weight: petrographic microscope 471 



of agreement with foregoing readings. Only in this way can a 

 proper random distribution of errors be obtained which will fur- 

 nish a good probable value. 



To apply this principle to the measurement of extinction angles 

 a simple flexible arm of brass was cut out and attached by means 

 of tightly fitting plugs into the clip holes on the microscope stage 

 (fig. 1, D). At the other end of the arm a needle point is sol- 

 dered. To record a setting, a mark by the needle point is made 

 in a sheet of millimeter cross section paper mounted in proper 

 position on a block of wood (shown greatly foreshortened in fig. 

 1). A convenient length of radius to use is 28.66 cm; each degree 

 on the arc of the circle ^s then 5 mm. and readings can readily 

 be made to tenths of a degree and even to fiftieths. 



Experience with this simple device which can easily be made, 

 in an hour has shown that much time can be saved by its use. 

 Settings are made by simply pressing down the needle and no 

 readings are required. A number of settings are made with 

 clockwise rotation of the stage, and an equal number with counter- 

 clockwise rotation. By reference to the graduated circle on the 

 microscope stage the angular position of the average position of 

 the points punched in the paper can be read off directly and with 

 it the most probable extinction position. Experience has shown 

 that the eye can estimate the average center of a series of points 

 grouped about the center with sufficient accuracy for practical 

 purposes. The actual angular position of each point can, of 

 course, be ascertained and an arithmetical average then taken, 

 but for most purposes this is unnecessary. 



It is of interest to note that the mean position of clockwise 

 rotation may be situated a whole degree away from the mean 

 position of counter-clockwise rotation, thus showing the import- 

 ance of making measurements by approaching the position of 

 extinction from the right and from the left as well. The above 

 device is useful also in enabling the observer, especially if he be 

 a student, to ascertain the probable error of the single settings 

 and at the same time to increase the precision of his measure- 

 ments without extra labor. 



