66 PROCEEDINGS OP SECTION A. 



showing that the chord PT" passes through the fixed point — 

 / I + 2 sin'A co t B cot C 1 + 2 gin'B cot C cot A 

 ( sin A sin B 



1 + 2 sin^C cot A c ot B |^ 

 sinC j 



and it may be easily verified that this point lies on the line joining the 

 centroid and orthocentre of the triangle ABO. 



7. If the axis of homology of any point P with respect to the 

 triangle ABC be parallel to that of its isogonal conjugate P', then the 

 line PP' always passes through the symmedian point of the triangle 

 ABC. 



The locus of P is the cubic curve — 



aa(l3'-Y)+l/3(Y-a'')+cy(a'-l3')=0: 

 the equation of PP' is — 



whence the above result at once follows. 



This cubic curve passes through the vertices of the triangle ABC, 

 the sjmmedian point, the centroid, the in- and ex- centres and the 

 points in which the lines joininj^ the vertices to the symmedian point 

 meet the sides of the triangle. The tangents to the curve at the in- and 

 ex- centres meet at the symmedian point. 



8. If the extremities of the diameters of the circle ABC perpen- 

 dicular to the sides BC, C \, AB are D„ D, : E„ E, : F„ F„ then— 



the axes of D, and D,, SB and SC, 



the axes of E, and E„ SC and SA, 



the axes of E, and E„ SA and SB, 

 form harmonic pencils. 



The locus of the centres of conies which are the isogonal trans- 

 formations of lines passing through the sjmmedian point of the triangle 

 of reference is — 



^aa + x/b/3 + ^/^ = 0. 



6.— THEOEY OT THE ALTERNATE CURRENT GENERATOR. 



By THOMAS R. LTLE, M.A., ScD., Profassor of Natural 

 Philosophy in the University of Melbourne. 



It has been usual hitherto to ascribe the distortion of the ware 

 form of the current given by an alternate current generator to : — 



1. "Lack of uniformity and pulsation of the magnetic field, 



causing a distortion of the induced e.m.f. at open circuit 

 as well as under load." 



2. " Pulsation of the reactance causing higher harmonics under 



load." 



3. " Pulsation of the resistance causing higher harmonics under 



load also."* 

 and, as far as I have been able to find out, another cause has been 

 overlooked — namely, the mutual reactions between armature and field, 

 which when the generator is loaded is at least as important as any 

 of the foregoing. 



* Steinmetz. Alternating Current Phenomena. 



