Notice of New Zealand and Antarctic Minerals. 495 



these two others; to multiply two pure imaginaries which 

 agree in direction, and to multiply two which are at right 

 angles with each other. In the first case the product is a pure 

 negative, equal to the product of the lengths or moduli with 

 its sign changed. In the second case, the product is a pure 

 imaginary of which the length is the product of the lengths of 

 the factors, and which is perpendicular to both of them. The 

 distinction between one such perpendicular and its opposite 

 may be made by the rule of rotation already stated. 



There seems to me to be something analogous to polarized 

 intensity in the pure imaginary part; and to unpolarized 

 energy (indifferent to direction) in the real part of a quater- 

 nion: and thus we have some slight glimpse of a future Cal- 

 culus of Polarities. This is certainly very vague*, but I hope 

 that most of what I have said above is clear and mathematical. 

 Hoping that you may be tempted to pursue the view which 

 has thus opened, I remain, with best wishes. 



Your sincere friend, 



William R. Hamilton. 



LXXIX. Notice of some Netio Zealand and Antarctic 



Mineralsf. 



'^r^HE recent voyages and travels in the southern portions 

 A of the globe, although they have not revealed any mi- 

 neral wealth, have still contributed some facts with reference 

 to the physical condition of these regions, which appear to de- 

 serve a passing notice. The following are the results of the 

 analyses of some mineral specimens, conducted by pupils of 

 Dr. R. D. Thomson in the Glasgow College Laboratory. 

 The specimens were presented by Dr. Dielfenbach and Dr. 

 Joseph D. Hooker. 



1. Phosphate of Iron, or Native Prussian Blue^. — For this 

 mineral from New Zealand Dr. Thomson was indebted to Di\ 

 Dieffenbach. The locality of the phosphate is thus described by 

 that naturalist: — "Near the Sugar Loaf Islands, by the river 

 Urenui, the cliffs on the shore were about 100 feet high. The 



* A pen has been drawn across a clause or two in the foregoing oopy of 

 this letter, as having reference only to this guess of a future physical appli- 

 cation. A postscript has also been suppressed, as being comparatively pri- 

 vate. In other respects, it has been thought that no change ought to be 

 made, if the letter were to be printed at all; and therefore the indulgence 

 of the reader is requested for some expressions which have the air of at- 

 taching to the subject an importance greater thali it may deserve. 



t Conununicated by the Philosophical Society of Glasgow, having been 

 read January 31, 1844. 



X [We think that this appellation ought to be discawled by mineralogists, 

 as the mineral is really not analogous to the artificial pigment called prus- 

 sian blue,] 



