48 Le Roy’s Memoir on the best Method 
It is not the mass of the spring which produces its 
strength ; without changing this mass, we may augment or 
diminish considerably its elastic power by giving it a higher 
or lower temper, or by other operations. To know, there 
fore, whether a spring, when unwound, is in the case of a 
constrained equilibrium, we must not, as M. Bernoulli did, 
consider the whole of the mass, which by itself is incapable 
of any motion, but examine what passes in the interior of 
its pores, where the agent works, whatever it may be, that 
produces the elastic force; the same as in a foot-ball, the 
covering 1s not the first cause of the spring, but the com- 
pressed air in its interior. Now whatever may be the cause 
of the spring, it is easy to see that all the particles which 
compose it are themselves so many springs already wound, 
being ’continually in action to develop themselves. We 
know, in like manner, that all these particles are in a centre 
of constrained equilibrium, since the active principle which 
they contain, and which tends to dilate them, is necessarily 
counterbalanced by the force which compresses the parts of 
the metal one against the other; by that same force, without 
which all in nature would be disunited. ; 
The constrained equilibrium is made manifest in effect 
very sensibly, when by a small excess of cold many springs 
break of themselves, and when we see steel become faulty 
when it is tempered. 
for 1736, M. Bernoulli showed several things analogous to the spiral springs 
that are applied to watches. He recommends to attach two of them to the 
centre of the balance, whose spires turn in a contrary direction, to have what 
he calls a centre of constrained equilibrium : he pretends to remedy by this means 
the fluttering, and to render the vibrations more equal; instead of which, 
with one spring, he says an idle centre of equililrium can only be had, which 
has not sufficient action on the balance to prevent fluttering, and to maintain 
the vibrations equal. What he understands by a constrained centre af equili- 
trium is the two springs, which, being wound, become antagonists to each 
other ; that is to say, the first spring which is placed will draw the balance all 
on one side, and absolutely out of its escapement; but the second spiral, 
drawing in a contrary direction, will bring’the balance so that the pallets are 
parallel to the balance wheel, and place it, as usual, in its escapement. 
What he understands by the idle centre of equilibrium, is a balance with its 
common spring fixed. This spring is neither wound on one side nor the 
other, consequently it remains in inaction, which is what he means by an 
idle centre of equilibrium.—T. S. E. 
Besides, 
