Account ^Huygens’ Theory of Double Redaction. S81 
VC : CD = N : GC, but VC : CD = BV : DS. Let ML be 
drawn perpendicular to CL, then, as formerly, we may consider 
BV =r CG, and DS a third proportional to N and CG. Hence, 
DP = CL. But since CG = 98778, CM being 100000, N is - 
150962. M^hence DS - 62613, but CL = 99324, consequent- 
ly PD : DS — 99324 ; 62163, and, therefore, the elevation of I 
by refraction is known, and is greater than in the section AH, 
Fig. 1. 
. But by the regular refraction of the crystal which was the 
value of 5 to 3, the elevation of the point I or P will be | of 
DP, as appears from Fig- 4., where P being seen by the rays-, 
PCR, cr equally refracted at the surface C c, it will appear 
at S in the perpendicular PD at the intersection of BC, re; 
and it is known that PC : CS=:::5: 3, since PC : CSrrsiu 
eSP or DSC : sin SPC. Since the eyes at R, r are supposed to 
be at a considerable distance above the crystal, we may reckon 
PD : DS = PC : CS, and, consequently, the elevation PS will 
also be f of PD. 
If we take a straight line AB, Fig. 5., for the thickness of 
the crystal whose bottom is at B, and divide it, in the ratio of 
the elevation above determined, at the points C, D, E, making 
A = f AB ; AB : AC rr: 99324 to 70283; and AB : AD = 
99324 to 62163, these points will be as in the figure, and will 
accord with the results of observation. That is, when the eyes 
are in the plane EF, Fig. 1., or the short diagonal of the 
rhomb, the regular refraction will raise the letters to E, Fig. 5. 
and the irregular refraction to D ; and when the eyes are in the 
plane AB, Fig. 5. the regular refraction still raising the letters 
to Ej Eig. 1. the irregu ar refraction mil raise them only to C, 
the elevation CE being quadruple of ED. 
In all other positions of the eyes, the unusual image does not 
appear directly above the usual one, but separates from it, be- 
ing removed farther from the equilateral solid angle of the crys- 
tal. In these cases, the unusual image of P will have an ele- 
vation intermediate between BC and BD. 
We shall now proceed to point out the method of finding the 
unusual refraction in all other sections of the crystal beside the 
two we have considered. Let us take any face of the crystal 
in which is the ellipse HDE, (Fig. 6.) whose centre is also the 
