of Edinburgh, Session 1874-75. 
433 
presentation to the Library of the Institute of a third copy of the 
great tables: yet he says, on page 995, that the collection of the 
leaves filled by interpolation was to form a double original ; that 
such was the object, the only object of the operation, “ Tel etait le 
but, le but unique de l’operation.” On what hypothesis, then, shall 
we explain the existence of this third copy a qui avait ete laisse a 
Prony a titre de Minute/’ M. Prony could not have possessed it 
and been ignorant of the fact that at least one of the three was the 
result of transcription. Yet for these three quarters of a century 
the whole mathematical world has been led to believe, has believed, 
has acted, and has spoken in the belief that these “Grandes Tables” 
were constructed with every, the most scrupulous, attention to the 
requirements of exactitude. 
Having made a most careful examination of the logarithmic part 
of the work — having performed the duty of a most conscientious 
witness in stating the facts as they appeared to him — M. Lefort has 
not ventured to sum up the evidence ; but, speaking of the tables, 
concludes his paper with the words, “ Je n’ai voulu aujourd’hui 
qu’en constater la valeur,” leaving to others to form their own 
opinions of the exact value determined by his revelations. 
He does, indeed, express a qualified commendation, for, at the 
foot of page 998, he says: — “ The Cadastre Tables, like all human 
works, are then not perfect ; they are so neither in their execution 
nor, perhaps, in the details of their conception nevertheless, they 
much surpass, not only in extent, but also and above all in correct- 
ness, all the tables- that have preceded them, and the more modern 
tables which have not been compared with them before publication.” 
Here M. Lefort has omitted to observe that he had been collating 
a manuscript calculation, in which there should have been no error, 
with printed books subject to all the chances of mistakes in reading 
and accidents in printing; he has surely also forgotten that these 
manuscript tables were so imperfect, and were known to their com- 
puters to be so imperfect as to be unfit for the verification of the 
last three places in the “ Arithmetica Logarithmica,” the very first 
work on denary logarithms, a work undertaken and completed by a 
private person, amid all the difficulties and round-aboutness of 
infant algebra. As to the details of the conception, he has told 
us that the orders of differences were extended to the .sixth, that 
