432 Proceedings of the Royal Society 
the same way, and, with trembling, the conscientious worker 
having toiled for several days, arrived at the end, to find, in spite 
of all his care, some lamentable errors. The search for the source 
of these, and their correction, might occupy more time and be 
more irksome than the actual work. But his collaborator had 
experienced the same troubles. In order to lessen these, and 
really to improve the performance, the two came to exchange their 
loose sheets; and the habit of working on separate papers from 
which copies were made upon the official sheets came to be firmly 
established. This was inevitable, and might easily have been 
foreseen. 
On page 998, M. Lefort details circumstances which seem to him 
to prove that the majority, if not the totality, of the calculators of 
the third section made their additions and subtractions on loose 
leaves, which they could dispose of freely; afterwards writing the 
results on the ruled official paper. He remarks, ‘‘ This was incon- 
testably a fault.” It was, in my opinion, a complete relinquish- 
ment of the safe-guard afforded by duplicate manipulation. Now 
this gross and habitual infraction of the official rules could not have 
remained hid from the superintendents. It must have been winked 
at; nay, it must have been controlled by them. The existence of 
many local and restricted “surcharges,” or corrections, proves that 
the loose paper of the one had been collated with that of the other 
computer; and thus the whole operation was conducted with a 
laxity of discipline which detracts enormously from its value. 
But M. Lefort tells us, on page 996, that Prony was so jealous 
of the errors induced by transcription, that, when pressed by the 
Grovernment to extract seven-place trigonometric tables from his 
extended ones, he preferred to proceed to their direct construction, 
rather than to incur the risk of the errors of copying. To me this 
appears an unintelligible motive ; because, whether computed 
directly or not, the table must be copied in type, while the pro- 
bability of exactitude is immensely in favour of the extended 
calculation. Lefort proceeds to say, “On no occasion did Prony or 
his collaborators say or give reason to think that there had been 
copying on the ruled sheets.” 
It is to be remarked, that Lefort does not advert at all to that 
very circumstance which gave occasion for his paper, namely, the 
