492 Scientific Intelligence. 



SCIENTIFIC INTELLIGENCE. 



I. Chemistry and Physics. 



1. On the Relative Size of Molecules. — An attempt has been 



made by Jager to determine the relative diameters of some of 



the elementary molecules and of certain atomic groups, based 



upon Kohlrausch's investigations on the electric conductivity of 



certain metallic hydrates and salts in aqueous solution. If in a 



cylinder of unit length and unit cross section of such a solution 



there are m molecules; then, the electromotive force along the 



axis being unity, we may represent by V the velocity with which 



the kathion will be propelled in the one direction, and by U the 



velocity of the anion in the other. If a represent the quantity of 



positive or negative electricity belonging to each molecule the 



coefficient of conductivity k will equal (u-\-v)m, in which £lJ=:u 



and sV=v; and the specific molecular conductivity A will be 



v 

 equal to u + v. But, according to Hittorf, =n, in which n is 



u ° u + v 



the number of molecules passing through unit space in unit time. 

 Hence m=(1— n)\ and v = nX. Since the molecules of the ions 

 have a certain velocity, they must meet in unit time a certain 

 number of molecules of a different kind moving in the opposite 

 direction ; and therefore they will require energy to overcome the 

 resistance, proportional to their rate of passage. Assuming the 

 molecules to be spheres, and assuming the solution so dilute that 

 no interaction takes place between the molecules of the dissolved 

 substance; then, if the number of molecules in unit volume is a, 

 and if a molecule of radius r passes in a certain direction through 

 an environment of molecules whose radius is p, we have r + p=R, 

 by resolving the forces in two directions. The result is the same 

 if the radius of the moving molecule is R and the molecules of 

 the environment are mathematical points. If for one given mole- 



C C 



cule we have «=— „= -. r-„ in which C is a constant of integra- 



K (r + p) 



C 



tion; while for another molecule «'=— i yaj then, dividing the 



v ~r~ P) 



first formula by the second, we have -;=-. ^ from which 



J v (r + p) 



r=(r' + p)\/ P- Substituting in this equation the values for 



the relative velocities determined by Kohlrausch, and using to 

 find r' and p, the diameters of the molecules of water and chlorine 

 as calculated by O. Meyer; i. e. for water 96X10 -9 and for chlo- 

 rine 44X10" 9 centimeters, the value of U for water being 49, 

 Ja^er has obtained the formula for calculating the diameter of a 



given molecule d=y 44, the values obtained being ex- 



