Gabbroid Rocks of Minnesota. — \ Vinchell. 239 
mum birefringence is greater in the Minnesota feldspar, but 
the difference is only slight. 
The mineral is positive, since {ng-Jim ) is greater than (/,!m- 
Angle of the optic axes. The value of the true angle of the 
optic axes calculated by the aid of the formula: 
nm 
tan 2 V 
gives the following results: 2Va-^82° o'. 
The direct measure of the optic angle was made from two 
sections perpendicular respectively to «g and ;/p with the con- 
ventional apparatus. The sections were immersed first in es- 
sence of cinnamon with an index for sodium light of 1.609 ^'^'^ 
then in distilled water. While this method gives the best re- 
sults at present known, it is not possible to avoid a maximum 
possible error of about 20', and, with only ordinary precau- 
tions, this may easily rise to 30' or 40'. Monochromatic light 
was used: sodium for yellow, lithum for red, and thallium for 
green. It was found that the measured value of the optic an- 
gle varies in dififerent parts of a single crystal, since successive 
measures in the same spot showed variations not exceeding 
ten minutes, while measures in different parts of a single crys- 
tal varied as much as 30' or 40' (in measuring the obtuse angle 
even rising sometimes to one degree). Since the crystals show 
no sign of a zonal structure, nor any variation in extinction 
under the microscope, it is probable that the variations are due 
either to the existence of thin twinning lamellae, or to defects 
in the preparation or adjusting of the section.* Therefore in 
order to obtain comparable values for the different colors, the 
optic angle was measured on the same spot with thallium, lith- 
ium, and sodium successively. The results may be tabulated 
as follows: 
Thallium Sodium Lithium 
2 Ha = 8i\36' 82^0' 82°24' 
2 Ho = 9i 10' 94' 0' 93^43' 
Whence from the formula: tan Va = ^'|| y^ - 
2Va = 83 29' 83' 47' 84 °9' 
*Mallard has shown (sec Traite de Crystallographie II. p. 431) tliat 
if the section varies 2° from the plane perpendicular to the bisectrix, 
it will cause an error of 40' in the value of 2E in the case of pyroxene. 
