Propagation of Luminous Waves in Transparent Bodies. 201 



results that cannot be depended on; because a minute error 

 of the thermometer is accompanied with a great variation of 

 the elevation. Even in great heights, the discrepancies are 

 so great as to warrant no more than this approximate con- 

 clusion, that the decrease of heat near the earth's surface is 

 proportional to the increase of elevation. By careful experi- 

 ments tlie rate of the decrease of heat at any place, that is, 

 the height required for depressing the thermometer 1°, may 

 be ascertained with considerable accuracy; and it has been 

 found that this imperfect element is sufficient for solving the 

 two chief problems relating to the atmosphere, namely, the 

 measuring of heights by the barometer, and the astronomical 

 refractions. 



XXX. On the Propagation of Luininous Waves in the Interior 

 of Transparent Bodies. By the Rev. Matthew O'Brien, 

 late Fellow and Mathematical Lecturer of Cains College^ 

 Cambridge*. 



ONE of the chief difficulties we meet with in applying the 

 general equations of motion to determine the circum- 

 stances of propagation of the waves of light in the interior of 

 transparent bodies, arises from our ignorance of the manner in 

 which the particles of the luminous asther are arranged in the 

 interstices between the particles of matter; for, supposing that 

 each particle of matter is surrounded by many particles of 

 aether, it is evident that the attractions or repulsions of the 

 material particles on any aethereal particle must in general be 

 different according to the different positions which that par- 

 ticle may occupy with reference to the material particles ; now 

 the consequence of thfs variation of force must evidently be 

 an unequal arrangement of the particles of the aether ; so that 

 if we consider any one particle, the rest will in general be 

 disposed unsym metrically with respect to it, according to some 

 law varying with the position it occupies with respect to the 

 particles of matter; and this law of course we cannot deter- 

 mine, as it must depend on the nature of the molecular forces, 

 both material and lethereai, of which we are quite ignorant. 



Now when we come to form the approximate differential 

 equations which determine the vibratory motion of the parti- 

 cles, we shall find that the coefficients of the partial differen- 

 tial coefficients with respect to xy z, which occur in these 

 tcjuations, become variable in consequence of the variable ar- 

 rangement of the particles just described; and hence, instead 



» Cominunicatetl by the Author. 



