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A new Instrument for comparing Linear Measures. 127 
may rest against the fixed stud, and its other end in contact with 
the moveable one; the whole being so disposed, that the axes of 
the rules, the axis of the linear measures, and the middle points 
of the divisions on the glass are exactly in right lines. The mi- 
croscope held by the same board, or the same table on which 
the other pwts of the apparatus and the linear measures are 
laid, must be so pointed to one of the divisions on the glass, 
that after some preliminary trials, or first: approximative data, 
on the ratios of'the linear measures, we may be certain that the 
_ second measure to be compared, when we have made the same 
dispositions respecting it, will bring the 100dths or 200dths of a 
millimeter under a stroke, which is afterwards to be determined 
when placed in the focus of the microscope; which microscope, 
when the collimation has been established, with respect to the 
beginning of the divisions, must be kept immoveable during the 
comparison of the two linear measures. 
The apparatus is to be disposed in such a way, that the glass 
carrying the divisions may be placed between the reflecting mir- 
ror of the microscope and the object lens ; and if we wish to 
adjust the focus-line to the line at the beginning of the divisions, 
we make the supports of the microscope to abut against the point 
of a fixed horizontal screw and nut ; this support being made to 
slide along a rule parallel to the linear measures. The parallelism 
between the focus-line and the strokes of the division is easily 
obtained by the hand, by causing the microscope to turn round 
in the circular horizontal ring in which it is inclosed. 
The collimation of the focus-line with one of the strokes on 
the divisions on the glass being thus well established, we remove 
the first linear measure, and replace it with the second, by rest- 
ing the moveable stud against one of its ends, and making its 
other end to abut against the fixed stud. The point of collimation 
will change, if the measures are not equal; and their difference 
of length will be given by the quantity that the second measure 
shall have removed the first stroke of the divisions from the divi- 
sion on which the collimation was established for the first ; which 
guantity of removal is measured by the number of millimeters, 
and 1 00dths of a millimeter, contained between the two successive 
points of collimation. 
I return to the line placed in the focus of the microscope. It 
is easy to conceive the extreme fineness that this line must have, 
since it ought to appear on the space contained between two 
consecutive divisions on the glass; which spaces are 10Qdths of 
millimeters, and so as to permit their evaluation by estimation 
to 1000dths of a millimeter. I believe it would be in vain to at- 
tempt to pérform this by placing a wire in the foeus; and that 
the finest of those that are commonly adapted to telescopes, 
either 
