of Edinburgh, Session 1876-77. 
359 
unlikely circumstance — the organism would have closer nemertean 
than annelid relations. But, if proof be ultimately obtained that 
the branchise-like organs referred to above were connected with the 
oval depressions, and that the transverse markings are really not 
strke but annuli, the zoological position of the animal will be 
among true annelids, characterised, however, by structural features 
widely divergent from recent forms. 
5. On Eisenstein’s Continued Fraction. By Thomas Muir, 
M.A. 
6. Note on an Infinitude of Operations. By Thomas Muir, 
M.A. 
The assumption that there is a limit in Professor Tait’s problem 
regarding the interpretation of Lim n =co (cos n a;) means that if we 
start with an angle x, and find the number which is its cosine, then 
the number which is the cosine of this number, and so on, we shall 
at last come to a limiting result w, such that cos w = w. The 
problem is thus transformed into the solution of the equation 
to = cos to, which may be accomplished as follows 
to = COS to, 
whence o> > /3-1, 
> * 73205 .... 
Taking therefore ’733 as a first approximation, we find that with 
it 
to — cos to- - *01 
and taking *75 or j as another approximation, which is readily 
seen to differ from the former by erring in excess, we find that 
with it 
VOL. IX. 
to — to = cos- 1 - "019 . . . . 
