, [59 3 
Ametican fodt ; and a rod of 10 siich indies will 
vibrate 132.73 times in the time that the second 
pendulum makes 60 vibrations. 
If then, a French mathematician is informed that 
the American foot is divided into 10 inches, and 
that a rod of the length of that foot will make 132,73 
vibrations in the same time that a second pendulurri 
makes 60 vibrations, he will immediately know, 
that the time of a single vibration in each must be 
inversely, as those numbers, and that the length of 
those pendulums were as the squares of the times, 
hence he would have the following equation : 
As the square of 132.73 to the square of 60, so is 
the length of the pendulum rod vibrating seconds 
in the 45th degree of latitude, in French measure, to 
the length of the American foot in French measure.* 
If this length should be found 11.25 inches French 
measure, he would know that the American foot 
was equal to 11.25 French inches, and consequent¬ 
ly 15 French feet equal to 16 American feet. 
Or, if a French mathematician should be in- 
i 
formed that if the length of a pendulum rod, vi¬ 
brating seconds of time in the 45th degree of lati¬ 
tude, was divided into 23 equal parts, 4.7 of these 
parts would make the American foot, he would 
find the length of such a rod in French measure, 
and dividing it into 23 equal parts, and taking 4.7 
of such parts he would find the length of the Ame- 
