10.  Again, if one turns the Crystal in such wise that an incident ray no, of sunlight, which I suppose to be in the plane continued from GCFH, makes with GC an angle of 73 degrees and 20 minutes, and is consequently nearly parallel to the edge cf, which makes with FH an angle of 70 degrees 57 minutes, according to the calculation which I shall put at the end, it will divide itself at the point O into two rays, one of which will continue along op in a straight line with no, and will similarly pass out of the other side of the crystal without any refraction; but the other will be refracted and will go along OQ.  And it must be noted that it is special to the plane through GCF and to those which are parallel to it, that all incident rays which are in one of these planes continue to be in it after they have entered the Crystal and have become double; for it is quite otherwise for rays in all other planes which intersect the Crystal, as we shall see afterwards.

11.  I recognized at first by these experiments and by some others that of the two refractions which the ray suffers in this Crystal, there is one which follows the ordinary rules; and it is this to which the rays Kl and OQ belong.  This is why I have distinguished this ordinary refraction from the other; and having measured it by exact observation, I found that its proportion, considered as to the Sines of the angles which the incident and refracted rays make with the perpendicular, was very precisely that of 5 to 3, as was found also by Mr. Bartholinus, and consequently much greater than that of Rock Crystal, or of glass, which is nearly 3 to 2.

[Illustration]

12.  The mode of making these observations exactly is as follows.  Upon a leaf of paper fixed on a thoroughly flat table there is traced a black line ab, and two others, CED and KML, which cut it at right angles and are more or less distant from one another according as it is desired to examine a ray that is more or less oblique.  Then place the Crystal upon the intersection E so that the line ab concurs with that which bisects the obtuse angle of the lower surface, or with some line parallel to it.  Then by placing the eye directly above the line ab it will appear single only; and one will see that the portion viewed through the Crystal and the portions which appear outside it, meet together in a straight line:  but the line CD will appear double, and one can distinguish the image which is due to regular refraction by the circumstance that when one views it with both eyes it seems raised up more than the other, or again by the circumstance that, when the Crystal is turned around on the paper, this image remains stationary, whereas the other image shifts and moves entirely around.  Afterwards let the eye be placed at I (remaining always in the plane perpendicular through ab) so that it views the image which is formed by regular refraction of