DOUBLE REFRACTION IN ISOMORPHOUS SUBSTANCES. 281 



of phosphate, base to base, in a hemitropic position, and thus 

 found that the inclination of the bisecting hne to the normal of 

 this base P amounts to 64° 35', to the normal of d 1 18° 7' ; since 

 the normals of P and d make with each other an angle of 53° 32'. 

 This result differs but little from that obtained by Mr. Miller ; 

 and further, from the extremely feeble double refraction, the 

 experimental examination is not very delicate. 



Double sulphates of potash or ammonia with sulphates of the magnesian series. 



BO, SO^ MgO, S03 + 6H2 O. 



This numerous family of isomorphous salts is remarkable on 

 account of the almost complete similitude of the crystalline 

 forms ; I took as the type of the class the sulphate of manganese 

 and potash, which presents the greatest number of faces. 



The figure (PI. IV. fig. 8) represents an orthogonal projection 

 of half of the faces upon a plane normal to the horizontal diagonal 

 of the base. 



The symbols of the faces are respectively — 



P 001, H 100, G 010, M 110, y 120, g 130, 

 OTOI, K 101, T 201, E Oil, b Til, a 111, 

 c 311. 



In the salts belonging to this family, the plane of the optical 

 axes is normal to the horizontal diagonal of the base, and the 

 axes of elasticity have very nearly the same direction, their 

 bisecting line being always included within the obtuse angle of 

 the normals to the faces H and P, and lying tolerably near to 

 the former. I have determined its direction by the first or the 

 second method, sometimes by both ; but as the frequent descrip- 

 tion of the same operation would involve much repetition, I will 

 once for all lay down a literal notation for the angles, and will 

 limit myself to giving for each separate experiment the numerical 

 value of these letters. 



First Method. — The crystals being always cemented together 

 by their bases P, — 



a represents the obtuse angle included between the normals 

 to the faces H and P; 



6 the angle which the bisecting line makes with the second of 

 these normals ; 



SCIEN. MEM.— A'af. Phil Vol. I. Part IV. X 



