( 137 ) 



position was not taken hv a siiiole leaf. Of tiiis species (here are 

 two specimens more in the Hortns liou'. iindci' Niiml)er 1 and 

 Number \A in garden-bed I 11. 



§ 5. Aden a n t h e r a micros p e r m a Tkvs.m. & Binn. — Tree 



grown undci- this name in Hortus i^>ogor. in garden-bed IB, Number 

 41). On 5 Fel)i'uar3' at 1) a.m. I found thai (lie leaves (in tin's species 

 iiipiimate), ar least the youngei- ones, pcM-formed I'lithor disliucl but 

 only feeble iri-itation movements after vigorous shaking of the branches. 

 These movements reminded of those typical for Polncianla, bul iu 

 AdenarUliciut the movement is much slightci-. 'J'he determination of 

 the species has been verified by me and, iu as much as the material 

 at hand allowed, found correct. 



§ 6. T e t r a p 1 e u r a T h o n n i n g i i Bk,nth. — A young tree 

 about 1 M. high, grown under the said name in the Ilorlus under 

 Number 14 in garden-bed I.G. The leaves ai-e bi|)iniiate and remind 

 of Adenanthera. At 7 a.m. on 5 February, the plant was vigorously 

 shaken. Within few minutes the younger leaves which before, like the 

 older ones, were quite expanded, plainly showed irritation movements 

 similar to the Poinciania type, but much less vivid. 



§ 7. S c h r a n k i a h a m a ta Hb. & Bpl. — Undershrub kept in 

 the Buitenzorg Hoitus under that name, which was verilied and 

 found right, in garden-bed A XXV of the Leguminosae herbs division, 

 under Number 2, with bipinnate leaves and very narrow leaflets. 

 Not only in the forenoon but also in the aftei'uoon, all the branches 

 when mechanically irritated (by shaking) reacted almost as quickl}' 

 as Mimosa pudica. 



Buitfinzorg, February 12, 1911. 



Mathematics. — "■On the .structure of -perfect sefs of pomfs" {^^ecoud 

 connnunication ')). By Dr. L. E. J. Brouwkr. (Communicated 

 by Prof. Kortb;weg). 



(Communicated in tiie meeting ul' April 28, 1911). 



§ 1. 



A furtJier extension of Cantor s fn,n<hiinent(il tlieoreni. 



The proof of Cantor's fundamental theorem and of its Schoenflies 

 extension, given in § 2 of the first communication, holds also for 

 the following property : 



1) For the first communication see these Proceedings, Vol. XII, p. 785. 



