LXXtl. On Chiviatite, a new Mineral from Teru. "^'^ 

 ^7/ Professor Rammelsberg*. '''^ 



MR. BROOKE sent to me a considerable time since a 

 mineral which he looked upon as a new species, and 

 which is said to have been met with at Chiviato in Peru. In 

 many respects it resembles bismuthine, is of a lead-gray colour, 

 and possesses a marked metallic lustre. The fohated crystalline 

 mass is cleavable in three directions situated in the same zone, 

 but most readily in the direction of a plane, with respect to which, 

 according to Professor Miller's approximative measurements, the 



ordinary treatises on the subject, nor so well known as it deserves to be) 

 for forming any such numerators or denominators by means of the principal 

 terms in each ; the rule, I mean, according to which the ith denominator 

 may be formed from qx-q^'qi-q^- ■ -q {q\, ^'2. • • • 5'i being the successive 

 quotients), and the tth numerator from q^.q^. . .q ,hy leaving out from 

 the above products respectively any pair or any number of pairs of conse- 

 cutive quotients as qp - qp+v Por instance, from 51 . 52 • 5'j • 94 • Qs> by 

 leaving out qi . g-g, q2 . 93' Qs • q4> and q^ . q^, we obtain 



qz . 94 .^s+ffi • 5^4 . gs+g'i 92 . 95+91 . 92 • 93 ; 



and by leaving out 91 . 92 X 93 . 94, 91 • 92 X 94 . 95, 92 • 93 X 94 . 95, we obtain 

 95 + 93+9t ; so that the total denominator becomes 



9i • 92 • 93 • 94 • 95+93 • 94 • 95 + 91 • 94.95+9i-92.95+9i-92.93+9i+93+95; 

 and in like manner the numerator of the same convergent is 



92.93.94.95I l+-^ + -^+-i-+ ^~ , 



^ 92-93 93-94 94-95 q2-qs-q4'qs 



i .e. 92 . 93 - 94 . 95 + 92 • 95+92 • 95+92 - 93+1- 



The most cursory inspection of the form of the generating matrix will 

 show at once the reason of this rule. It may furthermore be observed, that 

 every progression of terms constructed in conformity with the equation 



Un=an . Un-l — bn . Un-2+Cn . «^n-3+&C., 



may be represented as an ascending series of principal coaxal determinants 

 to a common matrix. Thus if each term in such progression is to be made 

 a linear function of the three preceding terms, it will be representable by 

 means of the matrix 



C" 



B" C" 



:!T7^ 1 A"B'"c"" 



*a.aiqr,bv.b h « « 1 A'" B"" 



1 A"" 

 indefinitely continued, which gives the terms 



1, A, AA'-B, AA'A"-BA"-AB"+C", &c. 



* From Poggendorif's Annalen, vol. Ixxxviii. p. 320. Communicated by 

 W. G. Lettsom, Esq. 



Phil Mag. S. 4. Vol. 5. No. 34. June 1853. 2 H 



