301 



instead of thus circulating, converges to a limit, the general va- 

 lue of 



was assigned for any arbitrary quaternion c, by the help of the 

 quadratic equation 



q 2 = 5qi+ 10/; 



and it was shewn that with only one exception, namely, the 

 case when c = (2k-4i), the limit in question was (for every 

 other value of c), 



5i 



2 h 



The Rev. Dr. Todd read a paper on the Khorsabad in- 

 scriptions, by the Rev. Dr. Hincks. This was the sequel to 

 a paper read on the 25th of June, 1849, and printed in the 

 twenty-second volume of the Transactions of the Academy. 

 To that paper, which was chiefly occupied with the ideogra- 

 phic element in the Assyrian inscriptions, and with chronolo- 

 gical investigations respecting them, an appendix was added, 

 in which the phonetic characters were arranged. It was main- 

 tained that they were all syllabic, and that the elementary 

 syllables represented four vowels and seven different forms of 

 combinations of a vowel and a consonant ; all of which, how- 

 ever, were not in use in the case of every consonant, while 

 some syllables had more than one representation. 



Up to the date of the publication of this paper, it was 

 maintained by all other writers on the subject that the elemen- 

 tary characters represented the letters of a Semitic alphabet, 

 though it was not denied that some characters represented 

 combinations of two others. After a considerable part of the 

 present paper was written, Colonel Rawlinson, abandoning his 

 former theory of the characters representing letters, proposed 

 syllabic values for them ; he, however, admitted only three 



