347 
of the Slide of Alpnach. 
the pressure is lessened by the velocity, and the poet was not 
so far mistaken as he is generally supposed to be, when he 
said of his heroine 
Ilia yel intactae segetis per summa volaret 
Gramina, nec teneras cursu laesisset aristas. 
However that be, we have a strong example here of the danger 
of concluding in many of the researches of mechanics, from ex- 
periments made on a small scale to the practice that is to be 
proceeded on in a great one. It requires some attention to 
enable us to discriminate between the cases where we can safely 
proceed from the small to the great, and those in which we 
cannot. A man, from finding that bodies of a pound or half a 
pound are in equilibrio when their distances from the fulcrum 
are inversely as their weights, might, without’ danger of error, 
transfer the conclusion to weights of hundreds of tons, or ^o 
whole planets, were it possible to make the experiment on so 
large a scale. But when he finds that the friction of a body of a 
pound, or a hundred weight, is one-fourth of the weight, he 
cannot, with equal safety, presume that the same will hold when 
bodies of immense weight and size come to rub against one ano- 
ther. There are many other cases of the same kind. In gene- 
ral, when our experiments lead to the knowledge of a fact 
and not of a principle, there is caution required in extending 
the conclusions beyond the limits by which the experiments 
have been confined. This is the case with the experiments 
on friction, where we know only facts, and have no prin- 
ciple to guide us ; that is, we have not been able to connect the 
facts with any of the kno^vn and measurable properties of body. 
In the case of the lever, we have connected the fact with the 
inertia of matter, and the equality of action and reaction. We .. 
have, therefore, a right to repose confidence on the one, when 
extended, though not on the other. 
‘‘ That friction belongs to the cases in which great caution is 
necessary in extending the conclusions of experiments, is indeed 
most strongly evinced by the operations that have now been de- 
scribed, the result of which is such as could not have been an- 
ticipated from those experiments. The danger here, however, 
is quite of an opposite kind from that which commonly takes 
place in such instances. The experiments on the small scale, 
usually represent the thing as more easy than it is upon tlie 
