Andersen. — New Zealand Bird-song. 669 



and half of each mouth before and after. Previously I had rather a poor 

 opinion of the bird as a songster, though a high opinion of him as a cheery 

 companion. I can thoroughly appreciate the choice of Maui, the 8un-god, 

 when he induced the small birds of the forest to accompany him on his 

 last and greatest adventure — the conflict with the Great Woman of Night, 

 the Western Darkness. And it is said that it was the laughter of a cheery 

 fantail that awoke the Woman of Night to a sense of her danger — alas for 

 Maui! On the morning of tlie 6tli April, 1910, I awoke at the day-spring, 

 and a fantail was singing vigorously just outside my bedroom-window : — 



, :^^n 4M^s^TTT^ '-^ 



The notes were still the constricted, almost vocal sounds previously de- 

 scribed, excepting the high e, which was nearer a sweet, pleasant whistle. 

 Easter thoughts and feelings permeated all things, and the fantail's song 

 at once carried me back to the days when, as a boy. Good Friday morning 

 meant tea and hot buns in bed before getting-up time. I can well remember 

 lying dozing, waiting to hear in the street outside, '' Hot-cross-buns— 

 ting-a-ling, ting-ting, ting-a-ling." This fantail's song was exactly like the 

 cry and bell of the H.C.B. man. I listened to it with pleasure for some 

 time : sometimes it opened with the common tweet-a-Uveet-a-tweet, sometimes 

 directly on g. I heard a much more frequent variation of this song many 

 times during the autumn : — 



S^^ 



GtC^. 



Here the lower notes were all g, the first two followed by a quick slur up to 

 c, resulting in a pleasing variation of the tiveet. The high notes e were 

 almost invariably much softer and of less volume than the lower f/, /, c, or f/. 



Art. LVII. — On Centroidal Triangles. 



By Evelyn G. Hogg, M.A., F.R.A.S., Christ's College, Christchurch. 



[Read before the Philosophical Institute of Ganterbiinj, 7th December, 1910.] 



1. Let the side BC of any triangle ABC be divided internally in the point 

 X' and externally in the point A' in the ratio p : q ; let CA, AB be 

 similarly divided in the points Y', B' and Z', C respectively. The 

 triangles X'Y'Z', A'B'C are termed "centroidal" triangles, inasmuch 

 as the centroids of these triangles are coincident with that of the triangle 

 of reference ABC. 



