I might now extend the account of my method of divi ding to a great length, by relating the alterations which the apparatus has undergone during a long course of years," and the various manner of its application, before brought it to its present state of improvement ; but I think I may save myself this trouble, for truly I do not see its use. I will, therefore, proceed immediately to a disclo sure of the method, as practised on a late occasion, in the dividing of a four feet meridian circle, now the property of Stephen Groombridge, Esq. of Blackheath.
The surface of the circle which is to receive the divi sions, as well as its inner and outer edges, but especially the latter, shall be turned in the most exact and careful manner ; the reason for which will be better understood, when we come to describe the mode of applying the roller: and, as no projection can be admitted beyond the limb, if the telescope, as is generally the case, be longer than the diameter, those parts which extend farther must be so ap plied, that they may be removed during the operation of dividing. Fig. I. and 2. Plate CCLXXXIII. represent the principal parts of the apparatus ; Fig. 1. showing the plan, and Fig. 2. the elevation ; in both of which the same letters of reference are affixed to corresponding parts, and both are drawn to a scale of half dimensions. AA is a part of the circle, the surface of which is seen in the plan, and the edge is seen in the elevation. 13B11 is the main plate or the apparatus, resting with its four feet a, a, a, a upon the surface of the are ; these feet, being screws, may be adjusted so as to take equal shares of the weight, and then are fastened by nuts below the plate, as shown in Fig. 2. ('C and DD are two similar plates, each attached to the main plate, one above and the other below, by tour pillars: and in them are centred the ends of the axis of the roller E. F and G are two friction wheels, the latter firmly fas tened to B, but the former is fixed in an adjustable frame, by means of which adjustment these wheels and the roller F. may be made to press, the former on the interior, and the latter on the exterior edge of the circle, with an equal and convenient At the extremities of the axis of the roller, and attached to the middle of the plates C and D, are two bridges c, c, having a screw in each ; by means of which an adjustment is procured for raising or lowering the roller respecting the edge of the circle, whereby the former, having its diameter at the upper edge about .001 of an inch greater than at the lower edge, (being, as before described, a little conical,) it may easily be brought to the position where it will measure the proper portion of the circle.
experience and thought upon the subject have taught me, that the roller should be equal to one sixteenth part of the circle to be divided, or that it should revolve once in 22° 30' ; and that the roller itself should he divided into sixteen parts ; no matter whether with absolute truth, for accuracy is not at all essential here. Each of such di visions of the roller will' correspond with an angle upon the circle of 1° 24' 22".5, or ath part of the circle. This number of principal divisions was chosen, on account of its being callable of continual bisection ; but they do not fall in with the ultimate divisions of the circle, which arc in tended to be equal to 5' each. .
The next thing to be considered is, how to make the roller measure the circle. As two microscopes are here necessary, and those which I use arc very simple, I will in this place give a description of them. Fig. 6. is a section of the full size, and sufficiently explains their construction, and the position of the glasses ; but the micrometer pat t and manner of mounting it, are better shewn at II, in Fig. 1. and 2. The micrometer part consists of an oblong square frame, which is soldered into a slit, cut at right an gles in the main tube; another similar piece nicely fitted into the former, and having a small motion at right angles to the axis of the microscope, has at one end a cylindrical guide pin, and at the other a micrometer screw ; a spring of steel wire is also applied, as seen in the section, to pre vent play, by keeping the head of the micrometer in close contact w;th the fixed frame. This head is divided into one hundred parts, which are numbered each way to 50 ; the use of which will be shewn hereafter. A fine wire is stretched across the moveable frame, for the purpose of bi secting fine clots. Two of these microscopes are necessa ry ; also a third, which need not have the divided head, and must have in the moveable frame two wires crossing each other at an angle of about 30° ; this microscope is shown Tt I, Fig. 1. In the two first micrometers, a division of the head is of the value of about 0".2, and the power and distinctness such, that when great care is taken, a much greater error than to the amount of one of these divisions cannot well be committed in setting the wire across the image of a well made dot. The double eye-glass has a motion by hand, for producing distinct vision of the wire ;. and distinct vision of the dots is procured by a similar ad justment of the whole microscope.