C 3 2 7 J 
XVI. New Method of computing Logarithms. By Thomas 
Manning, Esq. Communicated by the Right Hon. Sir Joseph 
Banks, K. B. P. R. S. 
Read June 5, 1806. 
If there already existed as full and extensive logarithmic 
tables as will ever be wanted, and of whose accuracy we were 
absolutely certain, and if the evidence for that accuracy 
could remain unimpaired throughout all ages, then any new 
method of computing logarithms would be totally super- 
fluous so far as concerns the formation of tables, and could 
only be valuable indirectly, inasmuch as it might shew some 
curious and new views of mathematical truth. But this kind 
of evidence is not in the nature of human affairs. Whatever 
is recorded is no otherwise believed than on the evidence of 
testimony ; and such evidence weakens by the lapse of time, 
even while the original record remains ; and it weakens on a 
twofold account, if the record must from time to time be 
replaced by copies. Nor is this destruction of evidence arising 
from the uncertainty of the copy's being accurately taken, 
any where greater than in the case of copied numbers. 
It is useful then to contrive new and easy methods for 
computing not only new tables, but even those we already 
have. It is useful to contrive methods by which any part of 
a table may be verified independently of the rest; for by 
MDecevr. U u 
