506 



Scientific Intelligence. 



9. Note on Nevil Maskelyne' s Article, " On the Trisection of 

 cm Angle" • by H. S. Uhler (communicated). — In the Philo- 

 sophical Magazine for April, 1912, a geometrical construction is 

 given by Maskelyne, on page 647, which he states will trisect any 

 angle. This claim is surprising because the construction is not 

 qualified as an approximation and also because no proof is sug- 

 gested in the article. It is the purpose of the writer to show that 

 the aforesaid construction is not valid. To accomplish this, it is 

 sufficient to prove that a right angle will not be trisected in the 

 manner indicated by Maskelyne. 



In the accompanying figure the letters have the same signifi- 

 cance as in the original article. 



Let = af = fd = db = ag = ge = ec = 1 . 



From the right triangle caf, cf = *\/\0. 



Since ah bisects L cab, ch — \ef = f VlO. 



ah 2 = «6 >2 + ch 2 — 2ac. ch. cos [Lacf) = -| = ak\ 

 Considering ac and ab as axes of x and y respectively, it 

 follows that the equation of the line ef is x + 2 y — 2 = 0, 

 and of the circle JK, 8 x 2 + 8 y 2 — 9 = 0. Consequently the 



coordinates of h are 



V26 + 4 



16 



10 



20 / 



