540 



NA TURE 



[October 5, 1891 



LETTERS TO THE EDITOR. 

 [The Editor does not hold himst'f responsible for opinions ex- 

 pressed by his correspondents. Neither can he, undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part <?/' Nature. 

 No notice is taken of anonymous communicaHons. ] 



The Thieving of Assyrian Antiquities. 



1. Had I known that after having dissected my reply to the 

 article entitled "Thieving of Assyrian Antiquities," which 

 appeared in Nature of the loth ultimo, you had intended to 

 add further objectionable remarks to it, I should have certainly 

 declined to have had it published. 



2. You seem, even now, to ignore the judgment of the High 

 Court of Justice in the slander case of " Rassam v. Budge," 

 and volunteer your own version of the story with which you 

 have been supplied. 



3. May I ask where you have found it reported about the 

 evidence of the British Museum accountant and Sir Henry 

 Rawlinson's deposition regarding the fragments of the national 

 collection? If you have obtained your information from the 

 latter's deposition that was certainly not revealed in the Press, 

 and if it was supplied you by men who had no business to do 

 so, then in fairness you ought to have quoted the other parts of 

 the evidence. As for the " accountant," no paper reported 

 what the Principal Librarian wanted him to say, and that was 

 for a very good reason, because the Judge did not consider his 

 evidence of any use, seeing that no one had disputed the 

 purchase by the authorities of the British Museum, of Baby- 

 lonian antiquities before I began my researches in Southern 

 Mesopotamia, at the time when I was there and afterwards. 



4. With regard to the cock-and-bull story about the bas- 

 reliefs which are alleged to be at " Comford Hall," if you had 

 said in your article, above referred to, that they existed in a 

 private house in England, instead of asserting that they were 

 obtained by purchase, I would have surprised you with further 

 revelations that such "slabs" do exist in other houses in Eng- 

 land and in different parts of Europe and America. Even half 

 of the sculptures I had discovered in Assur-beni-pal's palace in 

 1853, belonging legitimately to the national collection, have 

 been squandered, and part of them are now in the bottom of 

 the Tigris. 



5. As you seem to have allowed yourself to be imposed upon by 

 malicious men who are not brave enough to put their names to 

 the information with which they have supplied you, I must now 

 close my correspondence, as it seems to me that your journal 

 is not a proper channel through which justice can be obtained. 



H. Rassam. 



6. Gloucester-walk, Kensington, W. September 23. 



[The above letter calls for some additional "remarks." We 

 trust Mr. Rassam will find them less "objectionable" than the 

 former ones. 



1. The dissection to which reference is made consisted only 

 of omissions of personal attacks, not even courteously worded, 

 which moreover had nothing to do with the question of import- 

 ance to the public. 



2. Mr. Rassam is not happy here in his expressions. No- 

 thing was stated in our article which was not openly stated in 

 Court. 



3. He is still less happy here. In his last letter he wished 

 to make our readers believe that Sir H. Rawlinson's opinion on 

 the "rubbish" Mr. Rassam had sent home was not stated in 

 Court, and had been obtained by us in some improper way from 

 the British Museum. In our " objectionable remarks " we 

 charitably suggested that he had forgotten Sir II. Rawlinson's 

 deposition containing this opinion was read in Court. It now 

 seems that Mr. Rassam had not forgotten it in the least. 



With regard to the accountant ; the counsel for the defendant 

 did say what the accountant was to prove, and the Editor does 

 not see what the Principal Librarian had to do with it. 



4. Why does Mr. Rassam take the trouble to misquote us by 

 writing " Comford " instead of " Canford," and then to put his 

 misquotation in inverted commas ? The "story of a cock and 

 bull," which we took from one edition of Murray's Guide is re- 

 peated in more detail in a later one, and even the name of the 

 donor is mentioned, Sir A. H. Layard. 



The more "revelations" Mr. Rassam can supply ;the more he 

 can show that properly "belonging legitimately (the italics are 

 Mr. Rassam's) to the national collection "has been squandered ; 



NO, 1249, VOL. 48] 



the more reason there is for the inquiry 10 which we have 

 pointed. 



