Prof. Dr. Zkaria M. El-Sirafy

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????? ??????
Prof. Dr. Zkaria M. El-Sirafy Dr. Ayman M. EL
Ghamrey Mansoura University
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??????? ??????

• ???????? ???????? ???????
• Mathematical Relation of Yield

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????? ????? ???? Liebig Law

• ???? ??????? ??? ?? ?????? ??????? ???? ????
  ????? ??? ??? ?? ????? ??????? ?? ?????? ???? ??
  ????? ?????? ??? ???? ???? ??????? (???????)
  ?????? ?????? ?????? ?????. ????? ?? ??? ???????
  ????????? ??????
• Y C.X

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????? ?????? ?????? Mitscherlich laws

• ????? ????? ????????? ??????? diminishing yield
  law-
• ????? ??? ??????? ??? ?? ??????? ?? ???????
  ?????? ?? ?????? ????? ???????? ?? ?????? ???????
  ???? ???? ??????? ???? ???????.
• ????? ???????? ??????????? ??????? Physiological
  relations law-
• ????? ??? ??????? ??? ?? ??????? ????? ???
  ???? ????? ????? (?? ??? ???? ??????? ???????? ??
  ??? ????? ???? ??? ?????? ??????? ???? ????) .

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????? ????? ??????? ????? Mitscherlich Baules
concept

• ????? ?????? ??????? ??????? concept of
  sufficiency percentage ????? ??? ????? ??? ??
  ?????? ??????? ?? ?????? ???? ????? ?????? ????
  ????? ?? ??????? ?????? ???? ???? ??? ???? ???
  ?????? ????? ?????.
• ????? ???? Baule units-
• ??? ?????? ?? ???? ????? (??????) ???? ????
  50 ?? ??????? ?????? ????? ???? ????? ?????????
  Efficiency index.

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????? ??? ????? ???????? ???????? ??????? ??????
?????? ?????

• ????? ?????? Mitscherlich Theory
• ?? ????? ??? ????? ??? ?????? ???????? ??????
  ???????? ?????? ?????? ????? ????? ????? ??????
  ?? ????? ????? ???????? ??? ????? ????????. ?????
  ???????? ?? ????? ???? ????? ?? ???? ????? (????
  ???? Baule) ???? ???? ??? ??????? ?? ???????
  ?????? ?? ????? ?????? ??????? .
• Log (A Y) Log A C . (X b)

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?????? ?????? ??????? Spillmans Equation

• ??? ??? ????? ??? ??????? ?? ??????? ??? ?????
  ??????? ?????? ???? (??????) ????????? ???????-
• Y M (1 Rx)
• ??? ???? ?????? ??? ??????? ?????? ????????
  ??? ???????? ???????-
• Y A (1 10cx)

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???? ???????? ??????? ??????? ?? ????? ?????
??????? ?? ???? ????? Calculation of Relative
Yields from addition of increasing Amounts of A
Growth Factor

• ??? ????? ??????? ???? ????? ????? ??????? ??
  ??? ??? ????? ???????? ??????? ?????????
  ???????-
• Log (100 y) log 100 0.301 (x)
• ???? ???? Baule Unit-
• ?? ?????? ?? ???? ????? ???? ???? ???? ???
  ??????? ?????? ?????? .

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• ??????? ?????? Maximum crop yield-
• ??? ?????? ?????? ??? ???? ?? ??????? ???
  ???????? ??????? ????? ??? ??? 7.78 ???? ????
  7.87 ???? ??? ????? ?? ????? ????? ????? ?????
  ??? ???? ???? ???? ??? ?? ????? ????? ??? ??????
  ??? ????? ???? ?????? ???? ???? ???? ???? ?????.
• ???? ??????? ????? ????? ?? ??????? ??????-
• ??? ??? ?? ??? ?? ???? ???? ?? ?? ???? ???
  ???? ?????? ??? ????? ????? ??? ???? ???? ?? ??
  ???? ??? ??? ??? ???? ?? 10 ???? ?? ?? ???? ????
  ???? ???.

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• Thank You