L PHILOSOPHICAL SOCIETY OF WASHINGTON. 
effects of long use and restore the étalon to conformity with some 
more carefully preserved standard, is not quite clear." These old 
étalons were iron bars having their two ends turned up at right 
angles so as to form talons, and the standardizing of end measures 
was effected by fitting them between the talons. Being placed on 
the outside of some public building, they were exposed to wear from 
constant use, to rust, and even to intentional injury by malicious 
persons. Under such conditions every étalon would, sooner or later, 
become too long and require shortening. 
Respecting the ancient toise of the masons there are two contra- 
dictory stories. On December 1, 1714, La Hire showed to the 
French Academy what he characterized as “a very ancient instru- 
ment of mathematics, which has been made by one of our most ac- 
complished workmen with very great care, where the foot is marked, 
and which has served to re-establish the toise of the Chatelet, as I 
have been informed by our old mathematicians.”” Forty-four years 
later, on July 29, 1758, La Condamine stated to the Academy that 
“We know only by tradition that to adjust the length of the new 
standard, the width of the arcade or interior gate of the grand pa- 
vilion, which served as an entrance to the old Louvre, on the side 
of the rue Fromenteau was used. This opening, according to the 
plan, should have been twelve feet wide. Half of it was taken to 
fix the length of the new toise, which thus became five lines shorter 
than the old one.”* Of these two contradictory statements that of 
La Hire seems altogether most trustworthy, and the ordinary rules 
of evidence indicate that it should be accepted to the exclusion of 
the other. 
In 1668 the étalon of the new toise, since known as the toise-étalon 
du Chatelet, was fixed against the wall at the foot of the staircase 
of the grand Chatelet de Paris—by whom or at what season of the 
year is not known. Strange as it now seems, this standard—very 
roughly made, exposed in a public place for use or abuse by every- 
body, liable to rust, and certain to be falsified by constant wear— 
was actually used for adjusting the toise of Picard, that of Cassini,. 
the toise of Peru and of the North, that of La Caille, that of Mairan 
—in short, all the toises employed by the French in their geodetic 
operations during the seventeenth and eighteenth centuries. The 
lack of any other recognized standard made the use ofthis one im- 
11, p. 536 and 2, p. 395. 22, p. 395. $14, p. 484. 