5. Requires no comment except that not a single inaccuracy 

 on our part has been established.— Ed. Nature.] 



Vectors and Quaternions. 



I WISH to make some observations in reply to the letter of 

 Prof Knott which appeared in Nature (June 15, p. 148). 

 For my part I have nowhere condemned the system of HamiU 

 ton and Tait as "unnatural" and "weak"; on the contrary, 

 I have always spoken of it with respect and adrniration. To 

 appreciate its value and high place in analysis it is not neces- 

 sary to be blind to its imperfections and limitations. As to 

 whether my work is mere innovation and a lecasting of qua- 

 ternion investigations, I leave to the judgment of those who 

 read my papers. I wish merely to remark that Prof. Knott 

 says nothing about exponentials, and that he has not pointed 

 out what quaternion investigations are recast in my paper on 

 "The Fundamental Theorems of Analysis Generalised for 

 Space." It is the duty of a critic to state correctly and fully 

 the principles which he criticises ; this has not been done ; my 

 position has been misrepresented. It may aid the scienti6c 

 discussion of this matter if I state brieHy the principal positions 

 I have taken, and the replies that have been given. 



I have said that the quaternion notation can be improved. 

 As regards notation, Hamilton himself was an innovator, ana 

 in his writings he apologises for the introduction of the strange 

 symbols S, V, T, K, U, I, &c. My aim has been to generalise 

 as much as possible the notation of ordinary analysis, :i3 it is 

 desirable to have one harmonious algebra, with easy transition 

 from line algebra to plane algebra, and from plane algebra to 

 space algebra. Prof. Tait himself has said in one of the pre- 

 faces to his treatise that a revolution in the matter of notation 

 must ultimately come ; but I infer from the ecstacy of his ad- 

 miration, that Prof. Knott considers it part of the original 

 brightness of the Archangel. 



I have said that the quaternion definitions are not all that can 

 be wished for ; I have pointed out what appear to be defects, 

 and I have attempted to remove them. According to Prot 

 Knott, "the quaternion originally defined as the quotient of 

 two vectors, can also be represented as theproduct of two quad- 

 rantal versors." I reply that what is wanted is not an original 

 or temporary definition of "quaternion," but one that will 

 stand throughout ; that in strains we have a quotient of two 

 vectors which is not a quaternion, but a dyad ; that we do not 

 ask for a representation, but a definition ; and that the repre- 

 sentation indicated involves the idea of a versor, which, eaving 

 out a mere multiplier, is the very thing to be defined. Further, 

 the following questions may be asked : If by a quaternion is 

 meant the quotient of two vectors, how can the product of two 

 vectors be a quaternion? We have also the nice distinction 

 that a quaternion may be represented by the product, but not 

 by the quotient, of two quadrantal versors. It is certain that 

 the product and the quotient of two quadrantal versors are 

 quantities of the same kind ; if the one is a quaternion, so is 

 the other. 



I have said that some of the fundamental principles of qua- 

 ternions require to be corrected, especially the one which 

 identifies versors with vectors. I have said that if a denote a 

 unit-vector, then 0= = l, not = - i. It is not a bare assertion 

 that "to my mind" it appears so ; a reason is given. Let a 

 body of mass, m, have at any time a linear velocity whose 

 rectangular components are a along the axis off, b alongy, and 

 c along k ; the kinetic energy of the body is im(ai + I'J + ckf, 

 that is, hn (a- + b- +c-), not as quaternionisls would have it, 

 -hm[a:^+ b- + C-). The convention involved is one that per- 

 vades the whole of analysis, namely, that the product of two 

 lines having the same direction is positive, while the product of 

 two lines having opposite directions is negative. As kinetic 

 energy.is a square, the two lines must always have the same 

 direction. 



I have said that if o'^" denote a quadrantal versor, then 



(o^j = a" = - I, and that Hamilton's rules apply to versors, 

 not to vectors. Prof. Knott says that I advocate a system 

 which loses the associative principle and gains nothing .^ut » 

 positive sign and an undesirable complexity in transforming by 

 permutations. Readers of Nature will be surprised to learn 



