148 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
not be eliminated. Still other factors enter into the formation of the inter- 
ference figure, which are difficult to control and which tend to modify the 
figure to some extent, with the result that all measurements on interference 
figures are encumbered with a relatively large probable error exceedingly 
difficult to reduce under the ordinary conditions of observation. 
As the surface, on which the interference figure is formed (upper focal plane 
of the objective), is not a flat but a curved surface, it is necessary to focus 
the secondary microscope, consisting of Bertrand lens and ocular, on points 
midway between the center and margin of the field and also to use two small 
aperture stops, one in the eye-circle of the ocular and the second either 
directly in front of the Bertrand lens or in its upper focal plane, in order to 
reduce the parallax and to increase the depth of focus of the secondary 
microscope. With these precautions the interference figure appears fairly 
sharp, even though magnified up to 15 diameters. 
Different methods have been suggested for determining the exact posi- 
tion and angular equivalent of any point in a given interference figure. 
These methods consist in introducing scales of definite construction and 
value, either in the average plane of the interference figure itself or in one 
of its conjugate planes, and then ascertaining the angular equivalent of the 
divisions of the scale by means of minerals whose optic axial angle is known 
or by use of the apertometer. Having once determined this relation be- 
tween the scale and its angular equivalents, the angular position of any point 
in the field is ascertained by direct observation with the scale. The con- 
version of the scale divisions into their angular equivalents is accomplished 
ordinarily by use of the Mallard constant of the microscope or by direct 
calibration of the scale by use of the apertometer, as first suggested by Dr. 
J. S. Flett. 
THE MALLARD CONSTANT. 
"/- In 1882 Mallard* proved that the interference figure observed in the 
microscope is approximately an orthographic projection of the optical 
phenomena in space. In the measurement of optic axial angles only a low- 
power auxiliary microscope (magnification 3 to 15 diameters) is used; the 
rays from the interference figure which pass through the microscope sub- 
tend only a very small angle and may be considered practically parallel. 
The distance, therefore, of the different points in the interference figure from 
the center of the field is approximately the sine of the angle which the rays 
forming these points include with the axis of the microscope. It should be 
noted that these optic phenomena are observed as they appear in the ob- 
jective itself, i.e.. modified by their refraction in the glass. 
The actual distance d of a point in the interference figure is accordingly 
proportional to the sine of the angle which the ray it represents includes 
with the axis of the microscope ; this angle can be reduced to its equivalent 
angle E in air by means of the refractive index of the glass, \\ Ink- the dis- 
tance D, as observed in the ocular.is the magnified image of " </." If .I/be the 
magnifying power of the auxiliary microscope, then D = M . d = sin E, 
n 
or D = K sin E, wherein K is the Mallard constant of the microscope for 
the fixed position of the optical system used in the observations. 
B. Mallard. Bull. Soc. Min. Fr.. S, 77-87. 1882. 
