1832.] Description of an Instrument for trisecting Angles. 499 



II. — Description of an Instrument for trisecting Angles. By 

 Lieut. T. S. Burt, Engineers. 



I have the pleasure of sending you, for insertion in the Asiatic Jour- 

 nal, a description of an instrument I have lately made for trisecting 

 any plane angle, which I should not probably have been induced to 

 trouble you with, had 1 not seen, in the United Service Journal, for 

 January last, an account of Captain Burton's problems for effecting the 

 trisection, but they are all, you will have perceived, founded on trials, 

 which in these cases are not allowed : and also, in the same volume, 

 Major Mitchell's problem; but his attempt is very easily disproved, 

 notwithstanding the confidence with which he gives it forth, as the 

 true mode of trisecting an acute angle, which it is well known can- 

 not be effected geometrically, and which, moreover, has been proved 

 to be impossible. 



Description. The accompanying Plate XII. fig. 1, exhibits a sketch 

 of the instrument or trisector, which consists of four pieces of brass 

 connected together at, but moveable on the points A and O. The leg 

 or piece, A B, passing through a groove or opening at the extremity 

 of the leg O B, in order that it may allow of O B being slided at B, 

 over and along its length. The piece A D is made rather thinner than 

 the others to admit of its passing underneath O B, whenever O B is 

 made to slide along the leg A B towards A, as above noticed. A D is 

 moveable on the point A. 



This instrument will trisect any angle from 1° to 180o, and the cor- 

 rectness of its principle is evident from the annexed diagram, (fig. 2.) 

 It may not seem irrelevant to remark, that No. 22, volume I. of the 

 Mechanic's Magazine, contains the description of an instrument for per- 

 forming a similar operation, invented in the year 1824 ; but that ma- 

 chine contains, of necessity, no less than 14 pieces, (see note at the end 

 of this statement,) and its principle of construction is quite differ- 

 ent from that of this instrument, which, as above stated, consists of only 

 four pieces, and may, as I shall hereafter shew, be reduced to three. 



Application. Let a o c, fig. 2, be any angle required to be trisected. 

 Draw the chord a c, and lay the leg of the trisector, A O, upon one side 

 a o of the angle, so that the point A of the instrument may coincide 

 with the point a of the given angle, and O with o, respectively. Next, 

 place the leg A D, which, as before described, is moveable on the point 

 A, along the chord a c, without paying any regard to the length of 

 this chord, until the leg and the chord coincide. Then slide the leg 



