}}</ref> cites several such curves, including an 1828 or 1829 proposal based on the "[[Sinesine wave|curve of sines]]" by [[William Gravatt]], and the ''curve of adjustment'' by [[William Froude]] around 1842 approximating the [[Elasticaelastica theory|elastic curve]]. The actual equation given in Rankine is that of a [[Polynomial#Graphs|cubic curve]], which is a polynomial curve of degree 3., Thisat wasthe time also known as a cubic parabola at that time.
In the UK, only from 1845, when legislation and land costs began to constrain the laying out of rail routes and tighter curves were necessary, didwere the principles startbeginning to be applied in practice.
The "'true spiral"', where thewhose curvature is exactly linear in arclength, requires more sophisticated mathematics (in particular, the ability to integrate its [[intrinsic equation]]) to compute than the proposals that were cited by Rankine. Several late-19th century civil engineers seem to have derived the equation for this curve independently (all unaware of the original characterization of thisthe curve by [[Leonhard Euler]] in 1744). Charles Crandall<ref>{{cite book
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| year = 1922
| publisher = Van Nostrand
}}</ref> call the curve "Glover's spiral",attributingand attribute it to James Glover's 1900 publication.<ref>{{cite conference
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The equivalence of the railroad transition spiral and the [[clothoid]] seems to have been first published in 1922 by Arthur Lovat Higgins.<ref name="higgins"/> Since then, "clothoid" is the most common name given the curve, even thoughbut the correct name (following standards of academic attribution) is "'the Euler spiral"'.<ref>[http://www.glassblower.info/Euler-Spiral/AMM/AMM-1918.HTML Euler Integrals and Euler's Spiral--Sometimes called Fresnel Integrals and the Clothoide or Cornu's Spiral.] American Mathematical Monthly, Volume 25 (1918), pp. 276–282. Raymond Clare Archibald</ref>
