Drs. Blyth and Hofinann on Styrole. 97 



ftifhishes a good illustration of these remarks. By solving it* 

 for one of the variables, we have 



y = b± s/ —[x-af~ h±{x — a) i^^T, 

 which for x:=.a, however this value o^ x be reached, becomes 

 y = ^±0\/_i; therefore x — a,Tj = b are the co-ordinates of 

 a conjugate point. '^ 



Again, by differentiating the equation, we have 



dy _ x—a _ —{x — a) * 



'dx~ y — b~ [x—a)\/'^~ ~^ ' 



this, for a* = a, as indeed for every value of .r, is imaginary; 

 and as this value of x, conjointly with j/ = ^, satisfies the ra- 

 tional equation proposed, a conjugate point is thus indicated,^. 

 Lastly, by regarding the equation as the extreme case of .. 



i^x-df + i^y~bf^r\ 

 we have i 



^ — _ 'En^ — ~^^~^) 



dx~ y—b~ ^r^—[x—af ' 



For x=a, simply, this no longer becomes a vanishing fraction ; 

 the numerator only becomes zero : in order that the denomi- 

 nator may vanish also, we must introduce the additional hy-^ 

 pothesis r=0; thus numerator and denominator vanish in' 

 consequence of two distinct hypotheses, so that in this case the 

 fraction is necessarily indeterminate ; hence when the circle 



degenerates into a point, the values of-r^ are unlimited; and 



conversely, when these values are unlimited, the circle dege- 

 nerates into a point — the same point that was indicated by the 

 preceding methods. 



Belfast, June 9, 1845. ,. 



XVI I . On StyrolCi and some of the Products of its decomposition. 



By Dr. John Blyth and Dr. Aug. Wilhelm Hofmann*. 

 ^P^HE class of bodies comprehended under the general name 



-*- of Balsams has not been forgotten in that active investi- 

 gation of organic bodies to which chemists have with predi- 

 lection devoted themselves, since the discovery of easier and 

 securer methods of investigation have removed the chief diffi- 

 culties. An examination of these substances was indeed highly 

 desirable, as the knowledge of them derived from older works 

 no longer corresponded to the present state of the science, [ 

 The earlier investigations of these substances were purely 



* Communicated by the Chemical Societ\': having been read April 7, 

 1845. 



Phil. Mag. S. 3. Vol. 27. No. 1 78. August 1 845. H 



