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LXXXIII. On the Trisection of an Angle. 

 To ilia Editors of the Philosophical Magazine. 

 Gentlemen, — 



IN Mr. Maskelyne's figure (Phil. Mag. April, p. 647) 

 let 



ag = d\ ah=y, 



bac=a,j baj = 6. 



Then . 3 a 



aj=y= ^ cos-, 



and sin a , y sin 6 



— = tan at(q=. s — — ^, 

 2 — cos a ° ~^ — 'J cos U 



so that the equation to determine 6 is 



(5 sin # + o" sin («— 0) — 8sin^=0, 



which is not satisfied hy &= v, > 



Let *=6ft = 2j3 + e. 



Then if /3 is small, 



e — i s 3 — 



fc — . , H • • • } 



which gives an approximation to the error. 

 JSo pos&ibly the eminent men are right. 



Yours faithfully, 



Newuham College, Cambridge/ HlLDA P. HUDSON. 



April 1912. 



LXXX1V. On tlie Trisection of an Angle. 



To the Jiditors of the Philosophical Magazine. 



1 Selwyn Gardens, Cambridge, 

 GeNTLEMEN 3 — Icth April, 1912. 



IT seems unnecessary to give any formal proof that 

 Mr. Maskelyne's construction (Phil. Mag. April 1912, 

 p. 646) cannot trisect an angle with exactness ; hut it may 

 Ije of some interest to estimate the degree of accuracy in 

 his approximation. 



For a small angle the error seems to be of the order of the 

 cube of the angle; thus an angle 3a is divided by this method 

 into parts which are approximately a-f-Ja 3 , a — ^a 6 } a+} y a 6 7 



