22(5 Mr . Cavendish o» £/zr Manner of 
have a moveable wire with a micrometer, in the focus of the 
microscope, as well as a fixed one ; and then having brought 
the fixed wire to b, bring the moveable one to /3, and observe 
the distance of the two wires by the micrometer ; then reduce 
the distance of the two wires to one fifth part of this, and 
move the frame till the moveable wire comes to /3, and then 
the fixed wire will be in the proper position, that is four times 
nearer to /3 than to b. 
It will be a great convenience, that the moveable wire 
should be made in such manner, as to be readily distinguished 
from the fixed, without the trouble of moving it. 
In this manner of proceeding, I think a careful operator can 
hardly make any mistake : for if he makes any considerable 
error in the distance of the moveable wire from the fixed, it 
will be detected by the fixed wire not appearing in the right po- 
sition, in respect of the two scratches ; and as the mark is seen 
through the microscope, at the same time as the scratches, 
there is no danger of his mistaking which scratch it is to be 
nearest to, or at what distance it is to be placed from it. 
To judge of the comparative accuracy of this method with 
that of bisection, it must be considered that the arches a/3, 
/3 $, &c. though made with the same opening of the compass, 
will not be exactly alike, owing partly to irregularities in the 
brass, and partly to other causes. Let us suppose, therefore, 
that in dividing the arch a a into five parts, the beam compass 
is opened to the exact length, but that from the abovemen- 
tioned irregularities the arches «jQ, (3$, h, and s <p are all too 
long by the small quantity e, and that the arches af,fe , ed y 
and db are all too short by the same quantity, which is the 
supposition the most unfavourable of any to the exactness of 
