394 HOWARD E. PULLING 
tion. Notwithstanding this constancy at each position the variations 
in the readings at different portions of the screw were as large as 17.5 
percent of the smaller number and differences of from 5 percent to 
10 percent were common. Since no attempt was made to search for 
errors of great magnitude and since the object measured was the most 
favorable that could be found (the distance between two points on an 
irregular ink spot, moved with a rectangular mechanical stage) it is 
hardly to be doubted that such an instrument cannot be relied upon 
without investigating it for errors and constructing an error curve, or 
table, for the full extent of the screw. 
Since in designing the angular micrometer each member of the 
filar micrometer was separately considered with reference to its liability 
to structural errors and to its influence upon the observational and 
personal errors of the operator, a brief review of the defects of the 
latter instrument will curtail the explanation otherwise necessary. 
For accurate work, or even for general use with low and medium 
magnifications, the drum graduations are inadequate and an accessory 
scale is required. An instrument of precision should be accurately 
graduated beyond any demands which may be made upon it. 
Because the moving parallel Hnes extend across the field of view 
at right angles to their direction of movement, the fine connecting 
the two points whose spatial separation is to be measured must be 
accurately normal to the moving line. Experiments have shown that 
the line connecting these two points may often be inclined ten or 
fifteen degrees from the normal and the inclination be undetected 
unless the rotation was performed with the visual knowledge of the 
observer. No definite point exists that may be used as a datum point 
because the ends of the parallel fines are rounded and because the 
thickness of the cross Hnes and the sharp angle at which they meet 
prevent the operator from surely placing the point of their intersection 
directly over any particular point on the object-image. Averages of 
several observations are valueless because when one datum point is 
used all the errors tend to have the same sign and hence do not offset 
each other and because no two datum points can be selected which 
have their errors in exactly opposite directions. 
Perhaps it is in part such errors as these that led Farmer and 
Digby^ to adopt the method of drawing the object with a camera 
2 Farmer, J. B., and L. Digby. On dimensions of chromosomes considered in 
relation to phylogeny. Phil. Trans. London, B, 205: 1-25. 1914. 
