Dr. Day^s Mineralogical Notices, 137 



are such as to allow this to be done in various ways, and even 

 without entirely determining the constants. And it appears not 

 impossible that similar results may be obtained for higher values 

 oi n; or that associative^ polynomes of higher orders than quines 

 may be discovered. 



Observatory of Trinity College, DubUn, 

 July 4, 1854. 



[To be continued.] 



XX. Mineralogical Notices. By Dr. Alfred Day. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



THE following notices of British species and their localities, 

 which have not as yet found their way into our standard 

 works on mineralogy, may be interesting to a portion of your 

 readers. 



Ankerite. — For some years past I have noticed on the boards 

 of the mineral dealers at Clifton ornamental specimens of iron 

 ore, which have been sold as the produce of the neighbourhood, 

 but which after considerable inquiry I find are brought from 

 Whitehaven to the ports of South Wales. They consist of sili- 

 ceous ironstone covered with hsematite, then coated with spe- 

 cular iron, often of highly iridescent hues, with quartz almost 

 dodecahedral, or in which the prism planes are much reduced, 

 with a great variety of forms of carbonate of lime and what 

 appears to be brown spar. The latter, which has the curvilinear 

 faces common in this species, is sometimes dark brown and at 

 others of a nankeen-yellow with a wax-like surface. On analysis 

 I generally find that this last consists roughly of about one -half 



supposing either x=0, y—0, or t=.0, m=0. Compare the equations (85) 

 or (86), which are of the forms to=iO, ty=Q, tz=-b, ux=0, uy=^0, uz=zO, 

 vx=^0, vy=0, vz=.0. In the theory of quines, however, the forms are not 

 quite so simple. 



* The octaves, or octonomial expressions, which Mr. Cayley published in 

 the Philosophical Magazine for March 1845, and which had been previously 

 but privately communicated to me by Mr. J. T. Graves about the end of 

 1843, after my communication to him of the quaternions, are not associa- 

 tive polynomes. Thus in Mr. Cayley's notation, the four following of his 

 seven types, (123) (624) (176) (734), give i^. 1^1^ = iite= — 17, but 

 ij tg . 14=^3 t4=z-\-iy; or with Mr. Graves's symbols, the triads ijk, ion,jln, 

 klo, give i.jl=.inz=z — 0, but ij.l=kl=-^o. See note to page (61) of the 

 Preface to my Lectures. It was my perceiving this latter property of Mr. 

 Graves's symbols in 1844, which chiefly discouraged me from pursuing the 

 study of those octaves, as a species of extension of the quaternions, which 

 Mr. Graves as well as Mr. Cayley had designed them to be, and which in 

 one sense no doubt they are. 



