( 489 ) 
Finaliy we come to the last question, of great signification for 
the physiological bacteriology of the intestinal canal: Have the micro- 
organisms of the intestinal canal of the rabbit to play a part in 
the digestion ? 
If attention is paid to the following facts: 
1°. The very small number of living bacteria with respect to 
the number of grams of intestinal contents; 
2°. The very small number of living bacteria with regard to the 
number of dead ones, in particular perceptible from the high sterility- 
indices of the whole intestinal canal, and from the slight number 
of living bacteria found on 1 million of dead organisms, and 
3°, That at no single place there is a multiplication, on the 
contrary, that nearly in the whole intestinal canal there is a mortality 
on large scale of living bacteria, we are obliged to deny the bacteria 
playing any part in the digestion in the intestinal canal of the rabbit. 
Mathematics. — „On the motion of variable systems” by Prof. 
CARDINAAL. 
1, With considerations relative to the theory of motion, we 
generally start from the principle that two phases of the system 
are congruent. If the two systems considered in this way are 
situated in a plane the pole of the motion is the only real point 
of coincidence of the two systems; if they are situated in space 
the principal axis of the motion is their line of coincidence. If 
we suppose the second system to have approached the first at 
infinitesimal distance, the rays connecting the homologous points 
are directions of velocities and one of the principal problems of 
motion consists of the construction of the directions of these velocities. 
Special constructions exist for this, the second system not being 
suitable for use. 
2. In the plane the construction of the direction of velocities 
is a simple matter, the polar rays being normals to the orbits and 
the velocities touching them. In space the construction becomes 
already more elaborate; however, we can notice that the directions 
of velocities are the rays of a tetraedral complex; to this complex 
belongs moreover a focal system, the properties of which enable us 
to find the points belonging to these rays. This paper now purposes 
to investigate this same subject for systems of points in space changing 
projectively during their motion. ‘The investigation is independent 
