Intelligence and Miscellaneous Articles. 551 



ON THE RELATIVE MAGNITUDE OF MOLECULES. 

 BY DR. ALEXANDER NAUMANN . 



If i) denotes the coefficient of friction, m the molecular weight, 

 and u the molecular velocity of a gas, r the semidiameter of the mole- 

 cule assumed to be spherical, according to O. E. Meyer*, 



rnu 



Now the same physicistf has deduced the coefficients of friction of 

 several gases from the values of their coefficients of transpiration 

 found experimentally by Graham. But as molecular weights have 

 but relative values, the previous equation can also only be used for 

 deducing relative values of the molecular sections rV ; in what fol- 

 lows, these are given for those gases whose coefficients of friction are 

 known. 



Let y and y 1 be the coefficients of friction of different gases, m and 

 m x the molecular weights, u and u x the molecular velocities, r and 

 r x the molecular radii ; we have from the above equation, 



mu 



las*** = mVT ? 



Vi m x u x m x u x r 2 ' 



from which is obtained for the relative magnitudes of the molecular 

 sections, 



r 2 _ mui) 1 ,,v 



r i »WJ 



Now if r and t x are the absolute temperatures of the gases, we 

 have, since the vires vivce of molecular motions are proportional to 

 the absolute temperatures, 



— = - and — = _^™Z. 

 m x u x 2 r x u x tf mTi ' 



Introducing this value into equation (1) gives 



£ __ mij x V^r __ yj^mr # / 2 \ 



r i m x 7) V 7 mr x ^ V m x r x 



If the gases are compared at the same temperatures (the melting- 

 point of ice for instance) t = t x , equation (2) passes into 



kv; 



v; 



(3) 



* Poggendorff's Annalen, vol. cxxv. p. 597 (1865). 

 t Ibid. vol. cxxvii.p. 378 (1866). 



