( 820 ) 



meritum, the instrument (Probst's covered hook) passing through the 

 middle crus cerebelli. In tiiis eat were found a certain number of' fibres 

 degenerated, which passed through the regio reticularis of' the side of the 

 lesion and then, crossing the raphe and running upward in the 

 predorsal region of the other side, took their way towards the red 

 nucleus. This experiment tends to show, that there are direct fibres, 

 coming from the basal cerebellar nuclei, which do not join the 

 superior crus, but follow the ventral course to arrive at the red 

 nucleus. Lewandowsky,s fibres 0. P. (in fig. 66 and 37) are not to 

 be identified with these fibres on account of their entirely different 

 course. 



In cat LXI1 the anterior crus cerebelli was partially cut, and at 

 the same time an incision made into the middle crus. Also in this 

 animal there was found no degeneration on the distal side of the 

 lesion except the bundle of Monakow. Were the ventral bundle to 

 be regarded as being formed by descending collaterals of the anterior 

 crus this result could hardly be explained. A simular result was 

 obtained in eat LXVIII, where hemisection of the pons was effected. 

 Also here there was no degeneration on the distal side of the lesion. 



Mathematics. — "Equilibrium of systems of forces and rotations 

 in Sp t ." By Dr. S. L. \an < >ss. (Communicated by Prof. P. H. 

 Schoute). 



(Communicated in the meeting of March 30, 1907). 



Referring to the follow ing well-known properties : 



a. The coordinates p,j and sty of a line p and a plane n satisfy the 

 five relations : 



Pi = PU J'jm + Plj Pkm + Pjk Pirn = , JT t = 2 tffc/ X jm = 0, . (1) 



i 



of which relations three are mutually independent. 



b. The condition that a line j> and a plane 7t intersect each 

 other is expressed by 



Spijjtij—O (2) 



c. The coordinates of the point of intersection X of two planes 

 .t, n' and that of Sp 2 S through two lines />, p' are : 



& = 2 i»n p'j m , (3) 



we wish to draw the attention to the following properties : 



If (//) are ten arbitrary quantities : i.e. not satisfying the relations 



