For the sake of rendering the scale more accurate, a similar method was in fact pursued with several gold wires of different sizes, weighed with equal care; and the subdivisions of the exterior scale were made to cor respond with the average of their indications.
In making use of this micrometer for taking the measure of any object, it would be sufficient, at any one accidental position of the tube, to note the num ber on the outside as denominator, and to observe the number of divisions and decimal parts which the sub ject of examination occupies on the interior scale as numerator of a fraction, expressing its dimensions in proportional parts of an inch ; but it is preferable to obtain an integer as numerator by sliding the tube in ward or outward, till the image of the wire is seen to correspond with some exact number of divisions, not only for the sake of greater simplicity in the arith metical computations, but because we can by the eye judge more correctly of actual coincidence than of the conparative magnitudes of adjacent intervals. The smallest quantity which the graduations of this instru ment profess to measure, is less than the eye can really appreciate in sliding the tube inward or outward. If, for instance, the object measured be really 930,, it may appear or in which case the doubt amounts to part of the whole quantity. But the difference is here exceedingly small in comparison to the extreme division of other instruments where the nominal extent of its power is the same. A micrometer with a divided eye-glass, may profess to measure as far as of an inch ; but the next division is or and though the eye may be able to distinguish taut the truth lies between the two, it receives no assistance within k part of the larger measure."—Phil. Trans.1813, p. 119.
In this ingenious instrument, where the variation of the scale is produced by placing the scale of wires at different distances from the observer, it is necessary that the scale be viewed by the naked eye, which by its adapting power can command distinct vision of it at different distances. \Ve conceive, however, that it would be of advantage to have the scale at a per manent distance, and to view both the scale and the object to be measured with the aid of a lens, which may be easily done by placing a lens upon the small perforation. In this case it would be necessary to ob
tain a variation of the scale by means entirely different from those adopted by Dr. Wollaston.
A micrometer founded upon these principles has been proposed by Dr. Brewster, and may be easily con structed by a slight a•Idition to a good kaleidoscope. Let ABC (Plate CCCL XX VI. Fig. 24.) be the aperture of the reflectors, and let a b, d c be the portion of a wire of an inch in diameter, that is seen directly through the aperture. When the wire is perpendicular to the reflector BC, its image b c, of will coincide with the wire itself, and form an exact continuation of it. If we now turn round the cap till the wire comes into the position a' b', d' e', its reflected image 6' c', c' f' will be inclined to the wire, and the thickness b' t' , or the oblique section of the wire, will be to its thicknes b e ur yell of an inch as the secant of the arch (A) through which the wire has passed in going from the position a b, d e into the position a' b', d' e', is to 1, that is b' e X sec. sec. A. In this way the thickness of any wire may be made to vary and form a scale by which any other object may be mea sured by projecting against it, if it be very minute, and by juxta position if it is nearly of the same size. The unit of the scale, or a b d e, may be either a wire as al ready mentioned, or a luminous aperture, or the interval between two wires ; and in order that the arch A may be always small, in which case the secants vary slowly, different units or standards may be fixed upon the cap of the instrument, which is divided into degrees for the purpose of measuring the arch A.
When the object is very minute, it must be placed in the focus of a magnifying lens, while the eye looks at the scale either through a perforation in that lens, it it has a considerable focal length, or at its side, if it has a small focal length. If the object is not microscopical, as ABCD, it may be measured by introducing it at the object end of the instrument, and having raised the standard scale a in n d till its oblique section in n is ex actly equal to the diameter of the object ABCD. It is unnecessary to enter into any farther details respecting this instrument, as our only object at present is to ex plain the principle on which it is founded.