422 Proceedings of the Royal Society 
step, so that the genesis of any logarithm may readily be traced 
and examined. 
The logarithms of the composite numbers have been found 
addition ; the greater part of these have been twice computed, but 
the whole await a revision in the manner about to be described. 
Though very unlikely, it is yet possible that the same error may 
happen in each of the two calculations ; thus in computing the 
logarithm of 8447, two distinct formulas were used, namely — 
2 • 3769 • 10 s + 1 = 3 • 37 • 251 • 3203 • 8447 
643 • 10 7 - 1 = 3 • 89 • 2851 • 8447 
and the agreement of the two results would show conclusively both 
to be right, were it not for the possibility of a coincidence of error 
in some of the other logarithms, or of an error in the logarithm of 
3 which is common to both. 
In order to remove this exceedingly slight doubt, I prepared an 
index on movable cards, to show the page on which each formulae 
is found; and another index, laid on the table, to show the formulae 
into which each prime enters ; this list, however, being limited to 
the first five occurrences. The above prime is there found in two 
more combinations : — 
2017- 10 ; + 1 = 73-3271-8447 
8447 -10 1 + 1 = 3-7- 11 - 37 * 9883, 
which also consist with previous determinations. Such coincidence 
removes all doubt as to the accuracy of the logarithm of 8447, 
excepting, indeed, the last-place uncertainty incident to all com- 
putations of incommensurable quantities. 
To put the last touch to the trustworthiness of this table, I had 
begun to supply, from the larger primes downwards, a third formula 
to each prime having only two marked against it ; that is, to place 
each prime in at least three distinct combinations, with the inten- 
tion, when this revision shall have been completed, to cause the 
whole of the logarithms of the primes to be re-extracted from the 
minutes, and the summations to be redone by another hand; when 
my attention was drawn to a note in the scientific periodical 
“Nature,” in reference to the proposed publication of the Million 
