This section is from the book "The Engineer's And Mechanic's Encyclopaedia", by Luke Hebert. Also available from Amazon: Engineer's And Mechanic's Encyclopaedia.

An instrument used for protracting, or laying down on paper the angles of any figure. The protactor is commonly a small semicircle of brass, nicely divided it into 180 degrees; the ends of the arch are connected by a straight rule, the outside edge of which is the diameter of the circle. It serves not only to draw angles on a plane, but likewise to examine those laid down. For this purpose, there is a small point in the centre or middle of the edge of the straight rule, which point, being placed upon the vertex of the angle and the edge of the rule, so as to coincide with one of the sides of the angle, the other line of the angle then cuts through the number of degrees marked on the protractor, which is its true measurement. Protractors are now usually made in the form of a parallelogram, and graduated with diverging lines from a central point upon one edge, to the opposite edge where the degrees are marked.

Mr. Twitchell's improved protractor is stated in the Franklin Journal to consist of a circle, marked with the lines of sines, tangents, secants, semi-tangents, and chords. To the centre of the circle is annexed a scale of the shape of half a cross, agreeing with the line of chords on the circle, and marked on each limb with the line of equal parts. The cross limb of this scale consists of two parts; to one of which is annexed a semicircle, marked with the line of chords, the other part turning on its centre, and agreeing with the line of chords on the semicircle, serving both as a protractor and scale. To the centre of the whole circle is annexed a small limb, agreeing with the line of chords on the circle, and extending over the scale, and serving as a secant to the circle. This scale exhibits the use of chords, sines, secants, and tangents, and the mode of applying them to angles, giving the sides and chords of any triangle, and also its sine, tangent, and secant; likewise latitude, departure, course, and distance. For drafting, this scale is particularly useful; for in plotting, nothing more is required, than to turn the scale to the course, and mark the distance.

The correctness of the description thus given of the instrument by Mr. Twitchell, is corroborated by the valuable testimony of the learned editor of the Journal, Dr. Jones, who remarks in a note, that the instrument, "in addition to the purposes indicated," will be found "particularly useful in teaching trigonometry, as it renders the relationship of the angles objects of sense."

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