I have done some research into this.
Actually, Dodwell concluded that the earth’s axis recovered slowly after a sudden change ‘from a former nearly vertical position to an inclination of 26½ degrees, from which it was returned to an equilibrium at the present inclination of 23½ degrees.’ 
Here’s an extract from a paper on Dodwell’s thesis written by Dr. Carl Wieland:
‘A wobbling top will slowly right itself, but never moves all the way back to its former more upright position. If you plotted its behaviour on a graph it would show as a log sine curve. Dodwell’s graphs indicated that the earth had been pushed over 27 degrees and from that time until 1850 had been slowly moving back to 23½ degrees which it is today’. 
How did Dodwell arrive at his conclusions that the axis had tilted suddenly?
Well we are told in the history and science books that over 2,000 years ago great thinkers like Eratosthenes of Cyrene (276–194 BCE) and Abu Abdullah Al-Battani of Harran, (868–929 AD) had managed to calculate the tilt of the earth by using a simple stick. They would place a stick vertically in the ground on a level surface and then measure the length of the shadow.
They understood that the changing angles of the sun’s rays and at different times of the year should result in different length shadows if the same stick is measured at specific times – i.e., always at noon and especially during the solstices and the equinoxes.
The stick would measure a very short shadow during the Summer Solstice (caused by the sun being high in the sky) and a long shadow during the Winter Solstice (caused by the sun being low in the sky.)
They then used simple trigonometry to determine the angular variation of the sun and found that the angular height varies around 23.5o – or whatever the obliquity (tilt) of the earth’s axis was at that time – between either the equinoxes and the solstices.
With good reason I shall again quote Dr. Carl Weiland, who also informs us of this ancient method:
‘Measuring the lengths of the shortest and longest shadows was very important to these ancient astronomers, as their religious feasts were tied to these two special days. If you got the measurements wrong, your head would probably roll! So these results were carefully recorded on stone and papyrus. Many of the measurements taken over the past 3000 years from places such as China, Europe, England, India and Egypt are available to us today. The length of the shadow really depends on the tilt of the earth’. 
Or rather that the changing length of the shadow in one place at different times of the year, depends on the tilt of the earth, because if the earth were upright there would be no change – or maybe only a very slight change depending on the change in the elliptical orbit of the earth around the sun – i.e., how far or how near the earth is to the sun.
NOTE: with this information we can now decipher the painting by Guercino - ET IN ARCADIA EGO.
See here: [www.world-mysteries.com]
This is certainly not off topic and I'm not 'gatecrashing' Scott's thread here as this is all connected and needs to be said and acknowledged. These paintings are not - well not exclusively - about the bloodline of Christ as suggested by the authors of The Holy Blood and The Holy Grail and by others. I am certain these paintings are bringing attention to the ancient 'global catastrophe scenario' which I am now seriously considering in light of mine and Scott's own research and findings.
Anyway, we are told by Dr. Weiland that Dodwell began reviewing these ancient measurements and he noticed that the shadow lengths recorded before 1850 A.D. were different than expected and that the farther back in time he went with these measurements, the greater the difference. Dodwell knew these measurements were meticulously recorded and therefore were correct without a doubt and on pain of death – which could only mean that in the past, the earth’s axis was tilted differently. Again I will quote Dr. Weiland:
‘When Dodwell graphed the results of how the axis was tilted, based on shadow lengths, they formed a regular curve, known technically as a log sine curve. The results surprised him, but compelled him to conclude that the earth’s axis had been behaving as if it was a centre of a spinning top which had been pushed over’. 
That an asteroid or comet must have struck the earth – possibly changing the tilt of the earth’s axis and causing the Biblical Flood – a cataclysm that had been recorded by many different cultures around the world.
Thanks for reminding me Kim.
1. Letter from George F. Dodwell to Dr. Arthur J. Brandenberger, Professor of photogrammetry at Laval University in Quebec, Canada. Source: In Search of Noah’s Ark by Dave Balsiger and Charles E. Sellier Jr, 1976, USA, pp. 44 – 46.
2. Wieland. Dr., Carl, An Asteroid Tilts the Earth. Ex Nihilo, January 1983, pp. 12-14.