Crystalline Reflexion and Refraction. 37 



were used in obtaining the formula, were erroneous. It is to M. Seebeck that 

 I am obliged for pointing out this curious circumstance. In Poggendorff's 

 Annals,* he gave an abstract of my letter to Sir David Brewster, and compared 

 my results with his own numerous and accurate experiments, both on the pola- 

 rising angles of Iceland spar and on the angles of deviation. He found that 

 my formula represented the former class of experiments as well as could be 

 wished ; but the theoretical values of the deviations did not at all agree with his 

 experimental measures. These measures of the deviation he published on this 

 occasion ; and, with their assistance, I traced the error to its source, which was 

 the relation among the pressures. The principle of vis viva was therefore 

 introduced, instead of that relation, and the theory became much simpler by the 

 change. I now obtained, for the deviation, a new expression, which agreed with 

 the experiments of M. Seebeck ; but the formula for the polarising angle came 

 out the very same as before. This correction was made on the 6th of December, 

 and was published in the Philosophical Magazinef on the first of the present 

 month. '\~ 



In the interval I have arrived at very elegant geometrical laws, which can be 

 easily remembered, and which embrace the whole theory of crystalline reflexion. 

 In enunciating these, it will be convenient to draw our transversals always 

 through the same origin O, which we shall suppose to be the point of incidence, 

 as this point is common to all the rays^ whether incident, reflected, or refracted ; 

 and we may imagine wave planes to be drawn through the origin, parallel to the 

 plane of each wave, so that every transversal will lie in its own wave plane. The 

 Incident and reflected wave planes will be perpendicular to the incident and 

 reflected rays, but the two refracted vvave planes will in general be oblique to 

 their respective rays. In the latter case, a right line drawn through the origin 

 perpendicular to the wave plane, is called the wave normal. It is scarcely 

 necessary to remark, that all the four wave planes Intersect the s urfac e of the 

 crystal in the same right line which is perpendicular to the plane of incidence; 

 and that the angles of refraction are the angles which the refracted wave normals I J^m 

 make with a perpendicular to that surface. The index of refraction is the ratio 

 of the sine of the angle of incidence to the sine of the angle of refraction, just as 



* Annalen der Physik und Chemie, vol. xxxviii. p. 276. 



■f London and Edinburgh Philosophical Magazine, vol. x. p. 43. 



