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Until the mid 1920's, spreading manure was the primary means of adding nitrogen to agricultural fields.  The amount of nitrogen from manure for 1865 to 1925 was back calculated from available statistics on the number of livestock units.  By knowing the number of livestock, researchers in this study were able to estimate the amount of manure produced.  Interestingly though, the nitrogen content of manure changed during this period of time.  To account for this variability, these researchers found data on the amount of milk produced, and used a correlation between milk produced and nitrogen content to estimate the amount of nitrogen in the manure.  The correlation they used was "roughly for every 1000 kg increase in milk production, nitrogen in manure increased by 20 kg".   Hoffman et. al. also accounted for the loss of nitrogen (in the form of ammonia) as it transfers from  manure to soil.   Manure data after 1925 was obtained data from Statistics Sweden.  Data on the use of fertilizer nitrogen was based on sales statistics from Statistics Sweden as described in the journal article.

In the late 19th century it was realized that demand for manure nitrogen would exceed supply.  Just before World War I, the German researcher Fritz Haber discovered the commercial process (now referred to as the Haber-Bosch process)  to convert ammonia gas into fertilizer.  Note the rapid growth of the use of nitrogen from commercial fertilizer in Sweden after 1925.   The heavy use of commercial nitrogen today is a two edged sword:  modern levels of agricultural production could not be sustained without it, yet studies demonstrate negative impacts on water quality and ecosystems especially as nitrogen leaches from land to water sources.  As described in the reference article, "water quality data from major European rivers, such as the Rhine and the Daugava, indicate that a major increase in riverine loads of N coincided with the increased use of commercial fertilisers during the first decades of the post-war period".

Mathematically we see that the use of manure nitrogen is nearly constant with time.  Nitrogen from (commercial) fertilizer increases exponentially starting in 1925.   It's an interesting problem for students to obtain the linear and exponential best fit equation/models using 1865 as the base year.  The intersection point of a linear (or any polynomial) equation and an exponential equation cannot be found algebraically.

Reference:   "Leaching of nitrogen in Swedish agriculture - a historical perspective", by Hoffman, Johnsson, Gustafson and Grimvall,  Agriculture, Ecosystems & Environment, vol. 80 no. 3.

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 M. Hoffman et al. "Leaching of Nitrogen in Swedish agriculture - a historical perspective" year Fertilizer nitrogen input (kg/ha) Manure nitrogen input (kg/ha) 1865 0 122.3 1875 0 102.4 1885 0 104.1 1895 0 101 1905 0 106 1915 0 113.7 1925 26 120 1935 47 121.9 1945 87 111.3 1955 164 90.1 1965 294 114.4 1975 461 141.1 1985 476 159.3

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