246 New Protractor for Trisecting Angles. 



of these separate pieces may be found cumbersome and in- 

 convenient. I suppose the present combination to possess cer- 

 tain advantages. The body of the protractor, then, is a semi- 

 circle of metal or of ivory and of any diameter. . A diameter 

 of four inches, is about the most advantageous, for if it be 

 much larger, it leads to the necessity of prolonging the line of 



the given angle — an operation not merely imposing additional 



trouble but introducing occasion for inaccuracy : and if it be 

 much smaller, the possible error masked in the apparent coinci- 

 dences becomes of course proportionally greater. There is no 

 graduation on the protractor; only its centre is marked with A, 

 for precaution and reference. At C, as nearly as possible in the 

 intersection of the diameter and circumference, is centred the pin 

 or journal on which the movable arm works ; and the center 

 should be marked here for the same motive as at A. The mova- 

 ble arm itself is a cylindrical steel wire, eccentric to its axis but 

 parallel to the geometrical radius ; and on it, slides, retained by 

 two straps and hugging by a longitudinal faint spring inlaid be- 



neath and not visible from above, the ivory scale A'EC 7 of such 

 width and so adjusted as that its fiducial edge shall coincide with 

 any radius drawn from C and having the length of the original ra- 



dius A'C marked with a fine perpendicular notch through and 

 through. This notching instead of simply cutting on the surface, 

 is to avoid parallax and to compensate for the obliquities of inter- 

 section, as well as to allow the point A 7 to be pricked on the paper 

 or board, not external to, but in the actual line of the radius from 

 C. The proper horizontally of the scale necessary to maintain 

 the coincidence of its fiducial edge with such a radial line, is as- 

 sured by the constant contact of its lower face with the plane sur- 

 face of the limb (or if necessary of the diameter, through its 

 whole extent) of the protractor. 



After this description of the parts of the instrument and their 

 adjustment, the mode of its use is very apparent. It is only 

 necessary from the vertex of the angle given on the paper or the 

 board to lay off on each leg a distance equal to the radius of the 

 protractor ; to draw a line joining the points respectively termi- 

 nating such distance ; and to lay the protractor so that its centre 

 coincides with the terminal point on the left of the vertex and 

 its fiducial diameter with the angular leg, when the point C will 

 of course be adjusted to the vertex of the angle. Then holding 

 the protractor firm to its place with one hand, with the other move 

 at once both the revolving arm and the sliding scale until the 

 base of the triangle and the edge of the protractor are seen at the 

 same time through the notches A 7 and C . A fine needle pressed 

 down at A' will then give the point through which after the pro- 

 tractor is removed, a straight line drawn to the vertex of the an- 

 gle will lay off the trisection required. 





