Astronomical and Nautical 'Collections; 17 J 



genius of Huygens, affords us, as its consequences, the facts 

 which have been explained : the two kinds of rays possess 

 the same velocities in the direction of the axis, because in 

 this case the sine vanishes, and the difference of the velocities 

 increases gradually with the sine, as we go further from thq 

 axis, until it becomes greatest in the direction perpendicular 

 to it. 



This difference of velocity is positive in certain crystals, 

 and negative in others ; that is to say, in the one class the 

 ordinary rays advance more rapidly than the extraordinary, 

 and in the other less rapidly. The carbonate of lime, or cal? 

 carious spar, affords an example of the first case, and rock 

 crystal of the second. 



Such being the general principles of the progress of the 

 ordinary and extraordinary rays, we may now return to the 

 physical properties which they exhibit after their emersion, 

 when they are made to pass through a second crystal, capa-* 

 ble, like the first, of dividing the light into two separate pen^ 

 cils. It may here be remarked, that the word pencil will 

 be employed for a system of waves separated from another 

 by difference of direction, or simply of velocity, though pro- 

 perly borrowed from the system of emanation, as implying v^ 

 ^W7?t//e of distinct rays. 



We may first consider the state of the ordinary pencil 

 which has been transmitted through a rhomboid of calcarious 

 spar : and which, upon being transmitted through a second 

 rhomboid, produces two new pencils of equal brightness, when 

 the principal section of the second rhomboid forms an angle 

 of 45° with that of the first : in all other positions the two 

 pencils, and the images which they form, are of unequal 

 brightness, and one of them even vanishes entirely when the 

 principal sections are parallel or perpendicular : when they 

 are parallel, the extraordinary image vanishes, and the ordinary 

 image attains its greatest brightness ; when perpendicular, 

 the ordinary image disappears, and the extraordinary acquires 

 its maximum of intensity. The extraordinary pencil, on the 

 contrary, transmitted by the first rhomboid, exhibits exactly 

 contrary appearances in passing through the second rhomboid: 

 the ordinary image, that it affords, vanishes when the princi- 



