Effects of the storage conditions on the stability of natural and synthetic cannabis in biological matrices for forensic toxicology analysis: An update from the literature

The Bonne projection is a pseudoconical equal-area map projection, sometimes called a dépôt de la guerre,^[1]^: 104 modified Flamsteed,^[1]^: 104 or a Sylvanus projection.^[1]^: 92 Although named after Rigobert Bonne (1727–1795), the projection was in use prior to his birth, by Sylvanus in 1511, Honter in 1561, De l'Isle before 1700 and Coronelli in 1696. Both Sylvanus and Honter's usages were approximate, however, and it is not clear they intended to be the same projection.^[1]^: 60

The Bonne projection maintains accurate shapes of areas along the central meridian and the standard parallel, but progressively distorts away from those regions. Thus, it best maps "t"-shaped regions. It has been used extensively for maps of Europe and Asia.^[1]^: 61

The projection is defined as:

{\begin{aligned}x&=\rho \sin E\\y&=\cot \varphi _{1}-\rho \cos E\end{aligned}}

where

{\begin{aligned}\rho &=\cot \varphi _{1}+\varphi _{1}-\varphi \\E&={\frac {(\lambda -\lambda _{0})\cos \varphi }{\rho }}\end{aligned}}

and φ is the latitude, λ is the longitude, λ₀ is the longitude of the central meridian, and φ₁ is the standard parallel of the projection.^[2]

Parallels of latitude are concentric circular arcs, and the scale is true along these arcs. On the central meridian and the standard latitude shapes are not distorted.

The inverse projection is given by:

{\begin{aligned}\varphi &=\cot \varphi _{1}+\varphi _{1}-\rho \\\lambda &=\lambda _{0}+{\frac {\rho }{\cos \varphi }}\arctan \left({\frac {x}{\cot \varphi _{1}-y}}\right)\end{aligned}}

where

\rho =\pm {\sqrt {x^{2}+\left(\cot \varphi _{1}-y\right)^{2}}}

taking the sign of φ₁.

Special cases of the Bonne projection include the sinusoidal projection, when φ₁ is zero (i.e. the Equator), and the Werner projection, when φ₁ is 90° (i.e. the North or South Pole). The Bonne projection can be seen as an intermediate projection in the unwinding of a Werner projection into a Sinusoidal projection; an alternative intermediate would be a Bottomley projection.^[3]

References

^ ^a ^b ^c ^d ^e John Parr Snyder (1993). Flattening the Earth: Two Thousand Years of Map Projections. ISBN 0-226-76747-7.
^ Map Projections - A Working Manual Archived 2010-07-01 at the Wayback Machine, USGS Professional Paper 1395, John P. Snyder, 1987, pp. 138–140
^ Between the Sinusoidal projection and the Werner: an alternative to the Bonne, Henry Bottomley 2002

External links

Table of examples and properties of all common projections, from radicalcartography.net
An interactive Java Applet to study the metric deformations of the Bonne Projection
Bonne Projection (wolfram.com)

[Flattening-1] John Parr Snyder (1993). Flattening the Earth: Two Thousand Years of Map Projections. ISBN 0-226-76747-7.

[2] Map Projections - A Working Manual Archived 2010-07-01 at the Wayback Machine, USGS Professional Paper 1395, John P. Snyder, 1987, pp. 138–140

[3] Between the Sinusoidal projection and the Werner: an alternative to the Bonne, Henry Bottomley 2002

[1]

[2]

[3]

Effects of the storage conditions on the stability of natural and synthetic cannabis in biological matrices for forensic toxicology analysis: An update from the literature

See also

References

External links