( 347 ) 



F. Fornix. V.l. Lateral ventricle. 



L.c. Limbus corticalis. V.t. Third ventricle. 

 L.m. Limbus medullaris. 



Fig. 11. 



Frontal section through the more posterior part of the corpus 



callosum. Section 15 ft stained with haematoxylin and eosin. Enl. 

 13 diam. 



C- Zone of union of the pallia. L.c. Limbus corticalis. 



C.a. Anterior commissure. L.m. Limbus medullaris. 



C.c. Corpus callosum. L.tr. Lamina trapezoidea. 



C.ch. Corpus chorioideum. Ps. Fornix commmissure. 



C.str. Corpus striatum. V.l. Lateral ventricle. 



F. Fornix. V.t. Third ventricle. 



Mathematics. — "On <in infinite product, represented by a definite 

 integral." By Prof. W. Kapteyn. 



The object of this paper is to write the infinite product 



Jfol 1 + (« + «)V 

 in the form of a definite integral. 



This product is connected with mod. r(u -f- iv), for 



mod. r(u + iv) = r(«) . a- 1 ' "•"> (u > 0) 



where 



thus 



and 



1 » / v ' \ 



P(u t v) = -2 1g[l+ 7 —-) ') 



n (u) 



mod. 1 r(it -\- iv) = 



s =oV («+*)V 



77 l H = Li__ 



s=0 \ ("■ J r s )'J mod'' r(u -\- iv 



iv) 



To write the second member of this equation in the form of a 

 definite integral, we start from Wkiekstk ass' definition 



— — — c * 



t~ z dt 



W 

 where the integral is taken along a curve H commencing at negative 



'l Nielsen. Handbueh der Theorie dei- Gummal'unctionen p. 23. 



■r. j 



Proceedings Royal Acad. Amsterdam. Vol. X. 



