350 Proceedings of the Royal Society 
and the essence of their utility lies in this, that the labour of a 
single computer saves that of many others. 
It is indispensable that those who use the tables he able to rely 
implicitly on the accuracy of the tabulated numbers, and that they 
have a ready means of detecting any error should the existence of 
one be suspected. 
I do not mean, at present, to say a word on the mechanical 
arrangements of setting up the types, of stereotyping, revising the 
proofs, and printing; these have already often been discussed, but 
I shall take the matter up at this critical point : — The investigator 
has in his hands a set of printed or of manuscript tables, which he 
means to use in his researches, and he wishes to know whether the 
individual book be or be not to be trusted. His confidence must 
necessarily be influenced by the history of the book and by its co- 
relatives. Thus, if it be a stereotype copy of a work in extensive 
circulation, he may accept the general opinion as to its accuracy ; 
but if the table be one seldom used, such as those which serve as 
the foundation of working tables, this source of confidence fails him. 
The nature of the case may be most clearly seen from an 
example : — 
We propose to extend the logarithmic canon beyond the limits 
to which it has been already printed ; this extension must be 
founded on the logarithms of the prime numbers ; now Abraham 
Sharp computed, to 61 places, the logarithm of every prime num- 
ber up to 1097 ; these were printed in Sherwin’s collection, and 
thence reprinted by Callet in his Tables Portatives ; shall we then 
build our more extensive tables on the computation by Sharp ? 
Sharp was known as a most zealous and careful computer ; both 
Sherwin and Callet would take care that the numbers be correctly 
copied ; yet for all that, we cannot venture to found on Sharp’s 
work because there is an essential omission. 
If we were to proceed to compute, by help of these, the logarithms 
of larger primes, and if, after a lengthened series of operations, we 
were to find a disagreement, we should be left in doubt as to 
which of the many logarithms that had been used may be in fault ; 
we should have to recompute such of Sharp’s logarithms as might 
be implicated, while the labour and irksomeness of the search would 
become intolerable. 
