216 UNDULATORY THEORY OF LIGHT. 



aziraiUhs around the ray, it is evident tliat the elasticity of the ether iu the 

 crystal is the same in all directions at right angles to the optic axis. The mo- 

 ment, however, that we depart from the pole of the sphere — maintaining still a 

 perpendicular incidence upon its surface — a second ray makes its appearance. 

 The light is now equally divided. A part, which we call the ordinary ray, still 

 follows the radius and passes through the centre of the sphere. The other 

 portion is bent at the surface, and cro.^scs the diameter in which we found no 

 double refraction, above the centre or between it and our first supposed point of 

 incidence; that is, the point which we have called the pole. The deviation will 

 be slight at first, and will go on for a time increasing, as we descend in latitude; 

 but will afterwards diminish till we reach the equator, when it will become 

 nothing. But though the deviation diminishes, the double refraction increases ; 

 that is to say, the difference of velocity between the two rays becomes greater 

 and greater as we approach the equator, and in that plane attains its maximum. 

 Both rays now pass through the centre; but one is so far behind the other that 

 two images may be seen of any object beyond, at different apparent distances 

 from the eye. If the incidence be not perpendicular, the ray which has always 

 passed through the centre undergoes^ refraction according to the simple law of 

 Snellius, in all planes and in all azimuths ; but this is not at all true of the other. 

 The inference is that the velocity of the first of these rays is always deter- 

 mined by the same elastic force; which must be that force which we have seen 

 to be at right angles to the axis, or parallel to the equator of our supposed 

 sphere. 



And here, in order to avoid error or confusion, let it be observed that the 

 line which wc have called the axis of this sphere is not the optic axis of the 

 crystal, but only one of the optic axes. All lines parallel to this are equally 

 optic axes. In other words, the name optic axis is the name, not of a line, but 

 of a direction. 



Now if we once more follow, in mind, our ray at perpendicular incidence, 

 from the pole of the sphere to the equator, wc shall see that there is no difficulty 

 in imagining its molecular movements to be constantly parallel to the equator, pro- 

 vided we suppose them perpendicular to that meridian plane (principal section) 

 which passes through the ray and the axis of the sphere. The constant velocity 

 of the ordinary ray is thus accounted for without difficulty. 



The velocity of the extraordinary ray being variable, its molecular movements 

 must encounter a different elasticity in different directions of its progress. 

 Moi'eover, as its plane of polarization is at right angles to that of the ordinary ray, 

 its molecular movements should be so likewise. We have only to suppose these 

 movements to take place in the meridian, or principal section, plane, and we 

 shall see that they will turn with the ray itself, as we pass from the pole to the 

 equator: so that, while, in the first position, they are parallel to the equator 

 like those of the ordinary ray, they are inclined to it at increasing angles 

 as we descend in latitude, and become perpendicular to it in latitude zero ; 

 that is, when the ray is in the plane of the equator itself. Now this would 

 make no difference in the velocity, provided the ether were equally elastic 

 in all directions. As the velocity is variable, in point of fact, the conclusion 

 must be that the elasticity is variable also. In the direction of the axis we 

 must assume it to be greatest, and in intermediate directions to possess an inter- 

 mediate force. 



Now the plane of polarization of the ordinary ray (experimentally ascertained) 

 is the principal section of the crystal. And as we have been compelled to con- 

 clude that the molecular movements of this ray take place at right angles to the 

 principal section, it follows that, in plane polarized light, the vibrations are at 



