144 Intelligence and Miscellaneous Articles. 



On the disk A a line EH is scored, this line being at right 

 angles to the second line BC, and bisecting BC. 



The link B turns on a pivot at A, on a board C (fig. 3), and the 

 disk (which is placed over the link) turns on a pin at C, AC being 

 equal to CB. A pin B projects slightly through the under side* 

 of the disk and is fixed to the latter, so that when the disk is turned, 

 the pin presses against the straight edge of the link and moves 

 the latter through an angle which bears a certain proportion ta 

 the angular movement of the disk, as is obvious. 



In order to trisect any angle, say the angle a°, fig. 4, the link 

 would first be moved to the position where it banks against tho 

 pivot pin C (fig. 3), and then the disk rotated (thereby moving the 

 link) until it is observed that the intersection of the line EH with 

 the straight edge of the link comes on the radial line CP (fig. 4) ; 

 when this is the case, then the line BC will trisect the angle a° 

 in all cases. 



The proof of the foregoing is as follows : — 



From C as a centre (fig. 5), describe the semi-circle ABGr. 



Draw AI at any angle j3°, cutting the semi-circle at B ; join BC - r 

 bisect BC at D; draw DF perpendicular to BC, cutting AB 

 atE. 



Since DE is perpendicular to BC, and CD is equal to DB, the 

 angles CBE and BCE are equal. 



Also, since CA is equal to CB, the angles CAB and CBA are 

 equal. 



The angle AEC equals the sum of the angles EBC, ECB, 

 i. e., equals 2/3°; and the angle ECB equals the sum of the 

 angles AEC, EAC, i. e., equals 3/3°. 



JNow CB being the radius of the semi-circle, is a length of 

 constant value, and its extremity B is in contact with the line All 

 under all conditions, and ED (or ED prolonged to H) cuts AI 

 at E, and, as proved, if ECG equals 3/3°, then ECB equals /3°;, 

 hence the arrangement effects the trisection of the angle ECGr. 



Eor convenience of construction the line ED is drawn through 

 to H, though actually the intersection of AI with EH does not 

 extend beyond D, that is to say if the angles to be trisected do not 

 exceed 180°; theoretically the principle involved covers all angles 

 up to 360°. 



A ir Inventions Committee, 

 2 Clement's Inn. 



