experiment — can we hope to attain to a com- 

 prehension of " the wisdom of the body and of the 

 understanding of the heart," and thereby to the mastery 

 of disease and pain which will enable us to relieve the 

 burden of mankind. 



The Equation of Van der Waals.' 

 By J. H. Jeans, Sec. R.S. 



TTAN DER WAALS' equation 



expresses the result of supposing a molecule to be 

 endowed with two distinct physical properties — finite 

 size, giving rise to the term b, and cohesive force, 

 giving rise to the term ajv^. The physical meaning of 

 the equation is best exhibited by drawing diagrams of 

 isothermals of the familiar type. Representing differ- 

 ent gases there will be different diagrams corresponding 

 to different values of a and b. It is, however, readily 

 shown that one diagram of this type can be made to 

 represent all values of a and b, and so the isothermals 

 of all gases, by suitable expansions and contractions 

 of its horizontal and vertical scales. On removing the 

 scale from any single diagram we have a universal 

 diagram which represents the p, v, T relation for all 

 gases, but without specifying the scale. The circum- 

 stance that such a diagram is possible is equivalent to 

 the so-called " Law of Corresponding States " ; this is 

 now seen to be a mathematical consequence of Van der 

 Waals having confined himself to a two - constant 

 specification of molecular structure. 



Thus the accuracy, or the reverse, of the law of 

 corresponding states provides a test of the sufficiency 

 of Van der Waals' two-constant specification of a 

 molecule. In actual fact the law is not very closely 

 obeyed : the deviations show distinct correlation 

 with atomicity, and so suggest that the two-constant 

 specification is not altogether adequate — a full treat- 

 ment must take account of differences of atomicity (or 

 Dhysical shape) as well as of differences of size and 

 cohesive power. 



Van der Waals explained his cohesive power by the 

 supposition that all matter possesses inherent powers of 

 attraction for all other matter. Gravitational attrac- 

 tion is numerically far too small to come into the 

 question at all, so that it is to the electrical structure 



• Synopsis of part of the Van der Waals Memorial Lecture delivered 

 before the Chemical Society on November 8. 



NO. 2822, VOL. 112] 



of matter that we must look for the origin of this 

 supposed universal attraction. 



If molecules were electrically charged structures, 

 similar molecules would repel one another ; as they are 

 electrically neutral, they will repel in some orientations 

 and attract in others, but two molecules meeting at 

 random are as likely to repel as to attract. It is only 

 when the duration of molecular encounters is studied 

 that we find an explanation of the preponderance of 

 attraction over repulsion — attractive encounters draw 

 the molecules farther and farther into each other's 

 sphere of influence, and so last longer than repulsive 

 encounters. Comparing the two types of encounters, 

 the " birth rate " is the same for each, but the " ex- 

 pectation of life " is longer for attractive encounters, 

 so that for the encounters in being at a specified instant, 

 there is a preponderance of attractive encounters, and 

 hence a resultant attractive force. This attractive 

 force, however, originates far more in an abstruse 

 theorem of statistical mechanics and far less in an 

 inherent property of matter, than Van der Waals 

 supposed. 



If this interpretation is right, the cohesive forces 



' must disappear at ven.' high temperatures and must 

 steadily increase with decreasing temp)eratures, so that 

 a must be a function of the temperature and not, as 

 Van der Waals supposed, a constant. In point of fact, 

 all attempts to bring Van der Waals' equation into 

 closer agreement with observation begin by making a 

 a function of the temperature. Moreover, a is found 

 to vanish at infinite temperatures in conformity with 

 the suggested explanation. 



The second constant b was supposed by Van der 

 Waals to have its origin in the finite sizes of the mole- 

 cules. If, for example, the hydrogen molecule is 

 regarded as a sphere, its radius as calculated from the 

 observed value of i is found to be 0-64x10"' cm. 

 The same radius can be calculated independently in 

 other ways ; the coefficients of viscosity, of conduction of 

 heat and of self-diffusion all agree in yielding the value 



j 0'68 X io~® cm. The average of these, o-66 x 10"* cm., 



