( 504 ) 
The points of intersection of these curve with C, which are not 
situated at the same time on ‚rt, + 27,?— 0 lie on the conic &, 
3Ys (23 ie w,*) =2 (voe, sin gia a 243%) Eat 
So the tangential points of the four tangents out of any point of 
the double tangent lie on a come through the cusps. 
For y,=0, so y,:¥y,=0,:—6, (the point H) we find as it 
ought to be 
(Mer bya.) 2, = 0. 
The conies § form evidently a pencil of which two basepoints lie 
on h, the remaining two in O, and Qj. 
7. The curve of Hrssr of C, has as equation. 
6wv,°z,* + 18 (bz, + bee) 2,727,247, + (18e + 32) wv ww, + 
+ 60 (bie, + bw) 7, a,2,*° + (86b,6, + 24e — 8) x,2,2,* + 
+ 9 (bie, + bew) #4 + 18 (bw, + bew) 10° + (185,5, + ¢) 7° = 0. 
By combination with the equation of C, we find that the points 
of intersection of the two curves not lying in the cusps are situated 
on the curve 
12 (b,4,+6,a,)a,0, + (185,6, — 18e —30)r, m,r, — 27 (b‚e, Hb) er, — 
— (54e+22) (b,v,+b,0,)a,2 + (18b,b,—190— 18e’), =O. 
So the eight points of inflerion of the C, are situated on a cubic 
curve passing through the cusps and the point H. 
The polarcurve of the point O,=4,, consists of #,=0 and 
the conic . 
22,0, + 3 be, + 3 been, + 2cx,? = 0, 
passing through the cusps and through the points of contact of the 
four tangents which meet in the point of concurrence of the cuspidal 
tangents. 
It is easy to see that U, and H are the only points for which 
the polarcurve degenerates. 
Chemistry. — “On the system hydrogen bromide and bromine.” 
By Dr. E. H. Bicuner and Dr. B.J. Karsren. (Communicated 
by Prof. A. F. HOLLEMAN). 
The research, a report of which is given here,’ was undertaken 
in connection with a remark from Prof. HOLLEMAN, that the exis- 
tence of compounds of the type HBr, has been assumed several times 
in order to explain the mechanism of reactions in organic chemistry. 
In order to test the validity of this assuiaption it was thought desi- 
rable to ascertain, in the first place, whether pure bromine and 
