( 791 ) 



Waals in the following' words'): "This fonnnla viz. (1) — can 



only hold for I he cjise that the ciiaiice liial iiioi'c (liaii (wo nioUn^ides 



eome into collision al (he sanie (inie niav he considered as zero 



compared to the chance that only two come into collisioji." Kortkavp;g 



has expressed this more pointedly in the following way'''): "For a 



short time after each cojlisidu the possibilities of fi'esh collisions are 



considerably inthienced by the [n-oximity of the departing molecnle. 



This influence, certaiidy of very difficult mathematical treatment, is 



disregarded in my calculations." Claush's was the first (o take this 



influence into account •'), through which he came to foi-mida (2). 1 will 



discuss his [U'oof here, as it may lead to a closer approximated value 



of the length of path, even in principle to the drawing up of a strictly 



accurate equation, which we shall want for the derivation of the 



equation of state. 



Clausius [\o('. cit.) considers the general case of a point moving 



in a volume IT between several surfaces in rest. He calculates the 



chance, that the point will strike against a surface element with the 



velocity (//, by considering the jtoint for a moment as stationary, 



and by giving the surface element the opposite ^'elocity. Tf ^ is the 



angle of the normal to tlie element with tlie direction of motion, 



then the chance that the [joint lies in the cylindre co.^ 6 ds dl, is 



cos 6 th dl 

 equal to ~~ — . if we bring this in connection with the chance 



that sucli an angle 6 occurs, and if we integrate over all tlie angles, 



we find for the total chance that the element is struck -- dl , so 



4 n 



.s 

 for the total surface --- dl: if the mean \elocitv is w, so dl =i ïi dl 

 4]» 



then : 



~ 4 1 r " ^7i ' 



This derivation appears to be strictly accurate, as long as all 

 surface elements have an e(pial chance of being struck and all 

 volume elements have an eipial chance of containing the point. If 

 there should be elements for which this chajice is zei-o, (hey must 

 not be included in the integration. If wc think the surfaces to l)e 

 movable, then it is clear, that we must introduce the mean relative 

 velocitv in the w^av known. 



1; 1. c. p. 336. 



2) Nature 45 p. 152. 



3) Pogg. Ergbd. 7 p. 244, cf. Kinetische Theorie der Gase 1. c. 



