142 Mr. W. Sutherland on Molecular Refraction. 



modern science of energy : — the main mass of a transparent 

 body may be considered to be a field of constant potential, 

 and so also may the external free asther ; but in the passage 

 from the body to the a3ther there is a layer of space in which 

 the potential varies along the normal to the layer ; the change 

 in the kinetic energy of a corpuscle of light in crossing this 

 layer must be equal to the determinate change of potential 

 energy corresponding to the passage from one region of con- 

 stant potential to another. But only the normal component 

 of the velocity changes ; hence we have the result that the 

 difference of the squares of the normal velocities of a corpuscle 

 in sether and in the substance is proportional to the definite 

 change of potential ; or the square of the ratio of the normal 

 velocity in the substance to the normal velocity in sether, 

 minus unity, is proportional to the same quantity. Now 

 Newton does not expressly show how the change of potential 

 energy on passage from free aether into a substance should be 

 proportional to the density (this was afterwards done by 

 Laplace) ; but he proceeds to tabulate the indices and den- 

 sities for a number of bodies and to show that the square of 

 the index minus unity divided by the density is roughly the 

 same for them all. He comments on the fact that this quan- 

 tity has the same value for air as for glass, in spite of the great 

 difference in density between the two substances. 



Laplace was able, by the treatment of the subject of mole- 

 cular force, which he develops for his theory of capillarity, to 

 give precision and definiteness to Newton's proof {Mecanique 

 Celeste, book x. chap. i.). If, as in the gravitation theory, 

 the force due to a molecule is proportional to its mass, it is 

 obvious that the force exerted by a body on a corpuscle of 

 light near its surface will be proportional to the density of the 

 substance, assuming that molecular force is sensible at insensible 

 distances and insensible at sensible. Laplace is able to show 

 how it is only at the transition layer between aether and sub- 

 stance that a change of potential occurs, and how the change 

 of potential is expressible as a definite integral proportional to 

 the density. He thus gets the formula (w"-^ — l)/fZ = c, where c 

 is a parameter whose value depends only on the chemical con- 

 stitution of the substance. 



Biot and Arago [Memoires de I' Acad. vii. 1806) undertook 

 the experimental verification of this formula in the case of 

 gases, and found it to hold accurately. 



With the establishment of the undulatory theory and the 

 abandonment of the emission theory, the theoretical arguments 

 of Newton and Laplace failed to apply any longer to the actual 

 circumstances, but still Newton's discovery of a connexion 



