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A description of the instrument from Thacher's manual


Thacher's Calculating Instrument

The instrument consists of a cylindrical slide provided with a knob at each end, and which admits of both rotary and longitudinal movement, within an open framework or envelope of equidistant bars of triangular section. The bars are connected to rings at their ends, which admit of rotation within standards attached to the base. The surface of the slide is exposed in the openings between the bars, the lower edges of which are in contact with it. The diameter and length of slide and the number of bars may be varied at pleasure, but in the present instrument the slide is four inches in diameter and has a divided length of eighteen inches, and the envelope contains twenty bars. Upon the slide are wrapped two complete logarithmic scales, one on each side of the centre. Each scale from 100 to 1000 is divided into forty parts of equal length, the number of parts equals the number of exposed sides of the bars, and the length of each is one-half the graduated length of the slide. These parts follow each other in regular order around the cylinder, both on the left and right, and those on the right follow those on the left in regular order. The figures and divisions which constitute any part on the right are repeated on the left one line in advance. All figures and divisions on the scales are made to face both ways, that they may be read from either edge of the bars.

Upon the lower lines of the bars, and in contact with the slide, are two other scales of the same length and arranged in the same manner as those on the slide, there being a complete scale both on the left and right of the centre. When the commencement of the scales on the slide and envelope are in contact all divisions on the one are opposite corresponding divisions of the other. Upon the upper lines of the bars, and not in contact with the slide, is a scale of roots. This scale is double the length of the others, and is divided into double the number of equal parts. It occupies the entire upper part of the bars, both on the left and right of the dividing centre line. These parts are laid off in regular order, and in such manner that any number on the lower line of bar is the square of the number opposite to it on the upper line, and any number on the upper line of bar is the square root of the number opposite to it on the lower line. For numbers having 1, 3, 5, etc., or an odd number of places, their roots are found on the left, and for numbers having 2, 4, 6, etc., or an even number of places, their roots are found on the right. By the rotary movement of the slide any line on it may be brought opposite to any line on the envelope, and by the longitudinal movement any graduations or subdivisions of these lines may be brought opposite to, or in contact with, each other. One-fortieth of a revolution is equivalent to nine inches of longitudinal movement.

When the slide is set in position for use the divisions on it appear of about equal length on both edges of the bars, and two lines of figures marking their values appear in each opening between the bars, two similar lines also being covered by each bar. The divisions on the upper lines are transferred to the slide by means of a pointer fitting over the bars. This pointer is also convenient for retaining the position of any division on either line while the slide is being revolved into the required position.

Near the commencement of each scale on the envelope and slide is a heavy black mark, designed to readily catch the eye during the rapid movement of the parts. The former will be found to expidite multiplication, and the latter division.

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