326 F. E. Wriqkt — Measurement of the Optic Axial Angle 



field (F of the figure) and to adjust the lenses for these points 

 in order that the remainder of the field be as distinct as possi- 

 ble under the circumstances. 



In order to minimize the error due to the slight parallax of 

 rays near the margin of the field, a small stop, S, may be 

 placed above the ocular as shown in the figure. 



The exact position of any point in a given interference 

 figure can be determined with considerable accuracy by using 

 either a micrometer ocular with fixed scales or movable screw 

 micrometers, or by means of a projection by camera lucid a 

 on paper. The actual position in space of any point thus fixed 

 in the projection can then be stated if the relation between 

 projection and object be known. 



In 1882, Mallard* proved theoretically that the interference 

 figure observed in the microscope is approximately an ortho- 

 graphic projection of the optic phenomena in space. To take 

 the simplest case, let both condenser lens and objective consist 

 each of a simple hemispherical plane convex lens, C and O, 

 fig. 5. The rays which in the objective lens are parallel come 

 to a focus at F, where they can be viewed directly by the 

 unaided eye. Assuming the radius of the lens to be r, the 



T 



radius R (MF, fig. 5) of the focal circle is evidently— — , where 

 - ' " n — 1 



n is the refractive index of the objective lens glass. It should 

 be noted that under the microscope the optic phenomena 

 are observed as they appear in the objective itself, i. e., modi- 

 fied by their refraction in the glass. The distance 



EF = d = R sin < EMF (1) 



Replacing < EMF by its corresponding angle in air, E, the 

 relation between which is expressed by sin E = n. sin < 

 EMF, equation (1) can be written 



EF = d = — . sin E. (2) 



n 



By fixing rigidly the relative positions of objective, Amici- 

 Bertrand lens and ocular (fig. 5), the distance d for all angular 

 values E, which can be measured in the microscopic field, 

 bears a constant relation to D of the secondary interference 

 figure 



D = hd (3) 



This distance D can be measured accurately with the movable 

 screw micrometer ocular. Substituting D for d, equation (2) 

 becomes 



*E. Mallard, Bull. Soc. Min. Fi\, v., 77-87, 1882. 



