The Theory of Springs, though attempted by divers eminent Mathematicians of this Age has hitherto not been Published by any. It is now about eighteen years since I first found it out, but designing to apply it to some particular use, I omitted the publishing thereof.
About three years since His Majesty was pleased to see the Experiment that made out this Theory tried at White-Hall, as also my Spring Watch.
About two years since I printed this Theory in an Anagram at the end of my Book of the Descriptions of Helioscopes, viz.ceiiinosssttuu,id eft, Ut tenfio fic vis, That is, The Power of any Spring is in the same proportion with the Tension thereof: That is, if one power stretch or bend it one space, two will bend it two, and three will bend it three, and so forward. Now as the Theory is very short, so the way of trying it is very easie.
Take then a quantity of even-drawn Wire, either Steel, Iron, or Brass, and coyl it on an even Cylinder into a Helix of what length or number of turns you please, then turn the ends of the Wire into Loops, by one of which suspend this coyl upon a nail, and by the other sustain the weight that you would have to extend it, and hanging on several Weights observe exactly to what length each of the weights do extend it beyond the length that its own weight doth stretch it to, and you
Figures & Tables
In this chapter, we give a brief synopsis of each of the classic papers referred to in this collection. Where relevant, we reproduce the basic equations, recast in modern notation. Supporting works also are referred to. They are listed in the “General References” section.
Table 1 is a quick outline of the key contributions of each paper reprinted in this book.
Robert Hooke, “Potentia Restitutiva, or Spring” (Oxford, 1678)
The article by Robert Hooke, “Potentia Restitutiva, or Spring,” contains the statement of the proportional relation between stress and strain universally referred to as Hooke’s law. Although the English language has evolved somewhat since 1678, the article does not require translation. Hooke describes a variety of experiments, accompanied by illustrations, confirming the stress/strain relation over a wide range of applied loads. He emphasizes the great generality of his results.
Based on his experimental work from 1660 onward, Hooke first published his law in 1676 in the form of an anagram in Latin,
which he later revealed to be “ut tensio sic vis.” Roughly translated, this means “as the force, so is the displacement” (Love, 1911; Boyce and DiPrima, 1976).
In his treatise, Hooke examined the behavior of springs, so his first casting of the equations dealt with the restoring force on a spring, for a given displacement: