345 
(^the Slide of Alpnach. 
\ 
tinue the same that they are now, that no body, in the circum- 
stances just described, can perform its journey in less time than 
the above. 
“ But though the descent of the trees at Alpnach contains 
nothing inconsistent with the acceleration of bodies by gravity, 
it is not to be reconciled with the notions concerning friction, 
that are usually received even in the scientific world. 
“ It is common to consider friction as a force bearing a certain 
proportion to the weight of the body moved, and as retarding 
the body by a force proportional to its weight, amounting to a 
fourth or fifth part, or when least to a tenth or twelfth part of 
gravity. A body, therefore, that was descending along an in- 
clined plane, would be accelerated by its own gravity, minus 
the force of friction, a constant force that increased m propor- 
tion to the body. 
Now, in the present case, it will soon appear that the re- 
tardation is vastly less than would arise from any of these sup- 
positions. 
‘‘ Supposing it to be true, that friction in a given instance 
(the surface, the inclination, and the weight, being all given) 
acts as a uniformly retarding force, I have found that a body 
sliding along an inclined surface, under the acceleration of gra- 
vity, and the retardation of friction, will be accelerated, so that 
. it will have at every point the velocity that would be acquired 
by falling by its own gravity from a line incliried to the horizon, 
that is drawn from the point where the body began to move, 
and that makes with the horizon an angle, the tangent of which 
is the fraction, that denotes the ratio of friction to gravity. 
The velocity of the moving body is therefore as the square root, 
of the portion of a vertical passing through the body, and reach- 
ing up to the line just mentioned, or the line of no acceleration. 
“As the trees at Alpnach enter the lake with a considerable 
velocity, it is evident that the line of no acceleration, drawn 
from the top of the slide, does not reach the ground at the point 
where the slide ends, but is then still considerably above the sur- 
face; the tangent, therefore, of the angle which that line makes 
with the horizon, is much less than There is reason to think 
that it does not in reality amount to, ^ of thisj and is therefore 
