of Heat, Gases, and Gravitation. 133 
If two hard bodies move in opposite directions, upon the same 
fine, with different momenta, the momentum after the stroke will 
be equal to the difference of the momenta before the stroke. The 
body which had the greatest momentum before the stroke will be 
at rest after it, and the other hody will move with a momentum 
equal-to the difference of the momenta before the stroke. 
If the momenta be equal, both bodies will remain at rest after 
the stroke, as stated before. 
The whole doctrine of the collision of perfectly hard bodies 
turns upon this simple principle, viz. That the momentum before, 
and the momentum after the stroke, is the same when estimated 
in one and the same direction. 
These conclusions being most of them different from Mr. 
Herapath’s, and his first principles not supported by experience, 
i consider the principal support of his laborious superstructure to 
be removed ; further it is not necessary to proceed. 
{ may also remark, that there is a much more simple and con- 
sistent manner of accounting for the greater part of the phzno- 
mena he has attempted to explain. 
I am, sir, 
Your most obedient servant, 
No. 2, Grove Terrace, Lisson Grove, THomMas TREDGOLD. 
Aug. 13, 1821. 
XXX. Application of the Calculation of Probabilities to the 
geodesic Operations of the Meridian of France. By Count 
Dz LapLace.* | 
Tux part of the meridian which extends from Perpignan to 
Formentera rests on the base measured near Perpignan. Its 
length is about 460 thousand metres, and it is joined to the base 
by a chain of six-and-twenty triangles. It may be feared that 
so great a length, not being verified by measuring a second base 
near its other extremity, may be liable to a sensible error arising 
from the errors of the 26 triangles employed to measure it. It 
is therefore interesting to determine the probability that this 
error does not exceed 40 or 50 metres. M. Damoiseau, a lieu- 
tenant-colonel of artillery, who has just gained the prize offered 
by the Academy of Turin, on the return of the comet of 1759, 
has readily, at my request, applied to this part of the meridian 
the formula which I have given for this purpose in the second 
Supplement to my Analytical Theory of Probabilities. He has 
found that setting off from the latitude of the signal of Burgarach, 
a few minutes further north than Perpignan, and continuing to 
* From the Connaissance des Tems for 1822, page 346, 
Formentera, 
