"Riccati... has no clear conception of , nor does [his] theory... of acoustic experiments lead him to discover that law. In his third canon he states that the 'sounds' of a given length of stretched string are in the sub-duplicate ratios of the stretching weights. The 'sounds' are to be measured by the inverse times of oscillation. ...from this ...he deduces ...that, if u be a weight which stretches a string to length x and u receive a small increment \partial u corresponding to an increment \partial x of x, then the law of elastic force is that \frac{\partial u}{u} is proportional to \frac{\partial x}{x^2}. Hence according to Riccati we should have instead of Hooke's Law: \boldsymbol{u = Ce^{-\frac{1}{x}}}, where C is constant. For compression the law is obtained by changing the sign of x. Riccati points out that James Bernoulli's statements... do not agree with this result...He notes that the equation du/u = \pm dx/x^2 has been obtained by Taylor and Varignon for the determination of the density of an elastic fluid compressed by its own weight"