Description and Analysis of tivo Mineral Species. 499 

 from the theory of quaternions. For we shall have 



TP=TKP=^(PKP) = {(SPf-(VP)2}*; . . (46> 



T(j9±OT) = (;j2_^2)^. Tj5 = (;,«)^, Tot=(-ot2)*; (47) 



UP= /.^T^r,x , V(p + m)= P-"^ , ; . . . (48) 



\/(PKP)' ^^- ' (jj2_^2)4' ^ ' 



P=TP.UP = UP.TP; (49) 



TUP=UTP=1; TTP = TP, UUP=UP: . . (50) 



with some other connected equations. But, although the chief 

 terms (such as scalai'^ vector, conjugate, tensor, versor), and the 

 main notations answering thereto (namely S, V, K, T, U), of the 

 calculus of quaternions, along with several general formula result- 

 ing, come thus to receive extended significations, as applying to 

 certain polynomial expressions which involve n vector-units, and 

 for which as many as |(n^ + ?i) constants of multiplication are 

 still left arbitrary and disposable ; yet it must be observed, that 

 we have not hitherto established any modular property of either 

 of the two functions, which have been called above the tensor and 

 versor of a polynome ; nor any associative law, for the multipli- 

 cation of three such polynomes together. 



Observatory of Trinity College, Dublin, 

 June 6, 1854. 



[To be continued.] 



LXXVIIL Description and Analysis of two Mineral Species. 

 By T. S. Hunt, of the Geological Commission of Canada^. 



FOR the specimen which afforded the minerals here described 

 I am indebted to the kindness of Professor Williamson of 

 Queen's College, Kingston, C.W., to whom it was given by 

 Dr. James Wilson of Perth. The locality assigned to it is the 

 second lot of the ninth concession of the township of Bathurst, 

 and it is probably derived from the crystalline limestone of that 

 region. It consists of a white, massive pyroxene or diopside, 

 with small crystals of silvery-gray mica, prisms of bluish-green 

 apatite, portions of copper pyrites, and of a milk-white cleavable 

 calcite, together with a rose-red species, having in its aspect 

 some resemblance to acommon variety of Wollastonite. It occurs 

 massive, with cleavages which indicate an oblique system of ciy- 

 stallization ; according to Prof. E. C. Chapman of the University 

 of Toronto, who has examined a specimen of the mineral in the 



* From the Report of the Survey for 1852-53; communicated by the 

 Author. 



2L2 



