instead of having points like the beam compass, has two micrometer
microscopes adjustable to different distances, as aliquot parts of an
arc or line to be divided. For the purpose of marking on the surface
of the instrument any assumed interval between the microscopes,
certain thin pieces of small brass, carrying dots, are employed, with
a. clamp for fixing them to any part of the limb, and with proper
screws for adjusting them to any precise position.
In addition to these, which are adapted for finding aliquot parts of the circle under division, the apparatus is provided with a cutting point of the usual construction, and a third microscope fixed always in the same position, for the purpose of observing a certain line first laid down as a permanent point of reference, and for watching the performance of the cutting-point, while it marks the successive in- tervals, determined by means of the two adjustable microscopes.
As a specimen of the method in which this apparatus is to be used, the author describes the series of divisions and subdivisions which he thinks most convenient in a circle of two feet diameter.
He first divides into five parts of 72° each.
At the same time that the fixed microscope is kept steadily over the original line of reference, two adjustable dots are placed, by esti- mation, at the distance of 72° from each other, and in such a position with reference to the cutting-frame as not to interfere with its motion. The two adjustable microscopes having next been placed so that their wires exactly correspond with these dots, the circle is made to re- volve so that the second dot shall come under the first microscope when a third dot is to be placed under the second microscope; and in the same manner a fourth and a fifth dot in succemion, ti]l the fifth interval can be compared with the distance between the micro- scopes, when the first dot should be found to correspond exactly with the second microscope : if it be otherwise, the difference must be measured by the micrometer; and the distance between the twu mi- crometers, originally assumed at 72°, must be corrected by one fifth part of the error so found, and must subsequently be ascertained to be correct, by a careful repetition of the same operation of the ad- justable dots. When the fifth interval has thus been made accurately to correspond with that between the adjustable microscopes, the ori- ginal point of reference is then to be returned to its position under the fixed microscope, and the divisions are to be marked in succession as the series of dots are made to appear under the wires of the ad- justable microscopes, which are now known to be accurately 7 2" from each other.
The next step taken is to divide each of these intervals into three parts of 24 each, and again trisect into parts of 8°. These, by re- peated bisection, are reduced to half degrees; and these again, by trisection, are divided into spaces of 10’ each.
In the performance of the latter steps of this subdivision, the author suggests the periods when it maybe found convenient to bisect some larger odd number of divisions, instead of taking a single one for bisection, on account of the interference of the microscopes with each
