100 Experiments upon American Copper. 
weight at about one inch and a half from the middle of the pen- 
dulum “towards the great weight, must now be shifted (say one 
inch) towards the middle of the pendulum, in order to increase 
the number of vibrations which it may be recollected were left 
in defect, so that they may be in excess. It is evident that the 
true number of vibrations will be found, when the slider is some- 
where between its first and second position. Let the slider be 
now placed half-way between these two points. If the number 
of vibrations in this third position be still in excess, the truth 
will lie between the first and third positions of the slider. And 
thus, by continually bisecting with the slider, the distance of the 
two last found points, the number of vibrations when the great 
weight is /elow’, will rapidly approach the truth, being alternately 
in defect and in excess; and when the approximation is such as 
that the difference in either position of the pendulum becomes 
inconsiderable, the vibrations, when the great weight is below, 
may be taken for the truth; and thus the number of vibrations 
in 24 hours, of a pendulum equal in length to the distance be- 
tween the knife edges, will be known at a certain temperature, 
and at an observed height of the barometer. 
[To be continued. ] 
XV. Account of Experiments made by the Assay Master of the 
King of the Netherlands, at the Mint of Utrecht, on the Na- 
tive Copper existing in Blocks on the South Side of Lake 
Superior, communicated by a Letter from Mr. Eustis, Mi- 
, nister Plenipotentiary and Envoy Extraordinary from the 
United States, &c. to Dr. SamuEL L. Mircuitt, dated 
Hague, Oct. 12, 1817. 
Dear Sir, — Perceivine by the public newspapers, that my 
friend Dr. Le Barron had presented you a piece of copper, I in- 
close the analysis of a piece which he gave me at the mint of 
Utrecht, a portion of which, in its crude state, I presented to 
the minister of foreign affairs, to be deposited’ in the university 
of Leyden. My object in procuring an assay in a foreign coun- 
try, was first to add to the diffusion of information respecting 
our country; and secondly, that it might be compared with ex- 
periments made in the United States. I had hoped to return 
this autumn, and to have taken it with me; but the state of our 
commercial relations with this country has necessarily deferred 
that hope until the spring. I am, &c., ; 
The Hon. Samuel L. Mitchill. W, Eustis. 
The 
