On the Resolution of Equalions of the Fifth Degree. 125 



of the mineral as deduced from the third and fQjirlbrl^tiAtlfflPt 



of the preceding table: — 'lorff v-f ■/• 71J 



; /j;h.I -B OJni .5jt *»^ . By calculfltion. NO; of atoms. Atbmic weight. 



Silica . , . , . . 47-24- , 23 ^6 u< 



Protoxide of iron+ r. ii)fu 1^*4S iJ Jv1(«>^ ,\o<k\tottQ&-ift'^ 487/ 

 Protoxide of manganese 9*24' .9fn2R TirilooboTS 



Alumina . . . /a .'''a6'94 rnx\Qn\ xmc\<\i!6'75 



Lime . . . i\ ^ii^'yK \A>'^^ iku <W\ tr Im^^VAovi 



Magnesia . . .'liilirni^ 2*59 — ■ 1 .lir>ffnc)'i f)i8'Bfi3d 



Water :» 9riJ^M]d9cj»'_9'i,?!j!^j^iifi5tioJ5 y.id b»?t^n9ffclid3 .illSf d 



The formula to express the composition of babingtonite,^ 

 as deduced from tliese calculations, is as follows:— *';_t.~" ^ 



MgO SiO, + 4CaO SiO + 4FeO (SiO)2 + 2MnO (SiO)2 + 3A10 (SiOj^'4- ^i ^ 

 or it consists of two simple silicates and three bisilicales,,^ 



Babingtonite agrees with the amphibole class in possiessing 

 a complicated constitution. It contains nearly the same 

 amount of silica, but much less magnesia and a greater amount 

 of manganese. Its specific gravity is also much higher than 

 that of amphibole. My analysis approaches one by Bonsdorfl^ 

 of a black hornblende from Nordmark and Pargas, the mag* 

 nesia being replaced by manganese in babingtonite. 



XX. 0« the Resolution of Equations of the Fifth Degree, 

 'By James Cockle, Master of Arts, of Trinity College, 

 Cambridge ', of the Middle Temple^ Special Plead^nf{<fM[,ii<jj 

 1. IN the equation of the fifth degree in j/, 



/+;^iy+i>2y+?3/+^43/+P5 = o. . . (1.) 



and ^^ = || (^^ + ^p. A+ A«J, . * tuti^ 

 where A = j^g - ^ ; ^'^^r-'VI^A 



theti) if W — -^ be substituted foi' y Irt (l.), we obtain an equa« 



tion in v of the form of De Moivre. Denoting b^' x ftlie root 

 of the general equation of the fifth degree, let -,'> j^Tn .,,{ r 



y^^^{M,v^') + X^{Wx^') + N'y + F.i'-' + Q'.r''> X^a»»e>V (Sit 

 the suffixes denoting the number of quantities included under^ 

 <ttich 2, aftd the expressioh ft)f ^ 'Consisting, Consequentl)', o^ 



noiJisoc* Cdtntrtunicated by T. S, Davi^, Esq.; t'.lt.S., F.S.ftJi ^ill' 



