IN CRYSTALLIZED MEDIA. 329 



Now the fact of considering that the force in any direction is the 

 resolved part in that direction of the whole force put in play, re- 

 quires that the forces be all of the same nature : how does it happen 

 then that a part of them may be omitted altogether ? Should it be 

 urged in reply, that tlie motion of a particle in a given direction is 

 not affected by a force which acts always at right angles to that 

 direction ; I answer that this is not the solution of the real difficulty, 

 though most persons appear perfectly satisfied with it. That the ab- 

 solute motion of the particle will be such as continually to change 

 the plane in which it moves is quite obvious. If then, as M. Fresnel 

 supposes, the velocity depends on the position of this plane, the ve- 

 locity itself must be continually varying for the same ray. 



Nor has the plane in which the particle moves a reciprocating 

 motion. The construction consisting of an ellipsoid cut by the plane 

 of vibration through its centre sufficiently proves this ; for it is 

 found that the whole force due to a displacement in one of the axes 

 of the elliptic section acts in the direction of a normal to the ellipsoid 

 at the extremity of that axis. Suppose then the particle to be at its 

 greatest distance from its position of rest; the action of the normal 

 force causes it to return in a direction above the plane of its dis- 

 turbance, (suppose). When it has reached the other extremity of its 

 oscillation, the force tends to pull it below the line of its return : 

 by each action, therefore, the change from its original line of motion 

 is in the same direction, and this will take place continually, so that 

 the plane of motion will continually vary, and the velocity of trans- 

 mission constantly increase or constantly diminish. 



These points appear to me weak points in the theory : the former 

 is indeed of such magnitude, that were there nothing to limit its 

 effects, the results would be very far from the truth. The error, 

 however, which is committed by this step is exactly righted by the 

 second, and thus two hypotheses which individually are erroneous, do. 

 when combined, lead to correct results. Indeed it is manifest that 

 whereas the former error arises from not giving to the front of the 

 wave its due effect, the latter arises from giving it an effect wliicli 



