On Three Simultaneous Quadratics of the Fifth Order. 413 



The oxide of iron may be regarded as an impurity which exist.s 

 between the plates of the mineral. The composition of emery- 

 lite is represented by the formula — 



2R0, Si03 + 2(2AP 0^, SiO^) -f 2H0. 



The most beautiful specimens of emerylite come from Naxos ; 

 and as the blocks of emery from this island frequently contain 

 it, there will be no difficulty in procuring specimens for cabinets. 

 It is often mixed with diaspore. 



LVI. On the Solution of Three Simultaneous Quadratics of the 

 Fifth Order. By James Cockle, Esq., M.A., of Trinity Col- 

 lege, Cambridge; Barrister-at-Luio^. 



THE cubic solution of three simultaneous quadratics is a sub- 

 ject to which I alluded towards the conclusion of the second 

 part of my Analysis of the Theory of Equations (see Phil. Mag. 

 S. 3. vol. xxxvii. p. 509, art. 33). And I cannot refer to that 

 Analysis without adverting to the but yet recent death of him 

 to whom it was addressed, the illustrious geometer Thomas 

 Stephens Davies. To Nature's gifts, of commanding intellect 

 and expansive genius, his vast capacity and indu.stry had super- 

 added high acquirements and profound learning. And these 

 accomplishments were attained in the face of obstacle upon ob- 

 stacle piled in his path by the accidents of life, by ill health, and 



* Communicated by Dr. Cockle, Fellow of the College of Surgeons. 



