March. 1912. 



KXC)\VLl-,DGi:. 



105 



The authority for the French pronunciation is the "Dictionnaire Plionetique," by H. Mictiaolis, Paul 

 Passv. and M. Gaston Paris, .\dministrateur du College de France. 



KnjM, Effaceable 

 I.,., effQcable 



w .l.-n..i... li; 



isjt pare 

 £st_il pur„ 



music 

 musique 



.UmtH.'s :, l,,n- svlliil,!.'. 



mares 

 mers msres 



) 



c 



= o = o = w,a,n =E = ai =e, u =a 



or honest yon, wc ere, (fan) humble, murder pass 



dr ,11 honnete vans, oui fip, ais humble, meurtre passe 



= I, 1, y = t =6,1 



ill, primary, indict, idea machine, marine 

 11 primaires, origine, petit machine vivart 



= y 



yawl, opinion 

 y61e opiniop 



Tlic following French sounds have no exact equivalent in English. 



i^ ~l,,„r A l'<<z 



Q = 1 = iQborQtoire, mai, patte, part, e = e dependart (dependant) 



u lune, (lunar, moon), du, (dae). " =u liii, (Louie), piiis. 



= all role, (roll), au, auteur, (author) = Qr> ert, dQPs, p = n. 



CORRESPONDENCE. 



ABDLT I'HI-: I'RISKCTION OF AN ANGLE. 



To the Editors of " Knowledge." 



Sirs. — The division of an angle into three equal parts 

 forms, together with the quadrature of the circle and the 

 duplication of the cube, the three most renowned problems of 

 Greek mathematics. As its algebraic expression leads to an 

 irreducible equation of third degree, its construction cannot 

 be made by using only the line and the circle. Knowing that, 

 one mu.-:t be sure that the solution given by Mr. C. S. Bingley 

 in the November number of "Knowledge" (page 435) cannot 



be right. Mr. C. S. Bingley asserts, without any demonstration, 

 that — using his signs — the distances BJ=J K = KC, and from 

 this concludes that the arc B C is divided by J and K into 

 three equal parts. 



Now. it is easy to see that this is not true. By taking A D 

 and its perpendicular in A as axes of rectilinear coordinates, 

 and supposing A B = .\ C = l and the angle B A C = 2o, the 

 coordinates of E will be (i.O), and so will be B (cos o, sin o), F 



(:t+cos a, ^ sin 



o), H= (ji 



+ 



sino\ 

 4 ,'■ 



J being on the 



line A H and on the circle B C will have the coordinates 

 / 5 + 2 cos a 2 sin 



), instead of 



I cos , sin -^ 1 



1^29+10 cos a \/ 29+ 10 cos 

 which would be when the construction is exact. By designing 

 the angle J A D with «, the following table shows the error of the 

 construction for a = 10°, 20°, 30°, 40°. The angle S has been 

 5 + 2 cos a 



The difference S — — is, as we see, not inconsiderable, and 

 not onlv due to errors '' in the drawing." 



FlclKh 10/ 



BUD.\PEST. 



ERNEST 



