XV. The axiom _Vis unita fortior_, I apprehend, applies more justly to
civil and political things, than to natural ones. If we attend, we shall
find that two agents, each of which is strong in proportion to four,
by being joined together, will not be stronger than in proportion to
eight. If two men separately can support but four half hundreds each,
by joining them together, you would find them not able to support above
eight. It is true, that a man who breaks arrows one by one, cannot break
a bundle of arrows tied together, which is the comparison that Scilurus
availed himself of (Plut. in Apophth.) to persuade his sons to continue
in fraternal union; but we should not understand by this, that by binding
them together, each arrow separately acquired any additional strength,
for this example was only intended to shew, that he who could with ease
break each arrow separately, was not sufficiently strong to break the
whole bundle united together. Suppose, for instance, the bundle was to
consist of twenty arrows, if there was any thing less than a twentieth
part of the force exerted to break a single arrow, than it was necessary
to exert to break the whole bundle, it is as certain that that single
arrow would not be broke, as that the whole bundle would not. Thus this
example does not prove, that there is any additional virtue or strength
added to the wood of which the arrows are made, by uniting them together,
but only, that twenty joined together can resist a greater force than one
singly, which is a thing that is self-evident.
XVI. Nothing can be plainer than this; but abstracted from the force
of this reasoning, experience has shewn us, that in some agents,
in contradiction to the common opinion, their union has diminished
their strength. It is the general sentiment, that two threads twisted
together and united in one cord, will support more weight than they
will separately; and that a rope made of many fine threads, is stronger
than all these threads divided. Mons. Reamur, of the Academy Royal of
Sciences, demonstrated in 1711, that the fact was quite otherwise, and
that the threads separate would support a greater weight than they would
united. He made this experiment with two single threads, and found that
each by itself would support nine pounds and a half, which put together
make nineteen pounds; after this he caused them to be twisted together,
and they were broke with sixteen pounds. He made another experiment with
three threads, one of which supported six pounds and a half; another
eight, and another eight and a half; the sum of all which put together
amounted to twenty-three pounds; and after causing them to be made into a
cord, they would not sustain more than seventeen.
XVII. It may perhaps be answered to this, that the threads in twisting
them together might be stretched and made finer, and their strength
weakened; and that besides this, they might have been strained by
supporting the weight in the first instance; but this objection, although
specious, is insufficient; for by attending to the relation of this
matter in the History of the Academy Royal, we shall find, that by order
of the Academy, another experiment was made in a quite opposite way, for
a small silk cord which supported a little more than five pounds, was
afterwards untwisted, and they found that the single threads among them
all sustained six pounds and a half.
XVIII. The true cause of this phenomenon in my judgment, is, that the
threads in the twisted cord do not bear equally alike, because it seems
to me morally impossible in the twisting, to preserve the exact length or
bearing of all the fibres, but that some of them must be more tense or
tight, and some of them more slack than others; in consequence of which,
the bearing of some must vary more from the perpendicular or central line
of gravity, than that of the others, and that some part of them are upon
the stretch, and others rather slack at one and the same time. From hence
it follows, that the weight at first is not supported by all the fibres,
but only by those which are the most tense, and the least distant from
the central line of gravity, which not being of themselves sufficient to
resist the strain, give way, and that the weight afterwards falling upon
the others, they do the same; and that this is the case may be evidently
seen, by observing when more weight is hung to a rope than it is able
to sustain, it does not break instantly, but successively, and although
the total separation is performed in a very little time, there is space
enough before it is compleated, for us to perceive, that some threads
break first, and others afterwards.
XIX. But although my opinion should not exactly coincide with the
experiments made in the academy, I conclude, that the judgment we should
make of this matter is, that both in this, and all other physical agents,
virtue united is the same that it is separate; for the cord breaking
with a less weight than the threads sustained separate, did not result
from these last being stronger separate than they were united, but from
the fibres of the threads acting more together in their separate state,
than they did in their united one, as in the last case, the resistance of
the fibres to the force, was made more in succession than it was in the
first; or to speak more properly, although the threads were united in the
cord, their power or virtue of resistance to the force, was not united or
exerted together.