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1 Rectifying latitude

Rectifying latitude μ is the surface distance from the equator, scaled so the pole is "90°". Unfortunately, it is an incomplete elliptic integral:

Reduced or parametric latitude η is the latitude of the same radius on the sphere with the same equator.

Authalic latitude β gives an area-preserving transform to the sphere.

where

Conformal latitude χ gives an angle-preserving ( conformal) transform to the sphere.

Approximate difference from geographic latitude
φ reduced
φ − η
authalic
φ − β
rectifying
φ − μ
conformal
φ − χ
geocentric
φ − φg
0.00′ 0.00′ 0.00′ 0.00′ 0.00′
1.01′ 1.35′ 1.52′ 2.02′ 2.02′
10° 1.99′ 2.66′ 2.99′ 3.98′ 3.98′
15° 2.91′ 3.89′ 4.37′ 5.82′ 5.82′
20° 3.75′ 5.00′ 5.62′ 7.48′ 7.48′
25° 4.47′ 5.96′ 6.70′ 8.92′ 8.92′
30° 5.05′ 6.73′ 7.57′10.09′10.09′
35° 5.48′ 7.31′ 8.22′10.95′10.96′
40° 5.75′ 7.66′ 8.62′11.48′11.49′
45° 5.84′ 7.78′ 8.76′11.67′11.67′
50° 5.75′ 7.67′ 8.63′11.50′11.50′
55° 5.49′ 7.32′ 8.23′10.97′10.98′
60° 5.06′ 6.75′ 7.59′10.12′10.13′
65° 4.48′ 5.97′ 6.72′ 8.95′ 8.96′
70° 3.76′ 5.01′ 5.64′ 7.52′ 7.52′
75° 2.92′ 3.90′ 4.39′ 5.85′ 5.85′
80° 2.00′ 2.67′ 3.00′ 4.00′ 4.01′
85° 1.02′ 1.35′ 1.52′ 2.03′ 2.03′
90° 0.00′ 0.00′ 0.00′ 0.00′ 0.00′

2 Latitude and wealth

It is frequently observed that there is a distinct correlation between latitude and the wealth of nations. The continents along the equator, Africa, South America, and Indonesia are the poorest. Even within Africa and South America this can be seen as the nations furthest from the equator are wealthier. In Africa the wealthiest nations are the three on the southern tip of the continent, South Africa, Botswana, and Namibia, and the countries of North Africa. Similarly in Latin America Argentina, Chile and Uruguay have long been the wealthiest. The wealthiest nations of the world with the highest standard of living tend to be those at the northern extreme of areas open to human habitation, Canada, and the Nordic Countries. Within the wealthy continents, and even within large countries wealth increases with distance from the equator. The Southern Europe has long been poorer as has the Southern United States.

There have been a number explanations for this phenomena. The first to describe and try to assess it was the French philosophe Montesquieu who proposed that cold weather means less blood in the extremities, which makes the flesh less elastic; this gives northerners more strength and makes them less able to relax. This forcing of the blood inward, according to Montesquieu also means more flows through the heart, increasing vitality. These findings have been wholly discredited by modern science.

Also discredited, but still current among some groups, is a racial explanation. Those near the equator tend to be dark skinned, better to cope with more direct sunlight. Some have alleged that darker skin colour is linked to less intelligence. There is no evidence for this supposition.

Another explanation that is still widely held is that modern technologies and institutions were designed primarily in a small area of north western Europe. Thus agricultural techniques, machines, and medicines were designed to suit a temperate climate. These technologies and models readily spread to areas of similar climate, such as North America and Australia. As these areas also became centres of innovation this bias was further enhanced. Vastly less effort has been put into improving tropical agriculture than temperate because of this. Technologies, from automobiles to power lines are designed for colder drier regions and tend to work far worse in the tropics.

This vicious cycle of technologies being designed for the wealthy, which makes them more wealthy and thus more able to fund technological development. One piece of evidence for this is that the far north has not always been the wealthiest latitude. Until only a few centuries ago, the wealthiest belt stretched from Southern Europe through the Middle East, northern India and southern China. A dramatic shift in technologies beginning with ocean going ships and culminating in the Industrial Revolution saw the most developed belt move north, in Europe, in China, and in the Americas. Northern Russia became a superpower while southern India became impoverished and colonized. Such dramatic changes argue that the current distribution of wealth is not due to immutable factors such as climate or race.

Linked to this explanation is that of disease. The tropics are far more prone to devastating diseases due to their temperature that makes life easier on vectors such as insects and rodents. There has long been a malarial belt spanning the globe, this made human life more difficult, and most notably it made it almost impossible for most forms of northern livestock to thrive. These problems have been compounded by the wealth of the north, vastly more research money goes into curing the ails of northerners.





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