804 Dr. R. D. Kleeman on the Nature of the 



therefore be such that in the equations 



1 7 vm ~ m» 3 

 ' 3 47TO" 2 12pa 2 



cr 2 the square of the radius of sphere of action of two mole- 

 cules is inversely proportional to v the velocity of a molecule, 

 for then the coefficient of viscosity rj is proportional to v 2 

 and 8 th« coefficient of diffusion proportional to v 4 , which 

 corresponds to the first and second power of the tempe- 

 rature. 



Suppose the potential energy of two molecules varies in- 

 versely as the ?2th power of their distance of separation. When 

 a collision takes place and the force is repulsive as Maxwell 

 supposed, their nearest distance of approach is given by 



mv 2 h 



where h is a constant independent of the temperature. Now 

 in order that a 1 may be inversely proportional to v we must 

 have n = 4, and the attractive force therefore varies inversely 

 as the fifth power of the distance between the molecules. 

 If the force is one of attraction instead of repulsion, the 

 value of cr given by the above equation is the least it can 

 have to prevent the colliding- molecules from rotating round 

 their centre of gravity. 



The Passage of the u Particle through Matter. 



Maxwell has given an investigation in general terms of 

 the motion of a molecule through a gas consisting of mole- 

 cules of a different kind (Maxwell's Collected Papers, vol. ii. 

 p. 36). It has been applied by Sir J. J. Thomson to the 

 case of an a particle traversing a gas (' Conduction of Elec- 

 tricity through Gases,' second edition, p. 370). According 

 to an equation deduced by Sir J. J. Thomson the decrease of 

 the velocity V of a molecule of mass m x when it traverses a 

 gas of molecular weight m 2 for a distance d.c is given by 



2 n — 5 



doo ~~ ?»! + m 2 \ m l m 2 ) " , 



where A is a constant independent of ra 1? m 2 , and V, and the 

 force of attraction between two molecules separated by a 



,. . . . . Kj 



distance r is given bv — . 



Now, according to the result obtained in this paper, 



r n = ~5 f V'Wi • S V»<2. 



