140 Miscellaneous Intelligence, 



Having a plate of sheet metal, or other convenient material, let 

 A C B be an equilateral triangle ; divide one of its sides, A B, 

 into two equal parts, as at D, through which draw the line C E, 

 until it meets, as at E, another line A E, which latter makes 

 an angle of 70° with A B ; consequently, the angle E will be 20°. 

 The periphery of the rectilineal figure, F A B C D, will repre- 

 sent the instrument in question. 



To illustrate its application, suppose F G H the angle to be 

 trisected ; raise on one of its sides a perpendicular, as K H, 

 equal to AD or B D, and through the point K draw I K, par- 

 rallel to G H ; then place the instrument between this line I K, 

 and the other leg F G of the angle given, so that the line A B 

 touches these two lines at its extremities, whilst the line D E 

 passes by the apex G of the same angle : when in this position, 

 the angle A G D will be equal to one-third of the given angle 

 F G H ; for it is evident, that if from B the perpendicular B L 

 be drawn to the line G H, and that the points B andG be joined by 

 the line B G, that the rectangular triangles, L G B, D G B, 

 A G D, will be equal, the sides, AD, D B, and B L being 

 equal, and consequently, the opposite angles at G will also be equal. 



The reason why the angle C is made equal to 60°, and tlie angle 

 E to 20°, is as follows : — If the angle given was less than 60°, 

 and consequently, its third smaller than the angle E, the perpen- 

 dicular D E would, when employed as above, be too short 

 to extend to G, and the operation, in this case, would be a little 

 more complicated : instead of searching for the tliird of the angle 

 given, the operation is to be commenced by finding the third of 

 its supplement, which, once obtained, need only be subtracted 

 from an angle of 60° to give the third of the angle required ; 

 now by making one of the angles of the instrument itself 60°, 

 this graphical subtraction is very much facilitated, and the opera- 

 tion rendered so simple as to require no application. The line 

 m n indicates a small triangle, m A 7i, which it is convenient to 

 remove from the instrument, that the point A may have an acute 

 angle instead of the obtuse angle C A E. — Bib. Univ. xxvii. 169. 



10. Secret Writing. — Mr. Allsop describes, in a letter to the 

 Editor of the Technical Repository, a mode of secret writing 

 which he has long used for making private notes and memoran- 

 dums. It is simply to substitute the preceding or succeeding 

 letter for the one used ; thus, for the letter a substitute 6, for 6, c, 

 and so on. The following is a specimen: — 



" Sir, Among the numberless inventions adopted for Secret 

 " Sir, Bnpoh uif ovncfsmftt jowfoujpot bepqufe gps Tfdsfu 



Always addressing and concluding the letter in the usual manner, 

 to prevent a discovery, or giving a key to the cipher. — Tech. Rep. 

 vii. 174. 



