578 Proceedings of the Royal Society 
M. Le Verrier in the annals which he publishes; and I have 
endeavoured by my own exertions to exhibit all of Prony’s work 
that appeared to me to be most important. 
I do not know that it would be opportune at present to reply in 
detail to Mr Sang’s criticisms, and need only say, that the mystery 
which he thinks to result from the insufficient collation of Briggs’ 
Tables by MM. Letellier et Gruyetant is no mystery to those who 
have had recourse to the original sources. 
Although it be true that Briggs owes to Napier not only the 
fundamental idea of logarithms, but also that of the system computed 
according to the basis 10, of which system Briggs has without 
reason been held as the inventor, and to which his name has been 
attached, I appreciate in the highest degree the work of this fellow 
labourer with Napier. But the study of the Arithmetica 
Logarithmica has led me to discover errors in the fundamental 
basis of the calculation, and has superabundantly explained the 
faults which mar the great work of 1624. 
The table in page 10, “Numeri continue medii inter denarium 
et unitatem,” contains several errors, as is seen from an analogous 
and more extensive table calculated by Callet. 
The table on page 32, “ Tabula inventioni logarithmorum inser- 
viens ” is equally faulty, according to the works of Leonelli and 
of M. Houel. 
We must not then attribute to the calculations of Briggs, 
founded on pages containing various errors, any superiority over 
those executed in the Bureau du Cadastre. 
For all that, Mr Edward Sang goes farther; he attacks the 
method of differences made use of by Prony, and seems to prefer 
to it the processes followed by Briggs, or those which he himself 
has recently employed. I say nothing about these last, which are 
unknown to me; but having for long studied Briggs’ processes, 
and having myself practised the method of differences while com- 
puting to 7 decimals tables of logarithms of sums and differences, 
I believe myself to be in a position to repel the attacks on this 
latter method. 
Mr Sang’s principal objection is contained in the following 
phrase: — “ Also an error in the denomination of the first difference 
of the sixth order is augmented 82 472 326 300 times in the final 
