. 598 The American Naturalist. [July, 
mula 2CaO, 2MgO, H,O, AsO, The symmetry of the mineral is 
monoclinic and its relationships, both chemical and crystallographi- 
cal, are with triploidite, wagnerite and sarkinite. 
Optical Methods :—Friedel? has devised a new method for deter- 
mining the double refraction in thin sections of minerals on the stage 
of the ordinary petrographieal microscope. The method makes use of 
the quarter undulation mica plate. The nicols are crossed and the 
slide is raised a short distance above the stage on thin blocks, so as to 
allow of the introduction of the mica plate between the slide and the 
stage. The stage is now revolved until the directions of extinction 
make 45° with the principal sections of the nicols. The mica plate is 
introduced below the slide and carefully turned without moving the 
stage until that portion lying outside the mineral plate is extinguished. 
By now revolving the polarizer, the mineral can be extinguished or 
given the same illumination as the mica plate. The observations are 
made in monochromatic light. If the positive direction of the mineral 
plate passes through the upper right quadrant of the field and the 
positive direction of the mica plate coincides with the vertical cross 
hair, the polarizer should be revolved to the right, the angle v required 
to produce extinction, and the angle e, required to produce equal 
illumination of mineral plate and mica plate, yielding ¢ the difference 
in phase produced in the mineral section. The forutulas are ó— e, 
and /—2e, The greater part of the paper is devoted to methods of 
evaluating errors in the process. 
Harker* has determined trigonometrically the values of the extinct- 
ion angle in prismatie cleavage flakes of augite and hornblende, as 
dependent on the optical angle and the extinction angle in the plane 
of symmetry. His tables of values will be convenient for reference, 
but as he points out, the variation in the values with 2V is not great 
enough to determine the optical angle from measurements of the pris- 
matic and clinopinacoidal extinction angles. 
Isotypism :—Rinne’ compares crystals of the metals with crystals 
of their oxides, sulphides, hydroxides and haloid compounds. He 
points out that in this comparison we find strikingly close relation- 
ships between bodies markedly different chemically, and these relation- 
ships do not consist simply in identity of crystal symmetry, but in 
*Bull. Soc. Franc. Minér., XVI; 19 (1893). 
*Min. Mag., X (No. 47), p. 239. 
5Neues Jahrb. f. Min., etc., 1894, (I) pp. 1-55. 
