On the Porism of the In-and-circumscribed Triangle. 513 

 Now assuming, what I have no doubt to be the case that 

 both the analyses are correct, how is the difference to be accounted 

 for ? Either that there is in the felspar of the mountain ™t 

 diver S1 t y of constitution, or that the felspar selected by Prof! sor 

 SfcSSSfiT Similai> t0 that ^°-S the general = 

 To enable him and the Society to judge as to the specimen* 

 from which the analysis was made by M?. Campbell ft a™ 



disposal of the Professor it he wishes to examine it 

 1 have since received the following letter :— 



,,t.,' u , Al , "London, May 10, 1855. 



Estimation of the potash and soda in a specimen of eranite 



In my first experiments, before reducing the mineral to a 

 reStav'e,- nly ^^ ^ ^ ^ ° f ^^ 



Potash . . . 3-23 per cent. 

 Soda .... 3-75 



"In a second set of experiments just finished the mica was 

 carefully p 1C ked out, scarcely a trace ieing left, and the resXe 

 gave. 



Potash . . . 3-02 per cent. 

 k° da .... 3-98 



Francis M. Jennings." 



Dugald Campbell/' 



LXXI. On the Porism of the In-and-circumscribed Triangle and 

 on an Irrational Transformation of two Ternary (£drat 

 Forms each into itself. By Arthur Cayley, Esq.* 



rpiEllE is an irrational transformation of two ternary qua- 

 M. diat.c forms each into itself, based upon the solution of the 

 following geometrical problem, 

 Given that the line 



lx-\-my + nsz=Q 

 meets the conic 



{ a > b >c,f,9,hjx,y,zy=0 

 in the point (*,, y u a% ) . to find the other point of intersection, 

 lhe solution is exceedingly simple. Take ( Xq} y<ti z 9 ) for the 

 coordinates of the other point of intersection;^ must have 



* Communicated by the Author. 



Phil. Mag. S. 4. No. G2. Suppl. Vol. 9. 2 L 



