I believe that before answering this question it is important to note in the phrasing of this question the word "prosperity" is used in describing agriculture. Prosperity is different from a growth in output or an increase in productivity in that it implies that those involved with the agricultural sector on the whole become more affluent and the consequences of this must be kept in mind. By examining the timing of the "Agricultural Revolution", the changes that took place in agriculture and the effects these may have had on industrialisation we can consider the arguments for and against both sides of this question and then draw an overall conclusion.As is the case with most subjects in the Industrial Revolution there is no clear consensus on when the "Agricultural Revolution" took place. Many historians locate the majority of agricultural developments as taking place between 1700 and 1800 however more recent historians also claim many changes took place before 1700 and in the first half of the 19th Century. They also place greater emphasis on the gradual rather than sudden nature of these developments i.e. many small inventions and innovations where introduced one at a time with each one taking time to diffuse into general use across the country. On the whole though it is clear that agricultural development was not completely aligned with industrialisation, which mainly occurred in the period 1750 to 1850. This would suggest that agricultural developments should have had less of an effect that might otherwise have been expected. However, there was still a large overlap, enough to cause hindrance so this argument is not closed off. Similarly, changes that took place before industrialisation could be seen as pre-conditions to industrialisation thus supporting the argument that agricultural prosperity helped industrialisation.The output of the agricultural sector of Britain's economy is seen to rise rapidly from 1700 to 1850. Several methods can be used to observe the output change but all give similar results and this consistency adds strength to the findings. Deane and Cole's approach was to sum wages, profits and rents. This showed a slow growth in output from 1700 to 1800 followed by a rapid expansion till 1850 giving an increase of around 340% across the entire time period. Another approach made possible by research by Chartres and Holderness is to look directly at the increase in farm products e.g. corn, meat, wool, and cheese production. This showed a more gradual increase as a total with animal products in particular having the largest increase in output. The total output increase gave a similar result of 320% from 1700 to 1850.This increase in farming agricultural output facilitated the large increases in population that were also a phenomenon of the time, rising from 5 million persons in 1700 to 16.7 million persons in 1850 and so could be seen to have helped industrialisation by providing a larger labour force to work in industry and by keeping that labour force fed. However, these increases in output did not keep pace with demand as can be seen by rises in imports, in 1700 foodstuffs made up 33.7% of imports and by 1800 this was 45.1% of a larger number of total imports, and increased food prices as demand overtook supply. These increases in prices benefited first the farmers and then the landlords as they increased rents. This agricultural prosperity came at the cost of hindering industrialisation by contributing to increased inequalities.The increased wealth of agriculturists while perhaps not acting against industrialisation seemed not to do much to help it. Little of the windfall received by landlords was re-invested in non-agricultural enterprises instead agricultural capital was increased as investment was made in raising output further. Richer farmers may have been expected to purchase more manufactured goods and this increase in demand could have helped stimulate industrialisation however this did not appear to happen. Agriculture did not provide a very substantial home market for manufactures. Over the 18th century consumption of manufactured goods by agriculturalists increased by a third but at the same time manufacturing output increased three-fold. The majority of manufacturing output was exported or sold within the urban economy.The agricultural prosperity could be interpreted as having encouraged workers to stay in the agricultural sector instead of switching to industry and therefore hindering industrialisation. However, although male agricultural employment did increase from 628,000 in 1800 to 971,000 in 1851 it fell as a proportion of the total labour force and the number of women and boys employed fell so this argument does not hold well against the statistics. There where many innovations during the agricultural revolution in farming techniques such as the use of crop rotations and selective breeding as well as a move from open-field to enclosure farming. In open-field farming a community shares a piece of land and work on it together but under enclosure a farmer is assigned land all in one place over which he has exclusive control thus encouraging enterprise in new methods and investment. It is hard to determine exactly which of these changes had the largest effect on labour productivity but the overall result is clear, output per worker tripled from 1700 to 1850.
The increases in labour productivity are more usually seen as allowing a release of labour from agriculture and therefore of having the potential to help industrialisation by expanding its labour-force. Again though many historians contest this idea. Women and boys would be unable to move away from their villages so could only become involved in rural industry. Structural unemployment was created, as migration to cities did not take place at a fast enough rate to equalise differences in wages, and this inefficiency clearly lowers economic growth. On the other hand it is difficult to see how a larger proportion of the workforce could have worked in industry without the rising output and therefore prosperity of agriculturalists. Even women and boys moving into rural or "proto-industry", which is small-scale manufacturing taking place domestically, as opposed to factories still made a larger difference to the increase in manufacturing output. Labour release therefore still remains a major argument in favour of the idea that rising agricultural prosperity helped industrialisation.In conclusion therefore there are many arguments stating that agricultural prosperity helped industrialisation and many argument stating that it hindered industrialisation. This is reflective of the reality of the relationship between agricultural prosperity and industrialisation because this relationship was very complex. Some aspects of increased agricultural prosperity acted against industrialisation for instance higher food prices and a lack of investment in the urban economy while others such as the expansion of the population and the allowance of a greater proportion of that population to work outside of agriculture acted to help industrialisation. In summary I believe industrialisation would have been different without the agricultural revolution but it would still have occurred because it does not appear to depend directly on anything that resulted from the agricultural changes.