1808. ] 
ifthe fraction maintains the fluid a little 
more elevated at the interior of the plane, 
which would not he the case, if this cause 
existed not; a similar effect is daily 
observed in the descent of the barome- 
ter. It is farther evident from this ana- 
lysis, that when the surface of the plane 
susceptible of imbibing muisture becomes 
wet, the two planes begin to attract each 
other more rapidly and at a greater dis- 
tance than before. It is then not true, 
in general, that two planes, the one sus- 
ceptible, and the other not, of imbibing 
moisture always repel each other. It 
happens in this case, as with two globes 
charged with the same kind of electricity, 
yet which nevertheless attract each other, 
when the respective intensities of their 
electricities, and their distances are pro- 
perly varied. 
It is easy by means of the two follow- 
ing theorems, to measure the tendency 
which the planes have towards each 
other, as well as their mutual-repulsion. 
Whatever may be the substances of 
which the planes are formed, the ten- 
dency of each towards the other, is 
equal to the weight of a parallelopiped 
of the fluid, the height of which gives 
the elevation above the level of the ex- 
treme points of contact of the fluid with 
the interior plane, excepting that eleva- 
tion to the exterior, of which the depth 
is the half sum of these elevations, and of 
which the width is that of the plane ina 
horizontal direction. We must assume 
the negative elevation, when it becomes 
changed by sinking below the level. If 
the product of the three preceding di- 
mensions be negative, the tendency be- 
comes repulsive. 
When the planes are near to each 
other, the elevation of the fluid between 
them, is in the inverse proportion of their 
mutual distance, and it is equal to the 
half sum of the elevations which would 
occur, if we at first assume that the two 
* planes are formed ofthe same substance. 
We onght here to’remark, that we must 
assume the negative elevation at the time 
it becomes changed by sinking. 
It is evident trom these theorems, that 
in general the repulsive is much weaker 
than the attractive force, which is exhi- 
bited when the planes approach very 
near, and are carried towards each other 
by an accelerated motion.. In this case, 
the elevation of the fluid between the 
planes is very great, relatively to its ele- 
vation near the same planes at their ex- 
terior. In neglecting then the square 
of this last elevation, in relation to the 
Montuty Mac. No. 169, 
Proceedings of Learned Societzes. 
239 
square of the first; the fluid parallelo- 
piped, of which the weight expresses the 
tendency of the planes towards each 
other, in virtue of the first of the two pre- 
ceding theorems, will be equal to the pro- 
duct of the square of the elevation of 
the interior fluid, by the half-width of the 
plane of the horizontal direction. This 
elevation being, by the second of these 
theorems, reciprocal at the mutual dis- 
tance of the planes; the parallelopiped 
will be in proportion to the horizontal 
width of the plane, divided by the square 
of this distance. The tendency of the 
two planes towards each other, will then 
follow the universal law of attraction, 
that is, it will be in the inverse ratio of 
the square of their distances. 
_ Anxious to ascertain how far these re= 
sults of his theory were conformable to 
fact, M. Laplace entreated M. Hatiy to 
enter on a series of experiments to elu- 
cidate this curious and delicate point. 
The result of these researches fully de- 
monstrated, that the analysis perfectly 
agreed with experiment. They uni- 
formly beheld the singular phenomenon 
of an attraction converted into repulsion, 
by increasing the distance. 
They suspended by means of a very 
fine thread, a small square plate of lami- 
nated talc, so that the lower part of it 
was plunged into water. They then im- 
mersed into the same water, at the dis- 
tance of a few centimetres, the inferior 
part of a parallelopiped of ivory, se tha 
one of its surfaces was parallel to the 
plate of talc; they afterwards pushed 
very slowly this parallelepiped towards 
the plate of talc, taking care to preserve 
it in a situation parallel to the plate, and 
desisting at frequent intervals, in or= 
der to be certain that the motion they 
had impressed on the fluid, produced no 
effect on the result. When this plate 
remained at a distance from the paralle- 
lopiped, and when they continued to 
move it slowly towards it, till only a very 
small distauce remained between these 
two bodies, the plate of tale suddenly ap- 
proached towards the parallelopiped and 
rushed into contact with it. On sepa- 
rating them, they found the parallelo- 
piped moistened to a certain height 
above the level of the water. On re- 
peating this, the attraction commenced 
sooner, and sometimes in the first in- 
stance, without being preceded by any 
sensible repulsion. These experiments 
were frequently repeated, with the great- 
est care, and uniformly produced the 
same results, 
Ti ROYAL 
