10.) so placed that only one pair should be in the fiz1.1 of view at it time, and that the least angle of the second pair should be equal to the greatest angle of the first pair, and the least angle of the third pair equal to the greatest angle of the second.
When the micrometer is constructed on these princi ples, it is certainly free from almost all those sources of error with which the wire mictometer is affect& d. The imperfections of the screw, the errors at isin,.; from the uncertainty of the zero, from the bad ctntern g of the lenses, from the want of parallelism in the wires, and from the minuteness of the scale, are completely removed. Nay, if the scale is formed by direct expe riments, whatever eirors may exist in tile instruntent are actually corrected; for as the sources front which these errors proceed existed in the instrumcnt during the formation of the scale, they cannot possibly affect the result of any observation. The scale is in fact the record of a series of experimental results, and the ob servation must be its free front error as the experiments by which the scale was formed. It would, therefore, be of great advantage, in inicrometrical observations, to make the points 13, C, (Plate CCCLXXV. Fig. 11,) with which the wires appear to come in contact, as lu minous as the objects to which it is intended to apply the instrument, or rather to hate a series of results for objects of various degrees of illumination.
In the preceding micrometer, the angle of a pair of fixed wires is increased and diminished by the motion of a second object•glass along the axis of the telescope ; while, in the present instrument, the variation of the angle is effected by separating the two parts which com pose an achromatic eyepiece ; or, whet; the eye-piece consists of two or three lenses, by separating ,the lens next the eye from the remaining lenses.t If the small tube, which contains the field-glass and the first eye glass, be pulled out beyond its natural position, the mag nifying power of the instrument will be increased; and if the same tube be pushed farther in than its natural position, the magnifying power will be diminished. It will be found, in general, that if the tube already men tioned be allowed to move over the space of four inches, that is, about two inches on each side of its natural po sition, the magnifying power at one extremity of this space will not be very far from double of what it is at the other extremity.
The eyepiece micrometer is represented in Plate CCCLXXV. Fig. 12. with all the lenses in their natu ral position. The part AFG, containing the two lenses A, C, is fixed to the telescope, and a space is left be tween the tube AC and the outer tube, in order to per mit the moveable part of the eye-piece to get suffi ciently near to the lens C, and also to a sufficient dis tance from it. The other tube DB, containing the field glass D, and the first eye-glass 13, is moved out and in by a rack and pinion E. The scale is engraven upon the upper In, and the divisions are pointed out by the index of a vernier placed at the extremity ni of the outer tube FG. The zero of the scale is the point marked out by the index of the vernier, when the tube DB is pushed in as far as possible ; and the divisions may be road off, if necessary, by means of a convex glass at fixed to the tune AFG.
The value of the scale of this micrometer may be de termined by direct experiment, by the methods which have already been described.
The following method, however, is more simple, and perhaps equally accurate. After having found the greatest angle subtended by a pair of wires, placed in the focus of the eye-glass, or the angle when the index is at the zero of the scale, by the method in p. 224, note, take the eye-piece out of the telescope, and having push ed the tube Iv hick contains the moveable lens or lenses as far in as possible, direct it as a microscope to a scale minutely divided.* Mark the position of the index when the wires comprehend exactly a certain number of these divisions, say 50, which they may be made to do, by a very trifling motion of the moveable tube, and make this point the zero of the scale. Let the moveable tube be now pulled out till the wires successively compre hend 48, 46. 44. 42, &c. of the divisions, or any other numbers, diminishing in arithmetical progression, and mark these pones upon the tube. By this means, a scale will be formed, in which the divisions correspond to equal variations in the angle. If it should be found convenient to divide the scale into equal parts, the value of the divisions may be found in the same way.