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XIV. On a Method of examining the Divisions of astronomical 
Instruments. By the Rev. William Lax, A. M. F. R. S. 
Lowndes's Professor of Astronomy in the University of Cam- 
bridge. In a Letter to the Rev . Dr. Maskelyne, F. R. S. 
Astronomer Royal. 
Read June 1, 1809. 
Dear Sir, 
St, Ibbs, Aug. 27, 1 80S. 
I am persuaded that you must feel, in common with myself, 
how unpleasant it is to make use of an instrument in astrono- 
mical observations requiring extreme accuracy, whose exact- 
ness you have no adequate means of ascertaining, but are 
obliged to depend for it in a great measure upon the abilities 
and integrity of the artist. It is in vain that we observe with 
so much nicety, and read off with so much precision, if we 
are still uncertain whether there may not be an error in the 
instrument itself of much greater magnitude, than those which 
we are endeavouring to prevent ; and that our best instru- 
ments must be liable to such errors, no person can possibly 
doubt, who lias paid due attention to the sources from whence 
they may arise. I have estimated, as accurately as I could, 
the amount to which they may accumulate in Bird’s method 
of dividing by continual bisections, and have satisfied myself 
that they are much more considerable than is generally ap- 
prehended ; but as I cannot obtain such precise information as 
I could wish, respecting the exactness with which a bisection 
can be performed, or a length taken from the scale of equal 
