532 PROFESSOR CHALLIS, ON THE TRANSMISSION OF LIGHT, ETC. 



The equation consequently becomes 





Transforming it into rectangular co-ordinates by putting ,rr for r^y°, y' for J'^y, x^ for r^-y" 

 and x^ + v^ + 2^ for r^ there results 



a^ 6^ c^ Vfl! ft a'c' he' 



or, (c/ + / + «;') (o^r^ + b^y' + cV) - «'6'^ (ai' + y') - «'*•' {«'' + 2^) - ft'<.'' (y' + x") + a'^fc^'^ = 0. 



This is the equation of the wave surface in FresneFs Theory of Double Refraction. It is very 

 remarkable that principles and reasoning so widely different from those of that Theory should have 

 led to the same result. It is needless to go farther in the investigation, as all subsequent deductions 

 may be made in the same manner as in the received Theory. 



10. In conclusion, I beg leave to refer to an objection which may be raised against the 

 Theory of Polarization which I have brought forward. It may be urged, that as a wave is 

 conceived in this Theory to be composed of a vast number of rays in the same phase of vibration, 

 the transverse vibrations of the different rays will mutually destroy each other, leaving only the 

 direct vibrations, which by hypothesis do not produce the sensation of light. To this it may be 

 replied, that it is only the axis of a ray which can be considered as subject to the law of 

 refraction; for the motion of the aetherial particles along the axis is rectilinear, and coincident in 

 direction with the line of propagation, while at every other part of the ray the direction of the 

 motion of a given particle is continually varying, and is generally not coincident with the line of 

 propagation. Admitting the independent motion of each ray, it is possible that by refraction 

 through the eye, the directions of the axes of different rays may be brouglit to pass nearly through 

 the same point of the retina, in obedience to the common law of refraction, while the separate rays, 

 not being subject in other parts to this law, may not be altered as to the diameters of their trans- 

 verse sections. The constancy of the transverse section is, in fact, a necessary consequence of 

 a supposition already made in the course of this Theory, namely, that the quantity k is a fixed 

 numerical quantity, the same for rays propagated in media as for rays propagated in free space. 

 As, however, I am not at pi-esent provided with the means of ascertaining the nature and value 

 of that quantity, this part of the subject must be considered as open to further inquiry. 



Cambridge Obsebvatory, 

 May 17, 1847. 



J. CHALLIS. 



