Actinium and its Successive Products. 35 



In the silence of the authorities, I have myself suggested 

 that Boltzmann's e~ 2h x law supplies the necessary guidance. 

 The chance that any group or system of molecules shall be 

 in a configuration in which the potential of their mutual 

 forces, and of the external forces if any, is %, is proportional 

 to e~' 2h X. Or, if you prefer so to state it, the time during 

 which on the average of any very long time they will be in 

 that configuration is proportional to e~ 2h x. That gives the 

 minimum % f° r a statical system as a particular case. For 

 if ^ be the potential in the configuration A , and ^ in the 

 configuration A 1? and if %o<%i> A is more probable than A x 

 in the ratio e 2h ^~^ o) , that is in an infinite ratio in the 

 statical system, for which h is infinite. The statical system 

 must therefore be in minimum potential. Also if there be 

 only external forces acting, Boltzmann's law gives e~ 2h X as 

 the density at the point where the potential is ^, as in Max- 

 well's vertical column of air. I worked out the consequences 

 of the application of the law to the general case in a former 

 paper (Phil. Mag. for October 1901), and I think my con- 

 clusions were in the main right. If so, the law would be 

 inconsistent with Lord Ray 1 eights symmetry, and with its 

 consequences. In fact it seems to me that Lord Rayleigh's 

 symmetry and Boltzmann's law cannot both be true for one 

 and the same system in the same state. 



It may be said perhaps that Boltzmann's law holds only 

 for external, and not for intermolecular forces. Some English 

 writers, notably Dr. Watson, while not expressing their dis- 

 agreement with the law as applied to intermolecular forces, 

 prefer to let it alone. That I think arises from excess of 

 caution, or perhaps because the law, if so applied, leads to 

 results inconsistent with some favourite doctrines of the 

 orthodox theory of gases. The proof of the law given by 

 Boltzmann at p. 134 of his Vorlesungen, Part I., is formally 

 applicable to intermolecular forces. Why may we not so 

 apply it ? 



Y. Actinium and its Successive Products. 

 By T. Godlewski, Ph.D. (Cracow)*. 



RUTHERFORD and Soddy, in their well-known investi- 

 gations t on the activity of thorium, have shown that 

 it is possible to separate from it a very active constituent 



* Communicated by Prof. E. Rutherford, F.R.S. Presented before 

 the Academy of Sciences in Cracow, April 3, 1905. 



t Rutherford and Soddv, Phil. Ma£. Sept. and Nov. 1902; Trans. 

 Chem. Soc. lxxxi. pp. 321 & 807 (1902). 



D2 



