(580 ) 
of zr, and 6 the curve (a) consists of a curve of order (27 —1) and 
a right line (§ 3). 
On A lie besides the 2n-fold right line and a 2n-fold torsal right 
line 6n single right lines more. 
The plane o contains 2(n— 1) right lines of A and touches 4 in 
the points of a curve of order (n-+-1), which is the locus of the 
points where the curve of the complex (a) touches its „-fold tangent 
(oz). For, if the ray s, resting on / corresponds to the ray ¢, cutting 
o in 7, then one of the points of contact of the curve of the complex 
of the plane (/7,) with o lies in the trace L, of /; consequently 
the indicated points of contact lie on a curve of order (n +1). This 
curve is generated by the pencils (Z,) and (S) arranged in a (1, 7) 
correspondence ; so it has in S an n-fold point. 
The plane t+ touches A according to a curve of order (n + 1) 
which is the locus of the points of contact of the curves (2), in 
planes x through /, with the traces (ar). This curve has an n-fold 
point in the trace Z, of / on rt; the tangents in this multiple point 
are the traces of the planes a cutting (or) on the m rays s conjugate 
to the rays ¢ drawn out of L,. 
The plane r has farthermore the envelope rt, in common with 4. 
For, while a point P of the right line (ar) bears in general n 
tangents of the curve of the complex (a) determined by the rays s 
corresponding to the rays ¢ drawn through P, two of those 
tangents coincide as soon as P lies on the envelope vr; then however 
P belongs to the curve (a), thus to the surface of the complex 4. 
Microbiology. — “An obligative anaerobic fermentation Sarcina.” 
By Prof. M. W. Brrerrinck. 
The following simple but yet delicate experiment gives rise to a 
vigorous fermentation, caused by a sarcine, wherein microscopically 
no other microbes are perceptible and which, when rightly performed, 
can produce a real pure culture of this fermentation organism. The 
simplicity of the experiment is the result of many previous invest- 
igations, partly made conjointly with Dr. N. Gostines, which have 
gradually rendered clear the conditions of life of the examined 
microbe. 
Bouillon with 8 to 10°/, glucose, or malt wort, is acidified with 
phosphorie acid to an acidity of 8 ee. normal per 100 ce. of culture 
liquid and introduced into a bottle, which is quite filled with it 
and fitted with a tube to remove the gas. The infection is done 
