ON THE COMPARISON OF LINE AND END STANDARDS. 243 
also, that the plane of the cross-wires coincides with F. Then 
all rays emanating from 0 will converge at F, no matter 
where the points of incidence, A and B, are on the surface of 
the objective. In this case the cutting off of the rays which 
strike the lens at A would not affect the position of the image 
with respect to the cross-wires. 
(2.) If, however, without disturbing the relation 0 C, we 
move the plane of the cross-wires to a' b ', then the image of 
the point 0, formed by rays from A, will apparently be dis¬ 
placed, with respect to the wires, in the direction of A. 
(3.) If, on the contrary, we move the plane of the cross¬ 
wires to a" b", the image formed by rays from A will ap¬ 
parently be displaced, with respect to the wires, in the oppo¬ 
site direction to A. Exactly the same reasoning applies to B. 
In a micrometer microscope the distance between the ob¬ 
jective and the plane of the cross-wires is fixed, whereas the 
distance 0 C is variable, for the reason that it is determined 
solely by estimating when the image, viewed in the plane of 
the cross-wires, has its maximum clearness of outline—that 
is to say, we attempt to make the conjugate focus coincide 
with the plane of the cross-wires. If, however, the distance 
between the observed object and objective were made too 
great, the conjugate focus would fall in front of the plane 
of the cross-wires, and hence the image would apparently be 
displaced, with respect to the wires, in the opposite direction 
to A; and if the distance were made too small, the conjugate 
focus would fall behind the cross-wires, and the image of the 
object would apparently be displaced in the direction of A. 
It is evident from the foregoing that if an observer were 
to systematically focus in such a way as to make the distance 
between the objectives and the points or threads on the ends 
of the bar too great or too small constant errors would be in¬ 
troduced in the comparison; and it was to eliminate this 
source of error that the following arrangement, due to Cornu, 
was used in the International Bureau observations: 
In front of each microscope a movable screen, pierced by 
a small opening, was so mounted that the opening could be 
