TJ. S. Larsen — Relation between the Refractive Index, etc. 263 



Art. XXYIII — The Relation between theRefractive Index and 

 the Density of Some Crystallized Silicates and Their 

 Glasses ; by Esper S. Larsen. 



Investigators have long sought to discover a simple relation 

 between the index of refraction of a substance and its density 

 •which is independent of the temperature and also valid even 

 when the substance is mixed in solution with other substances. 

 Laplace* early derived the relation 



n* —.1 



— = constant (1) 



from a consideration of Newton's emission theory of light. 

 This formula did not satisfy later experimental data and in the 

 middle of the last century Gladstone and Dale derived the 

 relation 



n — 1 



— = K, where iT is a constant (2) 



which they called the specific refractive energy. Theoretically, 

 this formula is based upon the assumption that the molecules 

 in the line of transmission of a given light wave retard that 

 wave by an amount which is independent of their arrangement 

 and distribution along that wave. Their own statement is :f 

 " Every liquid has a specific refractive energy composed of the 

 specific refractive energies of its component elements, modified 

 by the manner of combination, and which is unaffected by 

 change of temperature, and accompanies it when mixed with 

 other liquids. The product of this specific refractive energy 

 and the density is, when added to unity, the refractive index." 

 More recently, Lorentz^ and Lorenz§, on the basis of the 

 electromagnetic theory of light, independently derived the 

 relation : 



i = * w 



n 2 + 2 d 



The specific refractive energy being an additive property, we 

 may immediately write the relation, 



* = *' fe _ (4) 



where iT is the specific refractivity of the mixture and k that 

 of any component, while p is the weight per cent of that com- 



* Traite de Mecanique Celeste, IV, x, 232. 



+ Phil. Trans., 337, 1863. 



tWied. Ann., ix, 641, 1880. §Ibid., xi, 70, 1880. 



