(93) 
product therefore contains a yellow impurity, which cannot be 
removed by recrystallisation. 
The intramolecular change was attempted in vain by means of 
the following reagents : 
Acetyl chloride, butyryl chloride, benzoyl chloride, phosphorus 
pentachloride, phosphorus oxychloride, phosphoric acid, aluminium 
chloride, aqueous caustic soda, copper oxide, zine oxide and zine 
carbonate. Of these reagents the following deserve to be specially 
mentioned on account of their action on azoxybenzene : 
Acetyl chloride : formation of p-p-dichloro-azobenzene and p-chloro- 
acetanilide ; benzoyl chloride: formation of azobenzene ; phosphorus 
pentachloride : formation of azobenzene with evolution of chlorine ; 
aluminium chloride: formation of p-chloro-azobenzene. 
Mathematics. — #On the connection of the planes of position of 
the angles formed by two spaces S, passing through a point 
and incident spacial systems.” By Prof. P. H. Scnourr. 
1. If in a space Sy, with 27 dimensions two spaces S, are given 
arbitrarily, these have in general only a single point OV in common 
and they form in this point with each other angles differing in general 
respectively. These angles are situated in » definite planes through 
Y and the line at infinite distance of such a plane of position has 
a point in common with the two given spaces S,(, S,@ as well as 
with the spaces 5/0, S:’@ drawn perpendicular to the just named 
spaces through any arbitrary point, say OV, not at infinite distance. 
In this way the two planes of position of two planes ¢,, e, taken 
arbitrarily in S, are determined by the common transversals of four 
lines: situated in a three-dimensional space, viz. of the lines g,, g, 
of «,, «, in the space S, at infinite distance in S, and the lines 
Jy’, Js, normally conjugate in this 133. 10! Oy ze 
2. Let us consider the particular case when the » angles formed 
by SD, S,@ are alike; as an introduction we take in JS, again two 
planes ¢,, ¢, forming with each other in their point of intersection O 
two equal angles. It is known that in that case the four above 
mentioned lines g,, 4, 41’, J’ ave generators of an hyperboloid ; so they 
admit of not only two but of an infinite number of common trans- 
versals, to which answer likewise an infinite number of planes of 
position. If the system of those transversals ¢ is indicated by (4), the 
