Mr. Cayley on certain results relating to Quaternions. 141 



turnnl dews, has been finally washed away by the sea-water. 

 This is rather an unsatisfactory mode of accounting for the 

 absence of the muriate of ammonia, which from what we know 

 of guano, and the existence of oxalate of soda in the saline 

 guano, we may fairly conchide must have been formed, but 

 which in the sample I have examined contains but little more 

 than one equivalent of muriate of ammonia to three of oxalate 

 of soda, so that nearly two equivalents have disappeared. 



As to the respective hypotheses of the coprolitic or recent 

 nature of these deposits, I have never held but one opinion, 

 the one I believe generally entertained, that this manure is 

 deposited by sea-fowl inhabiting coasts where no rain falls, 

 and which consequently is never washed away. This view is 

 supported by all ancient and most modern authorities, and 

 has recently received additional confirmation from Mr. Tesche- 

 macher of Boston, who has presented specimens of Peruvian 

 guano to the Philosophical Society of that town, containing 

 feathers; and after quoting the accounts given by the old Por- 

 tuguese historian respecting the formation and preservation of 

 this manure, very justly remarks, that the beds of the greatest 

 thickness hitherto observed might, without any extravagant 

 calculation, and at the rate only of two to three inches a year, 

 or less, be deposited in about three thousand years ; whilst 

 the theory of its coprolitic origin not merely requires a con- 

 siderable exercise of the imagination, but is opposed by the 

 direct testimony of eye-witnesses. 



P.S. The May Number of the Philosophical Magazine, 

 which has just come into my hands, contains an analysis of 

 African guano by our Foreign Secretar^^, Mr. E. F. Tesche- 

 macher, in which he finds humic acid to exist in a soluble state 

 in the African specimen, but no urate of ammonia. The 

 humus described to exist in the Peruvian specimens analysed 

 by me was extracted by dilute potash from the residue insolu- 

 ble in water ; and if it be true humus, and it possesses all the 

 characters assigned to that substance, the South American 

 varies from the African guano, amongst otiier differences, in 

 containing uncombined humus. 



XIII. On certain Results relating to Quaternions, By Arthur 

 Cayley, Esq.^ B.A., Fellow of Trinity College^ Cambridge. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 

 T N his last paper on Quaternions, Sir William R. Hamilton 

 -■- has alluded to a paper of mine on the Analytical Geo- 

 metry of (m) dimensions, in the Cambridge Mathematical 



