76 On a Possible Explanation of the Method employed by Nobert 
stage micrometers furnislied by dealers in microscopes, and I find 
the usual range of error to be between and r-oi^o of an inch. 
Of course the average error may fall far within these limits ; 
and, especially when the lines are closely ruled, the individual errors 
may seem by comparison insignificant ; but I have been unable 
to find any rulings which invariably surpass the limit which I have 
named. As an illustration of the limit of accuracy attainable, I 
give in Tables I., II., and III., measurements of an excellent Nobert 
diffraction plate, a Kutherford difi'raction plate, and a plate ruled by 
myself for the purpose of investigating the errors of my screw. The 
measures were all made with a iVth objective, and an eye-piece 
micrometer, 200 to the inch, the lines of which were about tAo-(j 
of an inch in breadth. Using a B ocular, the value of one division 
was found to be ts^o o of an inch. With this arrangement, it was 
found easy to measure any given space to sowtf of an inch with 
considerable certainty. To eliminate errors in the micrometer, the 
same divisions were used in all comparisons. In the Nobert plate, 
the width of the lines is about y^iir o of an inch ; in the Kutherford 
plate, of an inch ; and in my own, ^y^-o of an inch. The 
space measured was sixr of an inch. 
Table I. contains the residuals obtained by subtracting the 
measure of each space from the mean of all the spaces. 
Table II. contains the residuals obtained by subtracting the error 
of each space from the error of the next consecutive space. 
Table III. contains the periodic errors deduced from Table I. 
It is quite evident that in the three cases under consideration, 
there are numerous accidental errors amounting to ^olop i^^^ 
and more, while in the last case the evidence of periodicity is very 
decided ; its value at the maximum point being ^^^Vf of an inch. 
An examination of the values in Tables I. and II., column III., will 
show how easy it is to be misled by a seeming accuracy when 
only consecutive spaces are measured. It is only when the errors 
become magnified by successive increments that they attract 
attention. 
The following will be found a very convenient and accurate 
method for measuring directly the magnitude of the periodic errors. 
First, a series of equidistant lines is ruled on thick glass, care 
being taken to use glass having a plane surface. It is better also 
to have the spaces correspond to equal parts of a revolution of the 
screw. On one side a heavy finding line is ruled. This band is 
then reproduced on microscopic cover-glass, having a thickness of 
2^'[)out of inch. Of course care is taken to use the same part 
of the screw, and the same divisions of a revolution as before. By 
cementing the glasses together with balsam, face to face, but with 
the finding lines on opposite sides, the periodic errors, if they exist, 
will appear under the microscope with twice their real magnitude. 
