﻿64b" On the Trisection of an Angle. 



position of tantalum in the series of potentials has been 

 determined. Bv this method, also, the change of E.M.F. 

 Metal/Water with time of immersion of the metal can be 

 determined. 



4. The results of Mars den and Barratt on the branching 

 of the thorium series are consistent with the results obtained 

 on the electrochemical behaviour of thorium C. 



I have to express my thanks to Professor Rutherford for 

 his help and advice throughout these experiments, and also 

 for the radioactive material placed by him at my disposal. 



Physical Laboratories, 



The University, Manchester^ 

 Febniary*191^. 



LIII. On the Trisection of an Angle. 

 By Xevil Maskelyne, F.R.A.S* 



ri^HE trisection of an angle, irrespective of its magnitude, 

 X by means of any geometrical construction, has been 

 regarded as impossible. The problem has been associated 

 with perpetual motion^ the transmutation of metals, "zetetic" 

 astronomy, and similar absurdities. Mathematicians have 

 spoken in no measured terms of the folly displayed by those 

 who, in the face of proved impossibility, attempt to provide 

 a solution; In short, the subject has oeeii relegated to the 

 list of fallacies which are entertained only by very ignorant 

 or very much misguided persons. 



In the past 5 this view of the matter has given me some 

 uneasiness. The reason being that at any moment, in the 

 course of my everyday work 5 I might find myself called upon 

 to solve this very problem. I cannot, however, say that the 

 prospect troubled me greatlyi Judging by experience, I 

 felt confident that, when the difficulty arose, means for over- 

 coming it would not be entirely lacking. Nevertheless I 

 could not altogether set aside the adverse pronouncements 

 made by eminent men, whose opinions and decisions compel 

 the utmost respect, by virtue of authority. 



Eventually, as I had long anticipated, it became necessarv 

 to devise some simple link-motion which would perform the 

 function of trisecting a variable angle. That, necessarily, 

 involved the discovery of some geometrical construction, by 

 means of which any angle may be trisected. Reduced to 



* Communicated bv the Author. 



